Springer Series on Naval Architecture, Marine Engineering, Shipbuilding and Shipping Series Editor Dr. Nikolas Xiros School of Naval Architecture and Marine Engineering University of New Orleans 2000 Lakeshore Dr. Ste 914 New Orleans, LA 70124 USA E-mail: nxiros@uno.edu For further volumes: http://www.springer.com/series/10523 1 Chrystel Gelin A High-Rate Virtual Instrument of Marine Vehicle Motions for Underwater Navigation and Ocean Remote Sensing ABC Author Chrystel Gelin San Diego, CA USA ISSN 2194-8445 e-ISSN 2194-8453 ISBN 978-3-642-32014-9 e-ISBN 978-3-642-32015-6 DOI 10.1007/978-3-642-32015-6 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012943050 c Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. 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Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Dedication This work was conducted on the basis of the author’s thesis within Florida Atlantic University’s Ocean Engineering Graduate Program requirements with the advice of Dr. N. Xiros and advisory committee members Drs. M. Dhanak, F. Driscoll, P. Beaujean and J. VanZwieten. This book is dedicated to my family, friends and colleagues who have supported me through the years and kept on believing in the work I did and its happy ending. I’m dedicating it particularly to my dear husband, Gregory, who has put up with these many years of me working long hours, my teeth grinding preventing him from sleeping and the overall stress on our household during that journey. I also dedicate this work to my tiger team, my grandmother, Lea, my mother, Chantal, my father, Jacques, my little brother, Cyril and my best friend Anne. Finally I look forward for my son, James, to be of age to share that work and experience with him and why not inspire a scientific path… Thank you. Stubbornness does pay sometimes … Contents List of Figures ..................................................................................................... XI List of Tables ................................................................................................... XVII 1 Introduction ...................................................................................................... 1 1.1 Autonomous Surface Vessels for Hydrographic Data Acquisition ............. 1 1.2 Gateway USVs ............................................................................................ 2 1.3 Proposed System ......................................................................................... 4 1.4 Problem Statement ...................................................................................... 4 1.5 Contributions ............................................................................................... 5 1.5.1 Book Outline ..................................................................................... 6 2 Instrumentation and Data Acquisition System .............................................. 7 2.1 The Sensors ................................................................................................. 7 2.1.1 Acoustic Doppler Current Profiler (ADCP) ..................................... 7 2.1.2 Inertial Measurement Unit IMU ..................................................... 10 2.1.3 Compass TCM2.............................................................................. 11 2.1.4 Tilt Sensor ...................................................................................... 12 2.1.5 Global Positioning System GPS ..................................................... 13 2.2 Data Acquisition System ........................................................................... 13 2.2.1 Host Computer ............................................................................... 14 2.2.2 Target Computer ............................................................................ 14 2.2.3 USV Hardware Layout ................................................................... 15 2.2.4 Computer Networking .................................................................... 16 2.2.5 Software Overview ......................................................................... 17 3 Data Processing ............................................................................................... 19 3.1 Reference Frames ...................................................................................... 19 3.1.1 Earth-Centered Reference Frames .................................................. 20 3.1.2 North East Down Reference Frame ................................................ 21 3.1.3 Body Fixed Reference Frame ......................................................... 21 3.1.4 Vessel States ................................................................................... 22 3.2 Coordinate Transformation ....................................................................... 23 3.2.1 Transformation from Geodetic to ECEF and from ECEF to NED ........................................................................................... 23 VIII Contents 3.2.2 Transformations from Component Reference Systems to Body Fixed Reference System ................................................... 24 3.2.3 Transformations from Body Fixed Frame to NED ......................... 25 3.3 Data Fusion ............................................................................................... 25 3.3.1 Data Fusion Overview .................................................................... 26 3.3.2 Estimation of the Euler Angles....................................................... 27 3.3.2.1 Estimation of the Ship’s Velocity and Position ................ 33 3.4 ADCP Processing ...................................................................................... 34 4 Motion Observation and Experimental Results ........................................... 37 4.1 Vertical Motion ......................................................................................... 37 4.1.1 Study of the Acceleration ............................................................... 37 4.1.2 Velocity Calculations ..................................................................... 42 4.1.2.1 Vertical Velocity Resulting from Integrating Acceleration and Removing the Induced Trend ............... 42 4.1.2.2 Vertical Velocity Resulting from High-Pass Filtering the Integrated Acceleration ............................................... 43 4.1.2.3 Vertical Velocity Using the Data Fusion Technique ........ 44 4.1.3 Vertical Position Calculations ........................................................ 45 4.1.3.1 Vertical Position Calculated Using the High Pass Filtered Integrated Velocity .............................................. 46 4.1.3.2 Vertical Position Calculated Using the Data Fusion Technique ......................................................................... 46 4.2 Data Acquisition System Lab Testing ....................................................... 47 4.2.1 Step 1: Processing of Individual Measurements ............................. 49 4.2.2 Step 2: Validate the Choice for the Data Fusion Frequency........... 56 4.2.3 Step 3: Low-Pass Filtering of the Merged and DGPS Data at the Data Fusion Frequency and Conclusion on Their Agreement Using the Crosscorrelation Method ............................. 59 4.2.4 Step 4: High-Pass Filtering of the Merged Signals to Conclude on the Signals Standard Deviation ............................. 60 5 At-Sea Experiment of Data Acquisition System........................................... 61 5.1 Motion Data Acquisition Measurements and Navigational Data Fusion Results................................................................................... 62 5.2 ADCP Unreferenced and Corrected Measurements .................................. 64 5.2.1 Correction of the ADCP Data in the Beam Coordinate Frame ....... 65 5.2.1.1 Water Current Measured for the First Maneuver, L-Shape Track Heading South Then East ......................... 65 5.2.1.2 Water Current Measured for the Second Maneuver, Linear Track Heading South Then North ......................... 73 5.2.2 Correction of the ADCP Data in the North-East-Up Frame, the ADCP’s Earth Reference Frame ............................................... 77 5.2.2.1 Water Current Measured, at the First Bin, in the NEU Frame for the L-Shape Track and the Linear Track................................................................ 78 Contents IX 5.2.2.2 Water Current Measured Observing the ADCP Velocity Profiles in the NEU Frame for the L-Shape Track and the Linear Track............................................... 79 5.3 Conclusion on the At-Sea Mission ............................................................ 84 6 Conclusion ....................................................................................................... 85 References ............................................................................................................ 93 Appendix A – Native Output of the Instruments .............................................. 95 Appendix B – Setup and Acquisition of the ADCP ........................................... 97 List of Figures Fig. 1 Autonomous Surface Craft ACES. ................................................................ 2 Fig. 2 Autonomous Surface Craft DELFIM, part of the ASIMOV project, designed, and built by the Institute for System and Robotics, beginning in 1998........................................................................................................... 3 Fig. 3 Diagrammatic representation of the FAU Autonomous Surface Vessel ....... 4 Fig. 4 Picture of an RDI Acoustic Doppler Current Profiler ................................... 8 Fig. 5 Diagram of transmission principle of an Acoustic Doppler Current Profiler, mounted onboard a ship, showing the 4 directions of the 4 beams.......................................................................................................... 8 Fig. 6 ADCP Beam orientation with beam 3 at 45 degrees with respect to the heading, looking from underneath the boat. ........................................ 9 Fig. 7 ADCP velocity standard deviation in function of the size of the bins and number of pings per ensemble chosen on the mission command set. ... 10 Fig. 8 BEI Inertial Measurement Unit Motion Pack II. ......................................... 11 Fig. 9 TCM2-20 biaxial inclinometer and a triaxial magnetometer compass module ......................................................................................................... 11 Fig. 10 Fredericks Company ± 60 degree Angle Range tilt sensor ....................... 12 Fig. 11 Diagrammatic representation of the 24 satellites of the Global Positioning System .................................................................................... 13 Fig. 12 Picture of the GARMIN Global Positioning System 76 receiver .............. 13 Fig. 13 Overview of the data acquisition system, including the sensors, computers and links ................................................................................... 14 Fig. 14 Picture of the acquisition setup ................................................................. 15 Fig. 15 Block diagram of the acquisition hardware, including the sensors, computers and links ................................................................................... 16 Fig. 16 Belkin 802.11g Wireless Cable/DSL Gateway Router and the 802.11g Wireless Notebook Network Card. .............................................. 16 Fig. 17 Block diagram of the links between the host PC, the target PC104 stack, the sensors, and Operating Systems of the entities .......................... 17 Fig. 18 Representation of the axis of the Earth Centered Earth Fixed and Earth Centered Inertial Frames .................................................................. 20 Fig. 19 Schematic representation of the North East Down reference frame .......... 21 Fig. 20 Ship-fixed coordinate reference frame (red) and 6 degrees of Freedom motion variables for a marine vessel (sway, surge, heave, pitch, roll and yaw) (Fossen 1994)............................................................................. 22 XII List of Figures Fig. 21 Diagram of the sensors output variables and the coordinate transformations .......................................................................................... 23 Fig. 22 Representation of the Ellipsoid parameters ............................................... 24 Fig. 23 Acceleration measurements in function of the rotation angles .................. 28 Fig. 24 Comparison between the low frequency estimates of Euler angle (a) ( (b)) obtained from the IMU (blue) and from the Tilt sensor (red). ...... 29 Fig. 25 Diagram of the data fusion IMU / TCM2/ Tilt sensor to obtain Euler angles, ........................................................................................... 30 Fig. 26 Comparison between the Euler angles (a), (b) from accelerometers, blue and (a), (b) from data fusion, red and between the compass heading, blue and Euler angle from data fusion in red (c). The black is the difference of blue and red signals ................... 31 Fig. 27 During the third part of the test, high frequency set of motion, comparison between the high frequency component of the integral of Euler rate (a), (b), (c) in blue, and the high frequency component of the merged Euler angle (a), (b) and (c) in red. The black is the difference of the two signals in each plot ........................ 32 Fig. 28 In red, PSD of Merged Euler angle (a), (b) and (c); in blue, PSD of Euler angle from tilt sensor (a), (b), and (c); in black, PSD of integrated Euler rate (a), (b), and (c) .................................. 33 Fig. 29 Diagrammatic representation of the data fusion of the IMU data and the GPS data used to obtain the ships velocity ................................ 33 Fig. 30 ADCP beam and reference frame .............................................................. 35 Fig. 31 Vertical motion experiment setup. ............................................................ 37 Fig. 32 Vertical motion experiment: raw vertical acceleration Az. ........................ 38 Fig. 33 Az spectrum from top to bottom for the set 1 (a), 3 (c) and 5 (e) of periods about 5, 15 and 25 s (left side) and filtering effect on the signal (right side) for the set 1 (b), 3 (d) and 5 (f) ..................................... 39 Fig. 34 Measured and filtered acceleration for periods about 5 (a), 15 (b) and 25s (c). Acceleration measurements are in black while filtered accelerations are in red. ............................................................................. 40 Fig. 35 Az PSD for the set 1, 2 and 3 (b) of periods about 5, 10 and 15 s, and for the set 4, 5 and 6 (a) of periods about 20, 25, and 35 s. ................ 40 Fig. 36 Close up of the acceleration for the set 1 (a), 3 (b) and 5 (c) of periods about 5, 15 and 25s with the expected motion in red, the system acceleration in blue and the difference between the signals in black. ....... 41 Fig. 37 Difference, in black, between the expected velocity VZ, red, and the obtained velocity using the detrend function on the integrated acceleration in blue for the set 1 (a), 3 (b) and 5 (c). ................................. 43 Fig. 38 For the sets 1 (a), 3 (b) and 5 (c), velocity obtained using a high-pass filter on the integrated acceleration, in blue, plotted against the expected velocity VZ, in red. The difference between the two signals is in black. ......................................................................... 44 List of Figures XIII Fig. 39 For the sets 1 (a), 3 (b) and 5 (c), velocity obtained by data fusion, in blue, plotted against the expected velocity VZ, in red. The difference between the two signals is in black. .......................................................... 45 Fig. 40 For the sets 1 (a), 3 (b) and 5 (c), position obtained using a high pass filter on the integrated velocity, in blue, plotted against the expected position Z, in red. The difference between the two signals is in black. ..... 46 Fig. 41 For the sets 1 (a), 3 (b) and 5 (c), position obtained by data fusion, in blue, plotted against the expected position Z, in red. The difference between the two signals is in black. .......................................................... 47 Fig. 42 IMU, tilt sensor, and TCM2 compass attached to a rigid plate attached to the cart. .................................................................................................. 47 Fig. 43 Methodology used to find the data fusion frequency between IMU and GPS measurement to recover full frequency estimate of the system’s position and velocity. ................................................................................ 49 Fig. 44 Square path, as perceived by the DGPS. ................................................... 49 Fig. 45 Square path proceeding in a zigzag pattern between corners, as perceived by the DGPS. ........................................................................ 50 Fig. 46 Circle path as perceived by the DGPS. ..................................................... 51 Fig. 47 Roll and Pitch of the cart measured by the tilt sensor during the first trajectory ((a) and (b)), the second trajectory ((c) and (d)) and the third trajectory ((e) and (f)). ............................................................................... 52 Fig. 48 PSD of the north component, in blue, and the east component, in red, of the IMU acceleration during square trajectory (a), square path by processing in zigzag course (b) and the circle trajectory (c). ............... 53 Fig. 49 Influence of frequencies above 2Hz on the IMU acceleration measurements for the three trajectories of the on shore test of the data acquisition system. .................................................................................... 54 Fig. 50 PSD of the DGPS position (a), DGPS velocity (b) and IMU acceleration (c) for the first trajectory of the on shore test, following a square path. The blue signal corresponds to the north component of the measurement and the red signal to the east component. .................................................. 55 Fig. 51 Data fusion diagram between the IMU acceleration data and the DGPS velocity measurements in order to obtain the enhanced velocity estimate. ....................................................................................... 56 Fig. 52 PSD at particular steps of the data fusion process between the DGPS north component velocity and the IMU north component acceleration................................................................................................ 57 Fig. 53 Comparison in the time domain between the merged velocity (red) and the velocity obtained by direct integration of the raw IMU acceleration signal (black). The blue signal is the DGPS velocity measurement. The upper panel shows the north component of the signal (a) and the lower, the east component (b) ....................................... 58 XIV List of Figures Fig. 54 Data fusion diagram between the DGPS position measurement and the merged velocity estimate obtained by fusing the IMU acceleration data and the DGPS velocity. ............................................................................. 59 Fig. 55 Crosscorrelation (a) (respectively (b)) between the north, (respectively east) component of the DGPS velocity and the north (respectively east) component of the merged velocity estimates. Similarly, (c) (respectively (d)) corresponds to the crosscorrelation between the north (respectively east) component of the DGPS position and the north (respectively east) component of the merged position estimates............................................. 60 Fig. 56 The Florida Current ................................................................................... 61 Fig. 57 Trajectory perceived by the DGPS during the first (a) and second (b) maneuver at sea. ........................................................................................ 62 Fig. 58 Close ups around the data fusion frequency, 0.05Hz, of the PSD of the velocity measurement from the DGPS (blue), the acceleration estimate from the IMU (black) and the enhanced estimate of the velocity obtained by data fusion (red).................................................................................... 63 Fig. 59 Time series of the vessel’s enhance velocity measurement obtained by data fusion with its north (east, down) component in blue (red, black) for the first maneuver (a, b, c) and second maneuver (d, e, f) ................... 63 Fig. 60 Diagram of the necessary reference frame transformations to transform the vessel’s enhanced velocity measured by the data acquisition system into the ADCP Beam coordinate frame. .................................................... 65 Fig. 61 Ship velocity, in blue, along beam 2 (a), and 3 (d) compare to the contaminated measurement of the water current, in black, along beam 2 (b) and 3 (e), and to the true water current, in red, along beam 2 (c) and 3 (f) during the first maneuver while the beams 2 and 3 are looking forward. ..................................................................................................... 66 Fig. 62 Ship velocity, in blue, along beam 1 (a), and 4 (d) compare to the contaminated measure of the water current, in black, along beam 1 (b) and 4 (e), and to the true water current, in red, along beam 1 (c) and 4 (f) during the first maneuver while the beams 1 and 4 are looking aft. .......... 67 Fig. 63 Uncorrected ADCP velocity profile along beam 2, looking forward, during the first maneuver going south then east ........................................ 68 Fig. 64 Corrected ADCP velocity profile along beam 2, looking forward, during the first maneuver going south then east. ....................................... 69 Fig. 65 Uncorrected ADCP velocity profile along beam 3, looking forward, during the first maneuver going south then east ........................................ 69 Fig. 66 Corrected ADCP velocity profile along beam 3, looking forward, during the first maneuver going south then east. ....................................... 70 Fig. 67 Uncorrected ADCP velocity profile along beam 1, looking aft, during the first maneuver going south then east ........................................ 70 Fig. 68 Corrected ADCP velocity profile along beam 1, looking aft, during the first maneuver going south then east. ....................................... 71 List of Figures XV Fig. 69 Uncorrected ADCP velocity profile along beam 4, looking aft, during the first maneuver going south then east ........................................ 71 Fig. 70 Corrected ADCP velocity profile along beam 4, looking aft, during the first maneuver going south then east. ....................................... 72 Fig. 71 Ship velocity, in blue, along beam 2 (a), and 3 (d) compare to the contaminated measure of the water current, in black, along beam 2 (b) and 3 (e), and to the true water current, in red, along beam 2 (c) and 34 (f) during the second maneuver while the beams 2 and 3 are looking forward. ..................................................................................................... 74 Fig. 72 Ship velocity, in blue, along beam 1 (a), and 4 (d) compare to the contaminated measure of the water current, in black, along beam 1 (b) and 4 (e), and to the true water current, in red, along beam 1 (c) and 4 (f) during the second maneuver while the beams 1 and 4 are looking aft. ..... 75 Fig. 73 Diagram of the necessary reference frame transformations to transform the ADCP data into the North-East-Up coordinate frame where the enhanced velocity measurement of the vessel is available. ................. 77 Fig. 74 Time series of the north component of the ship (blue), of the contaminated water current measured by the ADCP in the middle of the first bin (black) and of the water current resulting from its correction (red) in the NEU during the first (a, b an c) and the second maneuver (d, e, and f). ............................................................................... 78 Fig. 75 Time series of the east component of the ship (blue), of the contaminated water current measured by the ADCP in the middle of the first bin (black) and of the water current resulting from its correction (red) during the first (a, b an c) and the second maneuver (d, e, and f). ..................................... 78 Fig. 76 Uncorrected north component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. .......................................................................................... 80 Fig. 77 Corrected north component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. ................................................................................ 80 Fig. 78 Uncorrected east component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. ................................................................................ 81 Fig. 79 Corrected east component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. .................................................................................................... 81 Fig. 80 Uncorrected north component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. ..................................................................... 82 Fig. 81 Corrected north component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. .............................................................................. 82 XVI List of Figures Fig. 82 Uncorrected east component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. ..................................................................... 83 Fig. 83 Corrected east component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. ..................................................................... 83 Fig. 84 Diagram of the data fusion IMU / TCM2/ Tilt sensor to obtain Euler angles, . ................................................................................................... 86 Fig. 85 Diagram of the data fusion between the IMU acceleration data and the DGPS velocity measurements in order to obtain the enhanced velocity estimate...................................................................................................... 88 Fig. 86 Diagram of the data fusion process between the DGPS position measurement and the merged velocity estimate obtained by fusing the IMU acceleration data and the DGPS velocity. ................................... 88 Fig. 87 Google Earth visualization of the mission at sea with the two maneuvers, first goes south-east then south-north ........................................................ 91 List of Tables Table 1 Specifications of the 300 KHz ADCP RDI Workhorse Sentinel ............... 9 Table 2 Specifications of the BEI Inertial Measurement Unit MotionPakII ......... 11 Table 3 Specifications of the TCM2 biaxial inclinometer and a triaxial magnetometer compass module ............................................................... 12 Table 4 Specifications of the Fredericks Company ± 60 Degree Angle Range tilt sensor .................................................................................................. 12 Table 5 Specifications of the GARMIN Global Positioning System 76 receiver ................................................................................................ 13 Table 6 Mean and standard deviation of the tilt sensors’ roll and pitch as well as the influence it could have on the IMU acceleration if not considered for the three trajectories of the on shore test of the data acquisition system. ................................................................................... 52 Table 7 Results from the peaks of frequency detection corresponding to the cart’s motion for the three trajectories............................................ 56 Table 8 Estimates of the standard deviation of the merged velocity signal for the three trajectories of the on shore data acquisition test. ................. 60 Table 9 Ship’s enhanced velocity measurement, uncorrected and corrected ADCP water current measurement in beam coordinates, at the first bin, during the first maneuver ......................................................................... 67 Table 10 Estimates of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in beam coordinates during the first maneuver. ...................................................................... 73 Table 11 Ship’s velocity, uncorrected and corrected ADCP water current measurement in beam coordinates, for the first bin, during the second maneuver ................................................................................................ 75 Table 12 Estimation of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in beam coordinates during the second maneuver. .................................................................. 76 Table 13 Ship’s velocity, uncorrected and corrected ADCP water current measurement in North-East-Up coordinates, for the first bin, during the first and second maneuver..................................................... 79 Table 14 Estimation of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in NEU coordinates during the first and second maneuver..................................................... 84 Table 15 Estimates of the standard deviation of the merged velocity signal for the three trajectories of the on shore data acquisition test. ............... 89 XVIII List of Tables Table 16 Summary of water current estimates obtain by correcting the ADCP data during the two maneuvers at sea. .................................. 90 Table 17 Estimated standard deviation of the ADCP velocity during the first and second maneuver at sea in correlation to the bin size, using the standard deviation of the error velocity .................................................. 91 Table 18 RS232 Registers ..................................................................................... 97 Table 19 PD0 standard output data buffer format ................................................. 98 Chapter 1 Introduction Unmanned Surface Vehicles (USVs) are self contained unmanned untethered vessels that can transit on the surface of the water autonomously or through remote control. Unlike conventional manned surface vessels that are usually large and costly to build and operate, USVs are typically smaller in size and lower cost resulting from the reduced payload requirement extending from being unmanned. In manned vessels, much of the volume is necessary to support the activities (such as control, navigation, maintenance, and mission related tasks), and sustainment (such as berthing, feeding, and entertainment) of the human occupants that recursively increases the size, volume, and power requirements. USVs have no such requirements and therefore are typically many times smaller and more efficient than manned surface vessels. In the last two decades significant effort has been invested in the development of Unmanned Underwater Vehicles (UUVs), while only a small effort has focused on Unmanned Surface Vessels/Autonomous Surface Vessels (USVs/ASVs). The major efforts in the design of USVs have focused in two areas: platforms for hydrographic data acquisition (Chaumet-Lagrange 1994; Manley 1997; and DSOR 1998), and GATEWAY platforms that provide positioning and communications capabilities through the air-sea interface for UUVs (DSOR 1998; ISR-IST and Oliveira 1999). The work presented in this book is part of a larger project that aims to develop a combination oceanographic and GATEWAY USV. In particular, a low-cost high rate position measurement system is implemented to increase the navigation, acoustic positioning, and oceanographic capabilities of the overall system. 1.1 Autonomous Surface Vessels for Hydrographic Data Acquisition Prior to 1994, little work focused on the development of surface robots. At this date, the Port of Bordeaux Authority and the University of Bordeaux began developing a USV to provide hydrographic data to serve engineers and researchers involved in the study of the sea (Chaumet-Lagrange 1994). This USV measures 5m in length, travels at speeds up to 15 knots, and has a range of 10 km. In the same year, the USV named ARTEMIS (Manley 1997) was developed C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 1–6. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 2 1 Introduction at the Massachusetts Institute of Technology. ARTHEMIS is 1.37m long, has an endurance of 4 hours, and has a maximum speed of 2 to 2.5 knots. A micro-processor and a digital compass were installed to provide rudimentary navigation and control functions. A USV for autonomous coastal exploration (ACES) was developed 3 years later by the Massachusetts Institute Fig. 1 Autonomous Surface Craft ACES. of Technology (Manley 1997) that used a 1.8m catamaran hull form to enhance roll stability and provide greater payload (Figure 1). The electronics suite and control software were directly transferred from the ASC (Autonomous Surface Craft) ARTEMIS and incrementally improved. Since 1997, worldwide interest in the analysis of mesoscale ocean dynamics has rapidly increased, leading to an interest in long range USVs capable of sustained oceanographic measurement. In June 1998 the 7m hull prototype USV CARAVELA was launched by IMAR/University of the Azores with capabilities that include a 2000 nautical mile range with at a 5 knot cruise speed, the project was completed in 2002. 1.2 Gateway USVs One of the major challenges in the navigation of underwater vehicles is obtaining precise and reliable geographic positioning (Grenon, 2001). Dead-Reckoning (DR) aided with Doppler velocity measurement has been, and remains, the most common method for underwater navigation for small vehicles (Babb, 1990). DR uses a set of navigation instruments to estimate the vehicle’s position by integrating the body-fixed velocity, accelerations, and angular rates with respect to time. Instrument error and bias lead to position error that increases exponentially with time. Thus, current DR systems require frequent position recalibrations. The Global Positioning System (GPS) provides measurements of geodetic coordinates for air and surface vehicles and it is often used to correct positioning error. However, underwater vehicles cannot use GPS for inflight navigation because GPS signals only penetrate a few centimeters past the air-sea interface. Thus, underwater vehicle navigation systems are limited to periodic position update from the GPS when they surface and extend an antenna through the air-sea interface. Alternatively, Long-Base-Line (LBL), Short-Base-Line (SBL), and UltraShort-Base-Line (USBL) acoustic positioning systems are often used in the place of the GPS for underwater inflight position measurement. The distance between the active sensing elements is generally used to define the acoustic position system. LBL has a baseline length from 100m to 6000m while SBL and USBL have a baseline length of 20 to 50m, and less than 10cm, respectively. LBL arrays of geographically stationary acoustic beacons of known position on the ocean 1.2 Gateway USVs 3 floor (LBL) or surface (inverted LBL) are used to triangulate vehicle position. If a LBL is used, the UUV is restricted to operate within the beacon grid to obtain geodetic position data. Offshore deep water deployment of LBL arrays is difficult and if moored on the surface, buoyed beacons are not clandestine and therefore vulnerable if deployed in a hostile theater. In a Short-Base-Line (SBL) system, arrays of transducers are hull-mounted on large vessels and typically separated by several tens of meters. Such large vessels are easily detected, leading to a non clandestine solution. Alternatively, in an Ultra-Short-Base-Line (USBL) positioning system, arrays of transducers are separated by up to several centimeters, and potted into a single small hydrophone array. Low system complexity and small size makes USBL an ideal tool to help navigate UUVs because they are easy to deploy and small enough to be clandestine. In addition, there is no need to deploy arrays of transponders because there is only a single transceiver (Vickery 1998). Thus, the USBL is an ideal UUV acoustic positioning system for GATEWAY type USVs. USVs are ideal mobile GATEWAY platforms that can provide communications and positioning to UUVs through the air-sea interface when mounted with a USBL and acoustic modem. Unfortunately, little work exists on operating UUVs and USVs in a cooperative manner. One such system, the Advanced System Integration for Managing the Coordinated Operation of Robotic Ocean Vehicles (ASIMOV) project, was developed with the objective of achieving coordinated operation of an Autonomous Surface Craft (ASC) and an UUV for marine data acquisition while ensuring a fast communication link between the two vehicles (ISR-IST 2000). In this project, two robotic ocean vehicles are used: the DELFIM ASC and the INFANTE AUV. The DELFIM ASC is a small catamaran that is 3.5m long and 2m wide, with a mass of 320 Kg (Figure 2). The DELFIM performs automatic marine data acquisition and serves as an acoustic Fig. 2 Autonomous Surface Craft DELFIM, part of the relay between submerged ASIMOV project, designed, and built by the Institute craft and a support vessel. for System and Robotics, beginning in 1998 Besides operating as a communications link, the DELFIM has a stand-alone sensor suite capable of maneuvering autonomously and performing precise path following while carrying out automatic marine and bathymetry data acquisition. This sensor suite includes on-board systems for navigation, guidance and control, and mission control; an Ultra Short Baseline unit (USBL) to position the AUV; an RF above water communication link; and a high data rate underwater acoustic communication system. Navigation is done by integrating motion sensor data obtained from an attitude reference unit, a Doppler logger, and a DGPS. Transmissions between the 4 1 Introductioon AUV, this ASV, the fixeed GPS station, and the control center installed on-shorre are achieved with a radio link that has a range of 80 Km. In order to achievve higher bandwidth acoustiic co-mmunications between the USV and the AUV, thhe vertical channel (high data rate underwater acoustic system) is used. 1.3 Proposed System m FAU has designed a multi-purpose m oceanographic and GAT TEWAY USV that is a low cost mo obile surface platform (Figure 3). Th he system is integrated with a motion measurement package (the focus of thiss work) to aid in navigation, control, and enhance acoustic performance. Th his USV also contains a USBL and a acoustic communication system to provide position updates and allow UUVs to communicate while in transit and surveying. It is also possible to interact with the underwater vehiicle to change the mission through an operator communicating with the USV via an RF uplink from shore or a distant vessel (Leonessa 2002).. Finally, the onboard sensors, includin ng an Acoustic Doppler Current Profiller (ADCP), provide oceanographic meeasurements. Fig. 3 Diagrammatic representation oof the FAU Autonomous Surface Vessel 1.4 Problem Statem ment The USBL acoustic positiioning method involves measuring the range and bearinng from a vessel based traansceiver to a single, remote underwater transpondeer that automatically respo onds to an incoming signal. The remote underwateer transponder, mounted on n a mobile target, is positioned using data from thhe vessel’s GPS and onboaard sensors. To do this, the geodetic position of thhe underwater vehicle is calcculated using the known surface vessel location (provideed by the onboard sensor suite) s and the measured relative position and bearinng between the surface vesseel and the remote underwater transponder mounted on thhe underwater vehicle/mobille target. Range between the AUV and ASV is calculateed by measuring the time taaken from sending a transponder interrogation signal tto receiving its reply. The phase p comparison on an arriving ping between individuual elements within a multii-element (3 or more elements) transducer is used tto determine the bearing from m the USBL transceiver to the remote beacon. 1.5 Contributions 5 The USBL hydrophone is mounted to the USV on a long rigid strut a distance from the GPS antenna. As a result, as the USV moves and responds to ocean waves, the USBL will also move. If the USBL is to provide accurate positioning, the position and orientation of the hydrophone must be measured at a high rate to correct the measured bearing and position offsets. However, standard GPS receivers are unable to provide the rate or precision required when used on a small vessel. To overcome this, a high rate and high precision position and orientation measurement system is developed. The work integrates a set of low cost inertial sensors and a GPS receiver to calculate the USV’s inertial motion. This will be used to correct/transform USBL based position and bearing measurements even when the surface vessel is required to operate in rough seas. Fundamental to any navigation and control system is the measurement of the vehicles geodetic position, orientation and velocity in 3 or 6 degrees of freedom. The system developed in this book provides this information. Included in the navigational instrumentation suite is an ADCP that measures the water velocity, but it can also measure the speed of the USV over the ocean floor. ADCPs measure the relative velocity between its sensor heads and the water using the Doppler shift and time dilation of an acoustic pulse. By transmitting acoustic pulses at a fixed frequency and listening to the Doppler shift of echoes returning from sound scatterers in the water, water velocity estimates can be made. While ADCPs non-intrusively measure water flow, they suffer from the inability to discriminate between motions in the water column and self-motion. When mounted on a moving platform, the measured velocity is the sum of the platform velocity and the water velocity. Thus, the vessel motion contamination needs to be removed to analyze the data and avoid long average times. The system developed in this book provides the motion measurements and processing to accomplish this task. 1.5 Contributions The work presented in this book integrates a set of instruments and develops a software package that measures and calculates the motion of the USV (Unmanned Surface Vehicle) to aid in the navigation and control and enhance the performance of the USBL positioning system. As well, the motion measurement system actively controls the onboard ADCP and corrects the water velocity measurements for ship motion contamination - ship surge, sway, heave, roll, pitch and heading. The simplicity of the data acquisition system allows it to be easily deployable and adaptable to new applications after setting the correct initial parameters. The motion measurement system of the USV consists of an Inertial Measurement Unit (IMU) with accelerometers and rate gyros, a GPS receiver, a flux-gate compass, a roll and tilt sensor, and an ADCP. Interfacing all the sensors is challenging because of their different characteristics. Some of the instruments have digital output (Compass/ADCP/GPS) while others have an analog output (IMU/tilt sensor). Among the sensors using RS232 serial port communication two different output formats are used. The TCM2 compass and the GPS use the NMEA 0183 (National Marine Electronics Association) standard while the RDI 6 1 Introduction ADCP uses ASCII (American Standard Code for Information Interchange) or binary output. The baud rate for the sensors are selectable, the TCM2 has a baud rate from 300 to 38400 baud, the ADCP from 300 to 115200 baud and the GPS from 4800 to 19200 baud. Thus, considering the characteristics of each instrument, a data acquisition system is developed that synchronously decodes data from all the instruments and converts them into a consistent format. These sensors cannot be used independently to measure the position of the vehicle and provide sufficient information for control and USBL motion correction. For example, the GPS provides accurate positioning, but its update is too slow and its resolution too coarse. The accelerometers are able to measure linear motion over a wide range of frequencies, but their signals contains bias and low frequency drift that cause position error to increase as the square of time. However, these sensors both measure linear translation and they have complimentary characteristics that can be used to reduce or eliminate their individual errors when they are combined. Thus, integration and data fusion methods are used to combine the measurements from the sensors to estimate the position of the vehicle (Driscoll 2000), in realtime. Using these techniques, a software package is developed where useful sensor measurements are preserved and erroneous data is rejected at all frequencies and the resulting, merged signal is drift free. Finally, the motion measurement system is used to remove the USV motion contamination in the ADCP measurements. To accomplish this, the motion measurement system is used to control the ADCP by commanding it to ping at a set rate and decoding the measurements returned by the instrument. The single ping water velocity measurements are decoded, motion corrected, and converted into an earth fixed frame. 1.5.1 Book Outline This book consists of six logically progressing chapters. Chapter 1 provides an introduction and motivation of the work, as well as, outlines the contributions of this work; Chapter 2 presents the different sensors and the data acquisition system; Chapter 3 covers the data processing; Chapter 4 illustrates the results of individual sensor tests; Chapter 5 presents and discuss the result of the data fusion of the sensors to obtain the position and velocity of the USV as well as the motion correction of the onboard ADCP; and Chapter 6 draws conclusions and suggest future work. Chapter 2 Instrumentation and Data Acquisition System Guidance and control of an autonomous vehicle requires measurement of its position and motion. To this end, the USV is equipped with instruments that include an Acoustic Doppler Current Profiler (ADCP), Inertial Measurement Unit (IMU), compass, tilt sensor, and Differential Global Positioning System (DGPS). The sensor outputs are either analog or digital, as well they differ within these formats. Thus, a data acquisition system is included aboard the USV to synchronously collect, decode, and process all data. A graphical programming language is used to develop the high-level modular program structure and perform some straightforward data processing while much of the complex processing is done with an imbedded low-level programming language. This strategy provides a software package that is quickly able to understand, modify, and transfer data while avoiding writing hardware specific drivers. Addition of imbedded low level programming provides efficiencies when needed. The first section in this chapter describes the instruments and details their performance and output, the second section overviews the data acquisition system and its layout, and the third section provides a high level description of the software. 2.1 The Sensors 2.1.1 Acoustic Doppler Current Profiler (ADCP) ADCPs use the Doppler effect to acoustically measure water velocity. They transmit sounds, in the form of acoustic pulses (pings), perpendicular to the transducer faces (the source and receivers) at a fixed frequency and record the echoes at discrete intervals of time (depth bins). The ping is reflected by scatterers moving with the water and the reflected signal is Doppler Shifted if the water has a relative velocity component parallel to the acoustic beam. Using four transducers pointed in different directions, each tilted at equal angles from the vertical axis of the ADCP and oriented in pairs that point in perpendicular planes, the ADCP computes the 3-Dimensional water velocity vector for each bin. All beams C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 7–18. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 8 2 Instrumentation and Data Acquisition System measure the vertical water velocity component and each transducer pair measure the horizontal water velocity in its plane. In a similar manner, broadband ADCPs use phase to measure time dilation, instead of frequency changes, by measuring the change in arrival times from successive pulses. The ADCP also contains internal tilt and Fig. 4 Picture of an RDI Acoustic Doppler Current Profiler compass sensors to measure its orientation during a ping. However, these sensors are low quality and have poor response characteristics and are therefore not used in this application. Fig. 5 Diagram of transmission principle of an Acoustic Doppler Current Profiler, mounted onboard a ship, showing the 4 directions of the 4 beams The 300 kHz RDI Broadband Workhorse ADCP (Figure 4) is mounted 45o counter-clockwise from its normal beam 3 forward orientation (Figure 6), so that beams 2 and 3 are looking ahead, and beams 1 and 4 are looking aft. In this configuration, all four beams detect similar magnitudes of Doppler shift in relation to surge and sway, which will aid in removing errors during post-processing (Figure 5). 2.1 The Sensors 9 Fig. 6 ADCP Beam orientation with beam 3 at 45 degrees with respect to the heading, looking from underneath the boat. The RDI Workhorse Sentinel ADCP communicates at 115200 baud (selectable from 300 to 115200 baud) via RS232. Initialization of the ADCP requires a wakeup signal (at least 300 ms serial break) and downloading a mission command set. For this work, the type of ensemble output data structure selected is binary (real water-current data set), and the data rate is set to 1Hz (Table 1). Table 1 Specifications of the 300 KHz ADCP RDI Workhorse Sentinel VALUE USED 126m (maximum) 8m (maximum) ± 0.5 % of the water velocity relative to the ADCP ± 5 mm/s 1 mm/s 5m/s (default) 20m/s (maximum) 1 – 128 PARAMETER RANGE CELL SIZE VELOCITY ACCURACY VELOCITY RESOLUTION VELOCITY RANGE NUMBER OF DEPTH CELLS TILT ±15° ±0.5° ±0.5° 0.01° RANGE ACCURACY PRECISION RESOLUTION COMPASS ACCURACY PRECISION RESOLUTION MAXIMUM TILT ±2° ±0.5° 0.01° ±15° 10 2 Instrumentation and Data Acquisition System The nature of the ADCP’s acoustic method of measurement results in low repeatability between single measurements, single pings, of the same current. Thus, measurements are typically filtered with a moving average to decrease the standard deviation of the signal – the standard deviation of the relative velocity measured by the ADCP is function of the number of ping per average/ensemble and the size of the bins that are specified in the mission command set (Figure 7). 1 ping per ensemble 0.18 2 ping per ensemble 0.16 3 ping per ensemble Standard Deviation [m] 0.14 0.12 0.1 0.08 0.06 0.04 0.02 2 4 6 8 10 Bin Siz e [m] 12 14 16 Fig. 7 ADCP velocity standard deviation in function of the size of the bins and number of pings per ensemble chosen on the mission command set. For this work, the single ping data is motion corrected and the variance of a single ping signal provides a basis to set the maximum level for the accuracy and precision of the vessel motion measurements. A value of less than 1 cm/s is desired for velocity measurements, which is about one half the value of the lowest single ping standard deviation (with an 8m bin size). 2.1.2 Inertial Measurement Unit IMU The low cost BEI Systron Donner Inertial Division MotionPak II contains three orthogonally mounted micromachined quartz angular rate gyroscopes and three 2.1 The Sensors 11 silicon based accelerometers mounted in a compact, rugged package, with internal power regulation and signal conditioning electronics (Figure 8). The MotionPak accelerometers measure acceleration and rate gyroscopes measure angular velocity in three perpendicular directions. The sensor produces an output voltage that is proportional to the rate of rotation and acceleration sensed (Table 2). Fig. 8 BEI Inertial Measurement Unit Motion Pack II. Table 2 Specifications of the BEI Inertial Measurement Unit MotionPakII RATE CHANNELS PARAMETER RANGE SCALE FACTOR ACCELERATION CHANNELS ANGULAR ANGULAR ANGULAR LINEAR LINEAR LINEAR X-AXIS Y-AXIS Z-AXIS X-AXIS Y-AXIS Z-AXIS ± 75 °/s ± 1.5 g 0.133 V/°/s 6.66 V/g ± 5.0 °/s ± 125 mg BIAS ERROR, MINIMUM INPUT AXIS ALIGNMENT 1 ° typical 2.1.3 Compass TCM2 The TCM2 compass module (Figure 9) is a biaxial inclinometer and a triaxial magnetometer. The biaxial inclinometer has no mechanical moving parts; instead it uses a fluid filled tilt sensor, which is an angle sensing device using gravity as a reference to measure the orientation of the compass. The TCM2 provides the heading while the roll and pitch angles from the internal tilt sensor do not have sufficient range to be useful and are only used as independent sensor measurements to check and verify the system performance (Table 3). The TCM2 communicates at 19200 baud via RS232, using the NMEA083 output protocol, the data are output at 8Hz. Fig. 9 TCM2-20 biaxial inclinometer and a triaxial compass magnetometer module 12 2 Instrumentation and Data Acquisition System Table 3 Specifications of the TCM2 biaxial inclinometer and a triaxial magnetometer compass module PARAMETER RANGE ACCURACY RESOLUTION REPEATABILITY HEADING INFORMATION when LEVEL: 0.5 ° RMS when TILTED: 1.0 ° RMS 0.1 º ± 0.3 º TILT INFORMATION ± 20 º ± 0.2 º 0.1 º 2.1.4 Tilt Sensor The tilt sensor is a Fredericks Company microprocessor based tilt sensor assembly (Figure 10). It is an accurate low power tilt sensor that allows sensor trim adjustments (Table 4). The sensor produces an output voltage from 0 to 5V that is proportional to the tilt perceived (± 60 degree angle range). Fig. 10 Fredericks Company ± 60 degree Angle Range tilt sensor Table 4 Specifications of the Fredericks Company ± 60 Degree Angle Range tilt sensor PARAMETER RANGE LINEAR RANGE NULL VOLTAGE REPEATABILITY RESOLUTION STABILITY @ 24 HRS TILT INFORMATION ± 60 º ± 25 º ≤ 0.025 V 0.1 ≤ 0.2 arc minutes 0.1 ANALOG OUTPUT RESOLUTION (0 TO 5V OUTPUT) 1.5 mV 2.2 Data Acquisition System 13 2.1.5 Global Positioning System GPS The Global Positioning System (GPS) is a satellite-based navigation system made up of a network of 24 satellites (Figure 11). The GPS works 24 hours a day by transmitting a signal from the satellites to the Earth. GPS receivers use this signal to calculate the distance between the satellites known location and the receiver’s antenna, then, Fig. 11 Diagrammatic repre-sentation of the 24 using multiple satellites signals, satellites of the Global Positioning System it triangulates the user's geodetic location. The Garmin GPS 76 receiver is used in this work (Figure 12). In addition to conventional triangulation methods, the GPS 76 is designed to provide precise positioning using correction data obtained from the Wide Area Augmentation System (WAAS). This unit uses a built-in quad Fig. 12 Picture of the GARMIN Global helix antenna that can provide Positioning System 76 receiver position accuracy to less than 3m when receiving WAAS corrections. The GARMIN GPS communicates at 4800 baud via RS232 using NMEA0183 format and the position data are output at 0.5Hz (Table 5). Table 5 Specifications of the GARMIN Global Positioning System 76 receiver PARAMETER UPDATE RATE GPS ACCURACY DGPS (USCG) ACCURACY DGPS WAAS ACCURACY VALUE 0.5Hz, continuous < 15 M (49 Ft) RMS 95% typical 3-5 M (10-16 Ft), 95% typical 3 M (10 Ft), 95% typical with DGPS corrections 2.2 Data Acquisition System A data acquisition and processing system is developed to record the data from the sensors and process the data to calculate the motion and orientation of the vessel, in real-time, using a host-target framework of xPC Target (Figure 13). 14 2 Instrumentation and Data Acquisition System Fig. 13 Overview of the data acquisition system, including the sensors, computers and links 2.2.1 Host Computer The host computer can be any PC that runs a Microsoft Windows platform supported by MathWorks. It must contain a serial port or an Ethernet adapter card and operate MATLAB, Simulink, Real-Time Workshop, xPC Target, and a C compiler. The aim of the host PC is to control the target PC. Indeed, it can start, stop, monitor, and tune the application running on the target PC. 2.2.2 Target Computer The USV is an open “wet” structure whose surface signature is to be minimized. Thus, to keep the visible and radar signature to a minimum while increasing the stability of the vessels, the electronics are packaged in a small pressure vessel that is located about 1m below the vessel water line. Since the instrumentation pressure case is small and the available power is limited, the selected onboard computer is of the PC104 format, which is compact and low power. The target computer is a “stack” of four or five cards that are used for data acquisition, processing, and storage. The computer is a MOPSlcd6 CPU board with a 166 MHz CPU and includes two serial ports, a parallel port, an Ethernet port, and a keyboard port. The computer and stack are powered with Direct Current to Direct current (DC/DC) converters that input the batteries unregulated 24 volts and output the needed regulated 5 volts. Although only two serial ports are needed for this work, five serial ports are needed to communicate with the full instrument suite of the USV: 1) the GPS and the compass, 2) the ADCP, 3) the Dual Purpose Acoustic Modem (DAPM), 4) the High Performance Standard Node (HPSN), and 5) a command and control computer. Thus, a serial expansion board with four serial ports is used. The serial hub chosen is the Emerald-MM serial expansion board manufactured by Diamond 2.2 Data Acquisition System 15 Systems. As the IMU and tilt sensor both output an analog signal, a DiamondMM-32-AT AD/DA converter board is included in the PC104 stack and is configured with 32 single-ended channels. A Simpletec flash IDE 1 GB drive mounted on its controller board is used to store data. A VGA card can be installed when needed, to facilitate software debugging. 2.2.3 USV Hardware Layout The instrumentation and data acquisition package consists of a central computer that is connected to five independent instruments, each of which has its own unique preprocessing equipment and data format (Figure 14). The MotionPack produces analog voltage signals that are filtered by a bank of DP68 Low-Pass Filters (Cutoff Frequency at 50Hz) prior to being input into the analog to digital converter and sampled at 128Hz. The tilt sensor is directly connects to the analog to digital converter with no prior filtering and sampled at 128Hz. Both the Garmin DGPS and the TCM2 compass output digital streams at the same baud rate that follow the RS-232 format and are encoded to meet the NMEA 0183 standard. As such, both signals are combined with a NM42 multiplexer from NoLand Engineering and input into the same serial port. The NM42 combines up to four NMEA 0183 instruments into a common output (Figure 15). This multiplexer reads and stores the incoming data from each instrument. Whenever a complete message is received, the multiplexer automatically dumps it to the outputs while it continues reading other input lines. Fig. 14 Picture of the acquisition setup 16 2 Instrumentation and Data Acquisition System Fig. 15 Block diagram of the acquisition hardware, including the sensors, computers and links While the data flow from the IMU, GPS, tilt sensor, and the compass is one way, from the instrument to the data acquisition computer, data flow is bidirectional between the data acquisition system and the ADCP over a digital serial communication line. Unlike the other instruments which are independent from the data acquisition computer and output data continuously (analog) or at fixed rates (digital), the ADCP is programmed prior to sampling and is interrogated to trigger each sample. Thus, the ADCP requires a dedicated serial port and communicates at 115200 baud with a sample rate set to 1Hz. 2.2.4 Computer Networking The communication between the host and the target computer is achieved with a Belkin 802.11g Wireless Cable/DSL Gateway Router connected to the target and with an 802.11g Wireless Notebook Network Card installed on the host computer (Figure 16). The Gateway Router uses the wireless 2.4 GHz signal and has a data rate up to 54 Mbps. It allows the host computer to start or stop the mission, reboot the target (PC104 stack), and monitor the application running on the target at distances up to 1800 feet. Fig. 16 Belkin 802.11g Wireless Cable/DSL Gateway Router and the 802.11g Wireless Notebook Network Card. 2.2 Data Acquisition System 17 2.2.5 Software Overview The acquisition software, Xpc Target, is a real-time graphical programming language that is based on a host-target configuration environment. This language was chosen because it provides a high level graphical development environment that rapidly enables the integration of software and hardware on PC-compatible hardware using visually organized functional blocks. Within these functional blocks, lower level graphical programming and embedded low level coding is done. As such, the software is developed on a PC, the host computer, which is separate from the data acquisition computer and contains all the individual development programs. In this work, the host computer includes MATLAB, Simulink, Real-Time Workshop, xPC Target interface blocks, and a C compiler. The software is compiled into a low-overhead executable file on the host computer and downloaded onto the target computer – the data acquisition computer. While the target computer is executing, the host computer is used to monitor the target and provide some level of data visualization (Figure 17). Fig. 17 Block diagram of the links between the host PC, the target PC104 stack, the sensors, and Operating Systems of the entities 18 2 Instrumentation and Data Acquisition System One guiding goal in the software development is that the program must be quickly and easily understandable and be developed in a framework that readily allows future modifications and additions without understanding of the program in its entirety. Thus, a modular approach is adopted that sees the software broken down into five key sections: 1) system initialization, 2) the data acquisition, translation and conversion; 3) rotational motion estimation; 4) translational motion estimation; and 5) ADCP signal decoding and correction. Each one of these main modules are themselves composed of sub-modules. Chapter 3 Data Processing The methods developed in this book are used to calculate high rate position and orientation states of a moving body relative to the earth using a comprehensive sensor suite. Unfortunately, the different sensors move relative to each other and measure quantities along different, uncoupled axes. For example, the MotionPack’s accelerometers measure acceleration and its rate gyros measure angular velocity along three perpendicular directions that move with the ship with the acceleration signals contaminated by gravitational acceleration, which is always orientated towards the center of the earth. Similarly, the TCM2 compass measures the heading of the moving body with respect to the magnetic North, and the tilt sensor measures the roll and pitch angles with respect to the ship. Conversely, the GPS computes geodetic latitude, longitude and height above sea level relative to the rotating earth. Therefore, the data measured from each one of the sensors need to be rotated into a common frame of reference. The first section of this chapter, section 3.1.1, defines the different reference frames used. The second section, section 3.2, derives the transformations necessary to convert vectors between the reference frames and into a common reference frame. The third section, section 3.3, describes the data fusion algorithm and its implementation. Finally, the last section, section 3.4, defines the method used to process the ADCP data. 3.1 Reference Frames From the GPS geodetic data, the GPS position is calculated in the Earth-Centered Earth-Fixed frame, ECEF, described firstly in the following section. The GPS velocity is obtained using the ground speed and the course over ground provided by the GPS and expressed in the North-East-Down (NED) frame described secondly in the following section. In the NED frame is also expressed the TCM2 compass heading. The third section explains the body-fixed frame, where the tilt sensor, the IMU and the ADCP outputs. C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 19–35. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 20 3 Data Processing 3.1.1 Earth-Centered Reference Frames Fig. 18 Representation of the axis of the Earth Centered Earth Fixed and Earth Centered Inertial Frames The Earth-Centered Inertial frame (ECI, i-frame) has its origin at the center of the earth, with axes [Xi, Yi, Zi]T that are non-rotating with respect to the fixed stars.The Earth-Centered Earth-Fixed (ECEF, e-frame) has its origin at the center of the earth, with axes [Xe, Ye, Ze]T fixed to the Earth that rotates at a rate of 15.041067 °/hr (7.2921.10-5 rad/s) with respect to the ECI. The Zi and Ze axes point from the center of the Earth upwards towards the North Pole. The Xi and Xe axes point horizontally in the plane of the equator from the center of the Earth towards the equator at zero latitude. The Yi and Ye axes are chosen to complete the right hand coordinate system (Figure 18). The ECI and ECEF frame are taken into account in the process of obtaining the GPS position data as described in section 3.2.1. 3.1 Reference Frames 221 Fig. 19 Schematic representaation of the North East Down reference frame 3.1.2 North East Do own Reference Frame Traditionally the North-East-Down (NED) coordinate system is local and is attached to Earth. Since the t motion of the Earth has minimal effect on low speeed marine vehicle, it is conssidered inertial. The NED coordinate system, ℑE, has iits origin at the location of th he navigation system, where the X-axis points northward, the Y-axis points eastwarrd, and the Z-axis points towards the center of the Eartth (Figure 19). For marine vessels operating in a local area defined by only smaall variations in longitude and latitude, the location of an object is best expresseed using NED coordinates (F m Fossen, 1994). The GPS position data are converted from the ECEF to the NED frrame as described in section 3.2.1. The TCM2 compass heading is also expressed in ℑE. 3.1.3 Body Fixed Reeference Frame The body-fixed frame, ℑB, is a moving coordinate frame rigidly attached to eitheer a ship or sensor packagee to which the sensors’ axes of sensitivity are aligned. Traditionally, The x-axis points p forward, the y-axis points starboard, and the z-axxis completes a right-hand orthogonal system by pointing downward. The IMU, thhe tilt sensor and the ADCP uses this coordinate system as described in sections 3.2.2 and 3.2.3. 22 3 Data Processing 3.1.4 Vessel States For a ship moving in six degrees of freedom (DOF), 6 independent states are necessary to define the position and orientate the vessel (Figure 20). Fig. 20 Ship-fixed coordinate reference frame (red) and 6 degrees of Freedom motion variables for a marine vessel (sway, surge, heave, pitch, roll and yaw) (Fossen 1994) These body fixed states are conveniently expressed in a vector representation with the position vector : T , , (1) , where x, y and z denote the distances from the origin of ℑB to the location of interest along the x, y and z axes respectively. Similarly, positions in ℑE are: T , , (2) . From here on, capitalized letter represent variables expressed in the NED frame while the lower case variables represent variables expressed in the body fixed frame. The linear velocity vector in the body frame is defined by T , , , (3) Where is the velocity in the x-direction (surge), is the velocity in the ydirection (sway), and is the velocity in the z-direction (heave). The Euler angle rotations are defined as: T , , , (4) Where is the roll about the x-axis, is the pitch about the y-axis, and is the yaw about the z-axis (Figure 20). The angular velocity in the body fixed frame is defined as: , , T , (5) Where is the angular velocity about the x-axis, is the angular velocity about the y-axis, and is the angular velocity about the z-axis. 3.2 Coordinate Transformation 23 3.2 Coordinate Transformation Fig. 21 Diagram of the sensors output variables and the coordinate transformations The following section describes the transforms used to rotate data from the different sensor frames to the NED reference frame, the common frame of reference (Figure 21). 3.2.1 Transformation from Geodetic to ECEF and from ECEF to NED The GPS measures the geodetic latitude and longitude of the vessel in an EarthCentered Inertial frame (ECI). To be useful for local positioning, this measure must be transformed into the NED local reference frame (Figure 21). The Geodetic latitude, , and longitude, , provided by the GPS are first transform to the ECEF coordinate system. Latitude and longitude are provided in the geodetic datum on which the GPS calculations are based, WGS-84 (World Geodetic System 1984). The transformation from the geodetic coordinates , T for a given height to the ECEF position , , T is: . cos . cos . 1 . cos . sin . sin , (6) 24 3 Data Processinng Where is the prime vertical v radius of curvature (Figure 22) given by: / 1 sin , is the height above ellipsoid, = 0.00669437999013 is the eccentricity squared, = 6378137m is the semi major earth axis (ellipsoiid equatorial radius), and = 6356752.3142m is the semi minor earth axis (ellipsoiid r the Ellipsoid parameters, prime vertical radiuus polar radius). Figure 22 represents of curvature (N), ellipsoid equatorial radius (a), ellipsoid polar radius (b), heighht above ellipsoid (h), geodeetic latitude (φ), and geodetic longitude (λ). Q represennts a point at the surface of th he Earth and P a point at a height h above Q. Fig. 22 Representation of thee Ellipsoid parameters Once the position veector is converted to the ECEF coordinate system, a transformation matrix iss applied to align the position vector with the NE ED reference frame. The transformation maatrix is (Fossen 1994): sin cos sin cos cos sin sin cos cos sin cos 0 sin , (77) Where the position vectorr in the NED frame is: . (88) 3.2.2 Transformatio ons from Component Reference Systems to Body Fixed Reeference System The IMU and the ADCP output data along axes that are defined relative to theeir individual orientation. Often O because the axes of the instruments may not bbe aligned with the axes of th he ship, this data needs to be rotated and translated to thhe ship fixed frame prior to transformation to the NED frame. For examplle, accelerations measured using u the IMU are transformed to the body fixed fram me using: , , , , , , , (99) 3.3 Data Fusion Where , , , , , 25 , and , represents the accelerations in the ship fixed frame, , and , , the accelerations in the IMU body fixed frame, and 1,1, 1 T in this application. , 3.2.3 Transformations from Body Fixed Frame to NED Measurements made or converted into the body-fixed representation are converted into the NED (the common) reference frame to simultaneous compare and process the signals. Sequential Z, Y, X Euler angle transformation is used to transition between the body fixed and the NED frames. This transformation is not based on a physical orientation but strictly on a set of sequential rotations (Etkin 1972). The rotation between the ship body fixed frame and the NED frame is: cos cos cos sin sin cos cos sin sin sin cos cos sin sin sin cos sin cos sin cos sin sin sin cos cos cos cos sin sin . (10) . (11) The inverse transformation from the NED frame to the body frame is: cos cos cos cos sin sin sin cos sin cos sin sin cos sin cos cos sin sin sin sin cos cos sin cos sin cos cos sin sin Unfortunately rotational velocities in the body fixed frame do not directly measure the Euler rates; instead they measure angular velocities about a fixed set of axes. These angular rates do not constitute a vector space and therefore can’t be integrated to provide a measure of orientation. Thus, the angular rates are converted to Euler rates using: Γ 1 0 sin tan cos cos tan sin (12) , 0 where the Euler rates are found by: Γ Γ , where the dot above the variable (·) represents a time derivative, (13) · . 3.3 Data Fusion and of some state output by two Consider the measurements distinct sensors (position sensor and velocity sensor for example). In navigation and positioning applications, the measurement, , is often accurate and stable, 26 3 Data Processing but the update is slow and the resolution coarse. The derivative measurement is often high frequency, but is subject to a bias that results in drift of the integrated signal. Thus, each one of these signals cannot be used independently for applications that require high quality navigation data. However, they have complementary characteristics that can be leveraged to obtain a combined useful signal. The data fusion techniques developed in this work combine the complementary outputs of sensors measuring a related state to eliminate the drift of integrating the measurement , while increasing the rate and resolution of . The pre-emphasized signal, , is obtained by summing the signal with the derivative signal , such that (Mudge and Lueck 1994): , Ω (14) where the scaling factor Ω , denoting the cutoff frequency, is a real positive constant. The choice of Ω is determined by the characteristics of the complementary region of the two sensors. For frequencies that are small compared to the cutoff frequency (Ω Ω , the signal portion of the spectrum comes predominantly from , while for Ω Ω , the signal is predominately from . In the frequency domain, the pre-emphasized signal is: Ω 1 Ω Ω , Ω (15) Where Ω is the Fourier transform of the signal . The enhanced version of the signal is then obtained by convolving with a single-pole, low-pass filter having the transfer function: Ω Ω Ω , (16) yielding: Ω Ω Ω 1 Ω Ω Ω Ω Ω , (17) where Ω can now be interpreted as the half-power cutoff frequency of Ω . The of the signal contains low-frequency information from enhanced signal the sensor measuring , and the high-frequency information from the sensor measuring . 3.3.1 Data Fusion Overview Prior to processing and fusing any translational measurements, they first need to be rotated to the NED frame using the Euler angles, which are not directly measured. Compounding this problem is that the Euler angles are implicit in the 3.3 Data Fusion 27 matrix Γ(12) , converting angular rates to Euler rates, and thus, they need to be known a priori to calculate from w (13). The Euler angles, , are obtained by , calculated from the tilt merging the low-frequency Euler angles, , and , with the high-frequency measurements and , and the compass heading, IMU angular rates, , , T . The estimated Euler angles are then used to convert the IMU acceleration from body-fixed frame, , , T , to the NED T frame, , , , where gravity is removed and the signal is merged with the , , . The result of the last data fusion leads to a high GPS velocity, , , . quality merged measure of the ship’s velocity 3.3.2 Estimation of the Euler Angles The angular rate sensors of the IMU are not fixed and they are subject to a low frequency drift. Therefore, these sensors cannot be directly integrated to calculate an accurate long-term measure of the angular position. Instead, they are merged with the tilt sensor and compass measurements that provide a low frequency measure of the roll, pitch, and yaw Euler angles. However, the tilt sensor does not directly measure the Euler angles but measures the angle between gravity and its axes of sensitivity and the relationship between the Euler angles and the tilt measurements and is , (18) sin cos (19) and asin The Euler angles calculated from the tilt sensor data were calibrated using the accelerometers. This was done using an accelerometer to measure acceleration along its axis of sensitivity and at frequencies where the translational acceleration of the IMU is negligible so that the accelerometers only measure gravity. Thus, at low frequencies, with little translational motion, the accelerometers can provide an independent measure of the Euler angles, (Figure 23), (Lueck, Nahon 2000): sin , , (20) and , cos sin (21) 28 3 Data Processing Fig. 23 Acceleration measurements in function of the rotation angles To compare the angular measurements of the tilt sensor with these of the accelerometer, the IMU and tilt sensor were mounted on the same rigid plate and very slowly rotated through the expected tilt range. Data for each sensor was simultaneously acquired and recorded (Figure 24). The vessel is expected to rotate less than 20°, and within this range, the angles measured by both the sensors agree within ± 0.54366° for and within ± 0.48737° for . At angles greater than 30°, the accuracy of the tilt sensor decreases with range. At the maximum tilt of 42°, the tilt sensor overestimated the tilt by up to 10° and this difference results because of the non-linear response of the tilt sensor, which can be corrected for using a calibration table. When the tilt sensor is steady, local vibrations can cause the fluid to slosh; this coupled with processes internal to the sensor causes a ± 1.1541° fluctuation in the tilt measurements. The tilt sensor can only provide reliable data at frequencies less than 1Hz and higher frequency signal is removed by applying 1st order Butterworth low-pass filter at a cutoff frequency of 1Hz to the tilt sensor roll, , and pitch, . 3.3 Data Fusion 29 Phi [Deg] 50 (a) 0 -50 0 100 200 300 400 (b) Theta [Deg] 40 20 0 -20 -40 0 100 200 300 T ime [s] 400 Fig. 24 Comparison between the low frequency estimates of Euler angle obtained from the IMU (blue) and from the Tilt sensor (red). (a) ( (b)) The TCM2 compass provides a direct measure of the yaw Euler angle, , but similar to the tilt sensors, it also has a finite response time and sudden changes in heading cannot be directly measured with this instrument. Thus, only the lowfrequency yaw signal is useful and the low-frequency estimate of , , is obtained by applying a 1st order Butterworth low-pass filter to the compass heading, with a cut-off frequency of 1Hz. At higher frequencies (> 1/30Hz) the rotation rates, , , T measured T , , , with the IMU provide the needed angular measurements, that are used as angular derivative signal in the data fusion. The compass, tilt sensor and IMU signals are combined to create the pre-emphasized signal T , , , according to (14): Ω Ω , (22) , (23) . (24) and Ω 30 3 Data Processing Fig. 25 Diagram of the data fusion IMU / TCM2/ Tilt sensor to obtain Euler angles, . The pre-emphasized signal contains the low-frequency information from the tilt sensors ( , ) and from the compass ( ) and the high-frequency is convolved with a 1st order Butterworth filter information from the rate gyros, to calculate the Euler angles, , , T using with a cutoff frequency (17). The Butterworth filter is selected because it has a more linear phase response in the passband compare to other filters like Chebyshev and Elliptic filters. The Euler rates are calculated from the angular rates using (13). Unfortunately, implicit in Γ in (12) are the Euler angles and that are not known at high frequency. Therefore, an iterative method is used to accurately compute the Euler rates. In the first iteration (n=1), the Euler angles at low-frequency, , are T , , , used to estimate Γ, yielding an initial estimate of (Figure 25). The first estimate for is then used to transform the angular rates to which is merged with , to provide Euler rates to obtain a second estimate of a more accurate second measure of , (Figure 25), and so forth. Values for the Euler angles converged to within 1×10-11° after only three iterations, and therefore, this is the number of iterations performed. The IMU rate gyros have a low drift rate and the data fusion point is chosen to be at 1/30Hz. This data fusion frequency is selected so that at frequencies lower than the cutoff frequency, the tilt sensors and compass heading, provide accurate and stable measures of the Euler angles, , and and at frequencies above the cutoff frequency, the rate gyros in the IMU provide accurate measures of the Euler rates, , and .The method of merging the data from tilt sensor, compass, and IMU rate gyros to calculate the Euler angles is verified for 3 sets of motions: 1. 2. 3. Turning the system slowly clockwise then anticlockwise through a range of different angles for each axis of rotation, Turning the system slowly anticlockwise, then clockwise 360° around the Z-axis, and Turning the sensor system simultaneously about multiple axes and rotation. Psi [Deg] Theta [Deg] Phi [Deg] 3.3 Data Fusion 40 20 0 -20 -40 0 40 20 0 -20 -40 0 31 (a) 50 100 150 200 250 (b) 50 100 150 200 250 400 (c) 200 0 300 320 340 T ime [s] 360 380 Fig. 26 Comparison between the Euler angles (a), (b) from accelerometers, blue and (a), (b) from data fusion, red and between the compass heading, blue and Euler angle from data fusion in red (c). The black is the difference of blue and red signals. To quantify the accuracy of the merged Euler angle signals at lower frequencies (< 5 Hz), they are compared with an independent measure of the Euler angles calculated using the accelerometer (Figure 26) for motion set 1. Figure 26 shows the comparison between the Euler angle from the accelerometers in blue and from Data fusion, red (a) from the first part of the test. On the second panel (b), from accelerometers in blue is from the first part of the test, the Euler angle compared to from the data fusion in red. Finally, on the last panel (c), from the second part of the test, the unwrapped heading from compass is in blue, and from Data fusion is in red. The black is the difference of the merged and IMU Euler angle. During the post processing, a low-pass filter (cutoff at 1 Hz) is applied to both the Euler angles derived from the IMU and the Euler angles obtained by the data fusion and the standard deviation of their difference is ± 1.9° for , ± 1.5° for (most likely due to inaccuracy of the tilt sensor pass 30°) and ± 8° for . The raw signals are filtered both prior to and during data fusion and this creates a frequency dependant phase distortion. Thus, to quantify any potential signal delay, the cross-correlation between the Euler angles measured strictly with the accelerometer are compared to the merged Euler angle estimates and normalized so that the autocorrelations at zero lag are identically to 1.0. Comparing the Euler angles from the accelerometer and from the data fusion, and are 99.23% correlated with a delay of 7 samples (0.0547s), and are correlated at 99.66% and delayed by 11 samples. The compass heading and correlate at 99.38% with no delay. The compass is a digital serial device that is first processed and coded into RS-232 format at the compass, broadcast, then received and processed by the data acquisition computer. Any delay is due to the lag associated with this overhead and should be accounted for within the motion correction of the ADCP although in our case an agreement of more than 99% is considered acceptable. 32 3 Data Processing Phi [deg] To validate the high frequency component of (Figure 25), the Euler rates are integrated and compared to the Euler angles, , yield through the data fusion (Figure 27). The figure shows the third part of the test during the high frequency set of motion. In the first panel (a), the high frequency component of the integral of Euler rate , blue, is compared to the high frequency component of the merged Euler angle , red. In the 2nd panel (b), the high frequency component of the integral of Euler rate , blue, is compared to the high frequency component of the merged Euler angle , red and in the last panel (c), the high frequency component of the integral of Euler rate , blue, is compared to high frequency component of the merged Euler angle , red. The black is the difference of the two signals in each plot. yields to a low As expected, the difference between directly integrating frequency drift. The standard deviation is ±0.44° for , ± 0.38° for and ± 0.58° for . To quantize the phase agreement between the Euler rates and the Euler angles, the corresponding cross-correlations are computed, and are 99.99% correlated with no delay, and are correlated at 99.99% with no delay. Looking at the first 10s of Figure 27 third panel (c) the high frequency component of the integral of Euler rate is not following the same behavior of the high frequency component of the merged Euler angle . This is due to the high-pass filtering process itself and leads to and being delayed by 4 samples and 84.30% correlated. 0 -20 Theta [deg] 400 Psi [deg] (a) 20 410 420 430 440 450 460 470 480 (b) 20 0 -20 400 50 410 420 430 440 450 460 470 480 (c) 0 -50 400 410 420 430 440 450 T ime [s] 460 470 480 Fig. 27 During the third part of the test, high frequency set of motion, comparison between the high frequency component of the integral of Euler rate (a), (b), (c) in blue, and the high frequency component of the merged Euler angle (a), (b) and (c) in red. The black is the difference of the two signals in each plot. 3.3 Data Fusion 33 PSD [dB/Hz] The distribution of variance with frequency (the power spectral distribution) of the merged tilt sensor, compass, and IMU gyros is also verified by comparing FFT( ) with FFT( ), for low frequency and with FFT( ) for high frequency. Below the data fusion point, 1/30Hz, the spectra of the merged Euler angles match the spectra of the low-frequency estimates of the Euler angles, and above the data fusion point, they match the spectra of the Euler rates (Figure 28). (a) 10 0 PSD [dB/Hz] 10 10 10 0 (b) 10 -2 10 -1 10 0 (c) 10 0 10 -2 -1 10 Frequency [Hz] Fig. 28 In red, PSD of Merged Euler angle angle from tilt sensor (b), and -1 0 10 PSD [dB/Hz] -2 (a), (b), and (a), 10 (b) and 0 (c); in blue, PSD of Euler (c); in black, PSD of integrated Euler rate (a), (c). 3.3.2.1 Estimation of the Ship’s Velocity and Position Fig. 29 Diagrammatic representation of the data fusion of the IMU data and the GPS data used to obtain the ships velocity . 34 3 Data Processing The enhanced velocity of the ship, , is obtained by directly fusing the high , and the low frequency (128Hz) acceleration measurement from the IMU, frequency (0.5Hz) velocity obtained from the speed and course overground output T , , (Figure 29). For this calculation, the from the GPS, accelerations are rotated to the NED frame from its instrumentation frame and the gravitational contamination is removed, where The and emphasized velocity , , using (14): T 00 T . (25) are then combined to create the pre- Ω , 1 Ω (26) (27) and 1 Ω (28) After this, is to be convolved with a 1st order Butterworth filter with a cutoff frequency Ω to obtain the full frequency measure of the ships velocity, , according to (17). The position is then obtained by merging the enhanced velocity, T , , , with the latitude and longitude measured with the GPS. The latitude and longitude, measured by the GPS, are converted to NED position measurements using (6) and (8), . (29) 3.4 ADCP Processing The ADCP consists of four transducers tilted at equal angles (20°) from the vertical axis of the ADCP in a convex configuration and oriented in pairs that point in perpendicular planes (Figure 30). The ADCP reference frame (xadcp, yadcp, zadcp) has its origin at the center of the ADCP, where the four transducers intersect. The axes xadcp and yadcp are coplanar with the horizontal ship plane and the xadcpaxis points from port to starboard and the yadcp-axis points from stern to bow. The zadcp-axis points positive upward. 35 Fig. 30 ADCP beam and reference frame Assuming that the water velocity is horizontally homogenous but varies vertically within the beam envelope of the ADCP, the three orthogonal relative water velocity components u, v, and w in the ADCP reference frame are , , ° , , ° 1.4619 , , , (30) 1.4619 , , , (31) and , , , , 4 cos 20° 0.2666 , , (32) , , . where the index i is the number of the bin, each bin representing a different depth cell of the profiled water column, from 1 to 128 in our case. The Earth fixed water velocity of bin i is obtained using the body to inertial transformation matrix and subtracting the measured velocity of the ship, . (33) Chapter 4 Motion Observation and Experimental Results This chapter details the experiments used to choose the best data fusion point (Ω ) to obtain the full frequency measure of the ships velocity, , and its position, . The first experiment investigates properties of the vertical NED acceleration and different methods available to obtain the merged vertical velocity, and merged position, . The second experiment investigates properties of the data acquisition system on shore, without the ADCP in order to validate the data fusion point of the velocity and position data. 4.1 Vertical Motion 4.1.1 Study of the Acceleration The intent of the experiment is to observe the vertical NED acceleration, , implement different integration methods and choose the most suited approach to compute the corresponding vertical velocity and position. The IMU is the only instrument in the data acquisition system providing information Fig. 31 Vertical motion experiment setup. about vertical motion. The experiment takes place in a machine shop and consists of mounting IMU, tilt sensor and TCM2 compass on a level plate (Figure 31). The plate is leveled and tethered to the extremity of a 1.03m rigid lever. The middle of the lever is connected to a gearbox itself attached to a rotating engine. C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 37–60. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 4 Motion Observation and Experimental Results 38 The extremity of the lever runs on circular trajectories of 0.515m radius at different speeds. The test consists of six sets of vertical roundtrip periods of approximately 5, 10, 15, 20, 25 and 35 s, each lasting about 10 minutes (Figure 32). The speeds are manually set in an automatic manner using the speed variator of the rotating engine. 4 2 Az[m/s2] 0 -2 -4 -6 0 500 1000 1500 2000 2500 T ime[s] 3000 3500 4000 Fig. 32 Vertical motion experiment: raw vertical acceleration Az. Filtering of raw data is necessary before concluding on the systems’ performance. The test is conducted in a noisy environment, with loud air conditioning on and heavy machinery, some of it running during the test, leading to perturbation on the data unrelated to the actual motion of the plate. In addition, even though the cord holding the plate was chosen to hardly extend, a low frequency perturbation still remains, likely due to the stretch of the cord. Since those perturbations are less likely to exist at sea, the filtering is taking into account the wave frequency range (0.03 – 0.3Hz). A 2nd order bandpass Butterworth filter with cutoff frequencies 0.01 and 0.4Hz is found to be the most suited preserving motion and filtering noise (Figure 33). Figure 33 shows on the left side, a close up on the motion using the PSD of , from top to bottom for the set 1 (a), 3 (c) and 5 (e) of periods about 5, 15 and 25 s. On the right side of the figure, the close up on the effect of the filtering for the set 1 (b), 3 (d) and 5 (f) is presented. The signals pre-filtering are in red while in blue are the filtered signal with a 2nd order bandpass Butterworth, cutoff frequencies 0.01 and 0.4Hz. All filters used in this book are Butterworth filters as they are typical and Elliptic filters may have been used as well. 4.1 Vertical Motion 39 16 550 (b) (a) 500 14 PSD:Az1 filtered, Az1 PSD:Az1 filtered, Az1 450 400 350 300 250 200 150 12 10 8 6 4 100 2 50 0.17 0.175 0.18 0.185 Hz 0.19 0.195 0 0.2 1 2 3 4 Hz 5 6 7 8 4 (d) 3.5 14 3 PSD:Az3 filtered, Az3 PSD:Az3 filtered, Az3 (c) 16 12 10 8 6 2 1.5 1 4 0.5 2 0.06 2.5 0.065 0.07 Hz 2.2 0.075 0 0.08 1 2 3 4 Hz 5 6 7 8 2.5 (e) (f) 2 2 1.6 PSD:Az5 filtered, Az5 PSD:Az5 filtered, Az5 1.8 1.4 1.2 1 0.8 0.6 0.4 1.5 1 0.5 0.2 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 Hz 0 1 2 3 4 Hz 5 6 7 8 Fig. 33 spectrum from top to bottom for the set 1 (a), 3 (c) and 5 (e) of periods about 5, 15 and 25 s (left side) and filtering effect on the signal (right side) for the set 1 (b), 3 (d) and 5 (f). A close up, in time domain, of three sets of period 5 (a), 15 (b), and 25s (c), is shown in Figure 34. The black signal represents the recorded data and the red signal the filtered data with a 2nd order bandpass Butterworth with cutoff frequencies 0.01 and 0.4Hz. Figure 34 highlights the filtering necessity as higher the period of the set, higher the noise and lower the signal to noise ratio. 4 Motion Observation and Experimental Results 40 (b) 1 1.5 0.8 1 0.6 Az Set3 [m/s2] Az Set1 [m/s2] (a) 2 0.5 0 -0.5 0.4 0.2 0 -0.2 -1 -0.4 -1.5 -0.6 -0.8 -2 200 250 300 -1 200 350 250 300 T ime[s] 350 T ime[s] 0.8 (c) 0.6 Az Set5 [m/s2] 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 200 250 300 350 T ime[s] Fig. 34 Measured and filtered acceleration for periods about 5 (a), 15 (b) and 25s (c). Acceleration measurements are in black while filtered accelerations are in red. The period of the movement is isolated to recreate the expected motion (Figure 35). 5 120 set 4 pic at 0.049 Hz => period of 20.07 s 4.5 100 4 3.5 set 5 pic at 0.0417 Hz => period of 23.95 s set 3 pic at 0.0705 Hz => period of 14.17 s 2.5 60 set 2 pic at 0.1035 H z => period of 9.66 s 2 1.5 (b) 80 PSD PSD 3 set 1 pic at 0.1838 Hz => period of 5.44 s (a) set 6 pic at 0.0288 Hz => period of 34.71 s 40 1 20 0.5 0 0.01 0.02 0.03 Hz 0.04 0.05 0.06 0 0.06 0.08 0.1 0.12 0.14 Hz 0.16 0.18 0.2 0.22 Fig. 35 Az PSD for the set 1, 2 and 3 (b) of periods about 5, 10 and 15 s, and for the set 4, 5 and 6 (a) of periods about 20, 25, and 35 s. 4.1 Vertical Motion 41 The expected motion ( ) is simulated using a sinusoidal signal with the period corresponding to the set ( ) and the amplitude according to: . . (34) The expected motion is going to be compared to the measured signal using crosscorrelation and an agreement of more than 90% is considered acceptable. Figure 36 is a close up on the sets 1 (a), 3 (b) and 5 (c) with the expected motion in red, the system acceleration in blue, and the difference between the signals in black. The black signal’s standard deviation represents the acceleration signal’s accuracy. (a) 0.8 (b) Az3 BP,Theo,Theo-BP [m/s2] Az1 BP,Theo,Theo-BP [m/s2] 0.1 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0.05 0 -0.05 -0.1 -0.8 200 250 300 350 200 250 300 T ime[s] 350 T ime[s] 0.04 (c) Az5 BP,Theo,Theo-BP [m/s2] 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 200 250 300 350 T ime[s] Fig. 36 Close up of the acceleration for the set 1 (a), 3 (b) and 5 (c) of periods about 5, 15 and 25s with the expected motion in red, the system acceleration in blue and the difference between the signals in black. The black signal’s behavior emphasizes that the slower the motion, the smaller its resulting standard deviation, the higher the agreement between expected and obtained signal. The black signal’s standard deviation is respectively 9.6 ± 8.5891 cm/s2 (taking into account the specification of the instrument), 1.5239 ± 1.2652 cm/s2 and 0.66908 ± 0.44294 cm/s2. According to a crosscorrelation calculation conducted, they agree respectively at 98%, 97.7% and 96% with a delay of 0.015s each. 42 4 Motion Observation and Experimental Results 4.1.2 Velocity Calculations The IMU has low frequency noise like most accelerometers and since the integration process amplifies significantly the low frequencies, different methods are evaluated that focus on minimizing the low frequency noise. Three methods are evaluated for obtaining vertical velocity from acceleration data. The first method integrates numerically the acceleration measurement using the cumulative summation (Matlab function cumsum) of the signal over the sampling frequency. The low frequency contamination is then removed using the Matlab function detrend considering the low frequency contamination from the integration as a linear trend. The second method numerically integrates the acceleration measurement then applies a high-pass filter to the obtained velocity signal. The last method applies the data fusion technique. The concept behind using this method is that the IMU, which is assumed accurate only at high frequencies, is merged with an ideal signal containing no low frequencies (null signal) to remove the low frequency noise from the integration. This sub-section describes each one of the 3 aforementioned techniques. In each of the sub-sections, the red signal represents the expected motion, the blue the system’s motion, and the black the signals difference. The black signal’s standard deviation is an indicator of the velocity signal’s accuracy. 4.1.2.1 Vertical Velocity Resulting from Integrating Acceleration and Removing the Induced Trend A close up of the effect of integrating the acceleration (using the Matlab function cumsum) and using a low frequency contamination removal function (detrend) is shown for the sets 1 (a), 3 (b), and 5 (c) in Figure 37. Detrending a signal refers to applying the matlab function detrend to the signal. The red signal represents the expected velocity obtained by integrating the expected acceleration, the blue signal is obtained integrating then detrending the obtained acceleration and the black signal is the difference between expected and obtained velocities. The black signal’s standard deviation is respectively 6.27 cm/s, 2.3 cm/s and 1.9 cm/s. The lower the standard deviation of the black signal the better the method since the goal of the method is matching obtained signal with expected motion. This method fails at removing all low frequency perturbations leading to the need for another method based on a high-pass filter use. 4.1 Vertical Motion 43 (a) (b) 0.25 0.2 0.4 Vz3 BP,Theo,Theo-BP [m/s] Vz1 BP,Theo,Theo-BP [m/s] 0.6 0.2 0 -0.2 -0.4 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.6 200 250 300 350 200 250 T ime[s] 300 350 T ime[s] (c) Vz5 BP,Theo,Theo-BP [m/s] 0.1 0.05 0 -0.05 -0.1 -0.15 200 250 300 350 T ime[s] Fig. 37 Difference, in black, between the expected velocity VZ, red, and the obtained velocity using the detrend function on the integrated acceleration in blue for the set 1 (a), 3 (b) and 5 (c). 4.1.2.2 Vertical Velocity Resulting from High-Pass Filtering the Integrated Acceleration A close up of the effect of high-pass filtering on the integrated signal is shown for sets 1 (a), 3 (b), and 5 (c) in Figure 38. The expected velocity is in red, the blue signal is the velocity resulting from integrating then high-pass filtering the obtained acceleration and the black signal is the difference between expected and obtained velocities. A 4th order Butterworth high-pass filter with cutoff frequency of 0.021Hz is found to be the most suited filter to minimize phase delay and eliminate low frequency perturbation due to the integration process. The Butterworth filter is selected because typical and an Elliptic filter could also have been used. The black signal’s standard deviation is respectively 6 cm/s, 1,8 cm/s and 1.3 cm/s which is overall lower than the standard deviations obtained through the first method. This method fails at removing all perturbations at low frequency leading to the blue signal following a trend different than the red signal. But the method provides better results considering the standard deviation of the black signal than the first method involving use of the detrend Matlab function. 4 Motion Observation and Experimental Results 44 (a) (b) 0.25 Vz3 CSHP,Theo,Theo-CSHP [m/s] Vz1 CSHP,Theo,Theo-CSHP [m/s] 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 200 250 300 350 200 250 300 T ime[s] (c) 0.15 Vz5 CSHP,Theo,Theo-CSHP [m/s] 350 T ime[s] 0.1 0.05 0 -0.05 -0.1 -0.15 200 250 300 350 T ime[s] Fig. 38 For the sets 1 (a), 3 (b) and 5 (c), velocity obtained using a high-pass filter on the integrated acceleration, in blue, plotted against the expected velocity VZ, in red. The difference between the two signals is in black. 4.1.2.3 Vertical Velocity Using the Data Fusion Technique Results for the data fusion method is shown for the sets 1 (a), 3 (b), and 5 (c) in Figure 39. The red signal is the expected velocity, the blue signal the obtained velocity resulting from the data fusion technique, and the black signal the difference between expected and obtained velocities. The IMU, which is assumed accurate only at high frequencies, is merged with a null signal at low frequency by replacing VLFZ by 0 in (28). The black signal is the difference between expected and obtained velocities. A data fusion point at 1/100Hz is found to be the best compromise to merge IMU with null signal. With this method, the standard deviation of the black signal is respectively 6.9 cm/s, 1.9 cm/s and 1.5 cm/s. Looking at the standard deviation of the black signal for each one of the three methods and since the best method will have the lowest standard deviations, this method is not as satisfying as the second method and better than the first method for the set 3 and 5. This method is selected over the second method because it introduces less delay than using a 4th order Butterworth filter. 4.1 Vertical Motion 45 (a) (b) 0.25 0.6 0.2 Vz3 F,Theo,Theo-F [m/s] Vz1 F,Theo,Theo-F [m/s] 0.4 0.2 0 -0.2 -0.4 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.6 200 -0.25 250 300 200 350 250 300 350 T ime[s] T ime[s] 0.15 (c) Vz5 F,Theo,Theo-F [m/s] 0.1 0.05 0 -0.05 -0.1 -0.15 200 250 300 350 T ime[s] Fig. 39 For the sets 1 (a), 3 (b) and 5 (c), velocity obtained by data fusion, in blue, plotted against the expected velocity VZ, in red. The difference between the two signals is in black. 4.1.3 Vertical Position Calculations Two methods are applied to obtain the vertical position from obtained velocity data. The first method is to integrate the velocity estimates at fixed time steps using the cumulative summation and to high-pass filter the result. The second method is to merge the velocity obtained in 4.1.2 with a null signal at low frequency by replacing Z,LF by 0 in (28). This sub-section describes each of the two aforementioned techniques. In each of the sub-sections the red signal represents the expected motion, the blue the system motion, and the black the difference between the two. The standard deviation of the black signal is used to quantify the accuracy of the position signal. 4 Motion Observation and Experimental Results 46 4.1.3.1 Vertical Position Calculated Using the High Pass Filtered Integrated Velocity 0.5 Z1 CSHP,Theo,Theo-CSHP [m] 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 200 250 300 350 0.5 0.5 0.4 0.4 Z5 CSHP,Theo,Theo-CSHP [m] Z3 CSHP,Theo,Theo-CSHP [m] T ime[s] 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 200 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 250 300 T ime[s] 350 200 250 300 350 T ime[s] Fig. 40 For the sets 1 (a), 3 (b) and 5 (c), position obtained using a high pass filter on the integrated velocity, in blue, plotted against the expected position Z, in red. The difference between the two signals is in black. Results obtained using the first method are shown for the sets 1 (a), 3 (b), and 5 (c) in Figure 40. The red signal is the expected position obtained by integrating the expected velocity, the blue signal is the position estimate obtained by integrating then high-pass filtering the velocity estimates in 4.1.2, and the black signal is the difference between expected and obtained position. A 4th order high pass Butterworth filter with cutoff frequency of 0.021Hz is found to be the most suited filter limiting phase delay and minimizing low frequency amplification due to the integration process. The Butterworth filter is selected because typical and an Elliptic filter could also have been used. The standard deviation of the black signal with the first technique is 4.8 cm, 4.3 cm, and 3.9 cm respectively. 4.1.3.2 Vertical Position Calculated Using the Data Fusion Technique Results obtained using the second method are shown for the sets 1, 3, and 5 in Figure 41. The red signal is the expected position, the blue signal the position obtained using the data fusion technique with the velocity obtained in 4.1.2 merged with a null signal at low frequency by replacing Z,LF by 0 in (28), and the black signal is the difference between expected and obtained position. A cutoff frequency of 1/50Hz for the data fusion is found to be the best compromise to 4.2 Data Acquisition System Lab Testing 47 merge the obtained velocity with the null signal. The black signal’s standard deviation is respectively 6.7 cm, 5.6 cm and 7.6 cm. Although this method provides a high standard deviation measurement for the black signal, it is selected for the processing of the vertical position moving forward since it is compatible with real time applications. 0.5 0.5 0.4 Z3 F,Theo,Theo-F [m] Z1 F,Theo,Theo-F [m] 0.4 0.3 0.2 0.1 0 -0.1 -0.2 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.3 -0.4 -0.4 -0.5 -0.5 200 250 300 200 350 250 300 350 T ime[s] T ime[s] 0.5 Z5 F,Theo,Theo-F [m] 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 200 250 300 350 T ime[s] Fig. 41 For the sets 1 (a), 3 (b) and 5 (c), position obtained by data fusion, in blue, plotted against the expected position Z, in red. The difference between the two signals is in black. 4.2 Data Acquisition System Lab Testing The following section presents the experiments used to investigate and optimize the data fusion between the IMU and GPS signals. This is accomplished by first observing the sensors outputs then selecting a frequency for the data fusion and finally Fig. 42 IMU, tilt sensor, and TCM2 compass attached to verifying the merged a rigid plate attached to the cart. signal obtained is combining the comple-mentary region of the two sensors. The complete data fusion process used to accurately determine the position and velocity signals 48 4 Motion Observation and Experimental Results consists of two data fusions: the first data fusion process, involving the IMU acceleration and the GPS velocity measurement leads to a full frequency assessment of the velocity measurement. This frequency for the data fusion is selected so that at frequencies lower than the cutoff frequency (to be determined) the GPS provides an accurate measure of the system’s velocity, and at frequencies above the cutoff frequency the IMU provides an accurate estimation of the velocity. The second data fusion is performed between the merged velocity, obtained from the first data fusion, and the GPS position measurement. Similar reasoning to that used for the first data fusion is applied, i.e. for frequencies lower than the cutoff frequency the position estimate is provided by the GPS, while for frequencies above the cutoff frequency the measure of position is derived from the merged velocity signal. The experiments take place in an open parking lot to ensure the GPS system has a clear and unimpeded signal. The experimental setup consists in mounting the IMU, the tilt sensor and the compass on a rigid plate that is fixed to a cart (Figure 42) where the rest of the data acquisition system (without the ADCP) is mounted. Once the sensors’ signals are acquired, decoded, and synchronized, they are sent to the PC104 logger stack to be saved to the flash drive. These signals are later post processed to find the best frequencies for the data fusions for the evaluated sensors. During each test the cart is initially stationary for at least two minutes. Because of the lack of automatic motion control, the cart is then moved manually between four spots on the ground that mark the corners of a square with 7.88m leg and the corners pointing towards the four cardinal points. The use of industrial foam and the choice of a cart with large wheels are among the precautions taken to minimize the vibrations caused by the uneven ground. Three trajectories are selected: a square path, a zigzag course and a circle. These trajectories are repeated at least three times each at different speeds. The path of the trajectories, speed and periodicity are selected to test the system’s ability to accurately measure the cart motion. Conventions used in this chapter are as follows: The GPS position vector is denoted which is composed of , its north, its east-west component, and , its vertical component. south component, and represent the north-south and east-west velocity Similarly, is the vertical component of the GPS velocity components, respectively, and vector, : , T , , , T , (35) . (36) Similarity the IMU acceleration vector is defined by: , , T . (37) The determination of the data fusion frequency for the data fusion process is based on 4 steps applied to each one of the three trajectories. The steps are as follows: 4.2 Data Acquisition System Lab Testing 49 1) processing of the raw data and selection of the data fusion frequency, 2) Observing the signal spectrum to validate the choice of the data fusion frequency, 3) Observing the crosscorrelation of the low-passed merged and lowpassed GPS measurements to quantify their agreement with each other and Step4; calculation of the standard deviation of the merged signal using a high-pass filter to remove any motion contamination (Figure 43). ^ƚĞƉϮ ^ƚĞƉϭ ͻWƌŽĐĞƐƐƚŚĞ ƌĂǁĚĂƚĂ ĂŶĚŚŽŽƐĞ ƚŚĞĨƵƐŝŽŶ ĨƌĞƋƵĞŶĐLJ ^ƚĞƉϯ ͻsĂůŝĚĂƚĞƚŚĞ ĐŚŽŝĐĞĨŽƌƚŚĞ ĨƵƐŝŽŶ ĨƌĞƋƵĞŶĐLJ ^ƚĞƉϰ ͻƌŽƐƐĐŽƌƌĞůĂƚĞ >W'W^ĂŶĚ>W ĨƵƐĞĚƐŝŐŶĂů ͻƐƚŝŵĂƚĞƚŚĞ ƐƚĂŶĚĂƌĚ ĚĞǀŝĂƚŝŽŶŽĨ ƚŚĞǀĞůŽĐŝƚLJ ƐŝŐŶĂů Fig. 43 Methodology used to find the data fusion frequency between IMU and GPS measurement to recover full frequency estimate of the system’s position and velocity. 4.2.1 Step 1: Processing of Individual Measurements During this analysis, the DGPS measurements are used to calculate distance travelled and duration for each trajectory. Since the start and end points of each shape are the same, it is possible to evaluate the period, i.e. the track periodicity. This is particularly important for the sensor’s data frequency analysis to distinguish the actual motion of the cart from possible perturbations and noise. The first part of this section describes the results from the analysis of the sensor’s measurements in the time domain and the second part describes the results in the frequency domain. The three paths as perceived by the DGPS are shown in Figure 44, Figure 45 and Figure 46. The first trajectory follows the 7.88m legs of the square starting at the coordinates Y= -2 and X= -2 on Figure 44 and going southwest, then southeast, then northeast, and finally northwest. 0 1. South W e st 4. North W e st 2. South East 3. North East X gps[m]=>North -2 -4 -6 -8 -10 -12 -8 -6 -4 -2 0 Y gps[m]=>East Fig. 44 Square path, as perceived by the DGPS. 2 4 4 Motion Observation and Experimental Results 50 The path is repeated four times in approximately three minutes. The first two squares are each completed in approximately 57.8s and the last two in 34.35s. The DGPS reflects the motion of the cart within its 3 meter accuracy. According to the DGPS velocity data, the cart is moving at 0.55m/s during the first two square paths and about twice as fast for the last two, at 0.93m/s. The second path, following the same general square trajectory but proceeding in a zigzag pattern between corners, is repeated four times 90.22s each with a total of a little over six minutes, (Figure 45). The DGPS responded sharply to the sudden change of direction of the cart. According to the DGPS velocity measurement, the cart moves at approximately 0.39m/s. 0 X gps[m]=>North -2 -4 -6 -8 -10 -12 -4 -2 0 2 Y gps[m]=>East 4 6 Fig. 45 Square path proceeding in a zigzag pattern between corners, as perceived by the DGPS. The last path follows a 39m perimeter circle which is repeated five times in approximately six minutes. The fourth circle travelled has an ellipsoidal shape due to the DGPS position’s error. The first three circles represent a 39.3m distance travelled in 83s. The ellipsoidal path is 32.83m and is conducted in 64s. Finally, the last circle takes 60.9s to travel 36.29m (Figure 46). The cart swerved less than 3 meters when attempting to manually recreate the same trajectory four times in a row. The DGPS measurements reflect both the cart’s swerve and its 3 meters accuracy range. 4.2 Data Acquisition System Lab Testing 51 0 X gps[m]=>North -2 -4 -6 -8 -10 -12 -6 -4 -2 0 2 Y gps[m]=>East 4 6 Fig. 46 Circle path as perceived by the DGPS. The uneven track induced the data acquisition systems to tilt and those angles are measured by the tilt sensor (Figure 47). Although pitch and roll applied to the data acquisition system impacts the IMU accelerometers, these are taken into account in the processing of the IMU acceleration measurement. As an example of that impact, the error induced on the IMU acceleration by tilting is calculated for the first trajectory test. The tilt sensor’s roll and pitch measurement of the square path have a mean of -0.4° and -1.275° respectively, with a standard deviation of ± 1.44° and ± 0.93° respectively. At the maximum roll angle, 1.84°, it influences the east component of the acceleration by -0.315m/s2 and at the maximum pitch angle, 2.2°, the north component of the acceleration by 0.376m/s2. The tilt sensor’s roll and pitch for the three trajectories are shown in Figure 47 and Table 6 presents their mean and standard deviation as well as the influence of the maximum deviation of the data on the IMU east and north component of the acceleration. 4 Motion Observation and Experimental Results a Roll [deg] 10 0 -10 Pitch deg] 250 300 350 400 200 b 0 -5 250 300 350 Time[s] 400 0 -10 450 5 c 10 Pitch deg] Roll [deg] 52 450 300 500 600 4 2 0 -2 -4 -6 d 200 300 10 Roll [deg] 400 400 Time[s] 500 600 e 0 -10 Pitch deg] 200 4 2 0 -2 -4 -6 200 300 400 500 600 f 300 400 500 Time[s] 600 Fig. 47 Roll and Pitch of the cart measured by the tilt sensor during the first trajectory ((a) and (b)), the second trajectory ((c) and (d)) and the third trajectory ((e) and (f)). Table 6 Mean and standard deviation of the tilt sensors’ roll and pitch as well as the influence it could have on the IMU acceleration if not considered for the three trajectories of the on shore test of the data acquisition system. Square ROLL PITCH Mean [°] STD [°] Influence on Ay [m/s2] Mean [°] STD [°] Influence on Ax[m/s2] -0.4 ± 1.44 -0.315 -1.275 ± 0.93 0.376 Trajectory Square in zigzag course -0.631 ± 1.253 -0.3225 -1.156 ± 0.946 0.356 Circle -0.6321 ± 1.096 1.7281 -1.165 ± 0.8169 0.3392 The study of the tilts concluded that the cart has rolled 0.55° ± 1.26°, and has pitched 1.19°± 0.89° on average. The second part of the processing of the raw sensor’s data is to observe the measurements in the frequency domain. For the study of the signals in the frequency domain, the power spectral density (PSD) of each signal is used. The IMU PSD accelerations are obtained for the three trajectories and shown in Figure 48. The notation PSD Ax/Ay means the graph is representing both the PSD of Ax and the PSD of Ay in two different colors. 4.2 Data Acquisition System Lab Testing 53 a 5 5 PSD Ax / Ay PSD Ax / Ay 4 3 2 1 0 b 6 4 3 2 1 10 20 30 40 Frequency [Hz] 50 60 0 10 20 30 40 Frequency [Hz] 50 60 c PSD Ax / Ay 4 3 2 1 0 10 20 30 40 Frequency [Hz] 50 60 Fig. 48 PSD of the north component, in blue, and the east component, in red, of the IMU acceleration during square trajectory (a), square path by processing in zigzag course (b) and the circle trajectory (c). Figure 48 shows significant spectral content for frequencies above 2Hz present in the measurements. The Notation PSD Ax/Ay indicates that the plot has both the PSD of Ax and the PSD of Ay represented. The scale is chosen to show the noise starting at 2Hz and most likely coming from the vibration of the cart and from the batteries located nearby the system. These high frequencies are most likely a combination of valuable high frequency component of the IMU measurement and noise from the vibration of the IMU on the cart and from the battery nearby the data acquisition system. Among the noise is valuable high frequency information on the IMU acceleration measurements essential for the data fusion process with the GPS. No low-pass filtering can be applied to the data prior to the data fusion process and high frequency noise is going to be relatively attenuated by the lowpass filter applied at the last stage of the data fusion process. To be aware of the signal to noise ratio of the IMU acceleration measurement, a first order Butterworth low-pass filter with a cutoff frequency at 2Hz is applied to the signals to remove the aforementioned noise at 2Hz and the result can be seen in Figure 49. The plots (a), (d) and (g) [respectively (b), (e), (h) and (c), (f), (i)] shows the north (respectively east and down) component of the acceleration in blue and the signal 4 Motion Observation and Experimental Results 54 2 0 a -2 Ay [m/s2] -2 Az [m/s2] 250 4 2 0 -2 -4 350 300 400 500 600 e -2 400 500 600 f 2 0 -2 200 300 400 Time[s] 400 350 Time[s] 500 600 Ax [m/s2] 250 0 300 450 450 c Ay [m/s2] Ax [m/s2] Ay [m/s2] 300 d 300 400 b 2 0 -2 200 Az [m/s2] 350 0 250 200 2 300 2 Az [m/s2] Ax [m/s2] after low-pass filtering the noise at 2Hz in red. The signal to noise ratio is approximately 1 to 2. The Butterworth filter is selected because typical and an Elliptic filter could also have been used. The filtering is only done for a better understanding of the frequency distribution of the signal and is not included in the data fusion process. 400 450 2 0 -2 200 2 g 300 400 500 600 h 0 -2 200 300 400 500 600 i 2 0 -2 200 300 400 500 Time[s] 600 Fig. 49 Influence of frequencies above 2Hz on the IMU acceleration measurements for the three trajectories of the on shore test of the data acquisition system. Finally, the DGPS position, velocity and the IMU acceleration are studied in the frequency domain to determine the complementary regions of the sensor. The detection of the frequency peak corresponding to the cart’s motion, which appears in each one of the signals spectrum, is the first step in observing the complementary regions of the sensors. Figure 50 presents the spectrum of the DGPS position signal (Figure 50.a), DGPS velocity signal (Figure 50.b) and of the IMU acceleration (Figure 50.c) during the first trajectory (square path). The frequency corresponding to the first two square paths is close to 0.015Hz and for the last two squares close to 0.02Hz. Once the frequency peaks corresponding to the cart’s motion are detected, around 0.02Hz in this example, the visualization of where the DGPS and IMU measurements have most of their significant spectral content is used to choose the data fusion frequency. 4.2 Data Acquisition System Lab Testing 55 PSD X gps / Y gps 4000 a 3000 2000 1000 0 0.02 0.04 Frequency [Hz] 6 b 40 30 20 10 0 0 0.06 c 5 PSD Ax / Ay PSD Vx gps / Vy gps 0 4 3 2 1 0.02 0.04 0.06 0.08 Frequency [Hz] 0.1 0.12 0 0 0.02 0.04 0.06 Frequency [Hz] 0.08 0.1 Fig. 50 PSD of the DGPS position (a), DGPS velocity (b) and IMU acceleration (c) for the first trajectory of the on shore test, following a square path. The blue signal corresponds to the north component of the measurement and the red signal to the east component. The DGPS has most of its significant spectral content around the peak of interest (Figure 50.a and Figure 50.b) corresponding to the cart’s motion and almost no significant spectral content at higher frequencies. On the other hand, Figure 50.c shows how the IMU sensed the low frequency motion of the cart, smothered by other frequencies, while still responsive over a frequency range greater than the DGPS. This observation shows the importance of the IMU data being filtered out of the region where the DGPS delivers accurate measurements in order to avoid perturbations on the low frequency estimate of the merged signal. To do so, a 3rd order high pass Butterworth filter with a cutoff frequency at 0.1Hz (Nyquist frequency) is applied to the IMU acceleration measurement prior to the data fusion process. The Butterworth filter is selected because typical and an Elliptic filter could also have been used. The detection for the frequency peak corresponding to the cart’s motion is applied for all the trajectories and results are compiled in Table 7. 56 4 Motion Observation and Experimental Results Table 7 Results from the peaks of frequency detection corresponding to the cart’s motion for the three trajectories. Frequency peak corresponding to the cart’s motion [Hz] North Component East Component North Component DGPS VELOCITY East Component North Component IMU ACCELERATION East Component DGPS POSITION Square First two Last two paths paths 0.01489 0.02173 0.015 0.02 0.01489 0.021 0.01489 0.021 0.015 0.021 0.015 0.021 Square in zigzag course Circle 0.01074 0.01074 0.01074 0.01123 0.01074 0.01074 0.01318 0.01318 0.01245 0.0127 0.012 0.012 The study of the spectrums for the other two trajectories leads to similar observations as in Figure 50 where the DGPS has most of its significant spectral content just after the peak of interest corresponding to the cart’s motion. These observations suggest that the complementary regions of the sensors overlap around 0.05Hz, which is used as the data fusion point. 4.2.2 Step 2: Validate the Choice for the Data Fusion Frequency As aforementioned, the IMU acceleration measurement is high-pass filtered prior to the data fusion process and the data fusion point is selected at 0.05Hz. Figure 51 shows the diagram of the first data fusion process. Fig. 51 Data fusion diagram between the IMU acceleration data and the DGPS velocity measurements in order to obtain the enhanced velocity estimate. The data fusion frequency validation is applied observing the signals though key sequential steps, depicted in Figure 51. The frequency domain is selected for that investigation. Figure 52 shows the results of this analysis for the north component of the DGPS velocity and the north component of the IMU acceleration during the square maneuver. The same process is applied for all the signals and trajectories. 4.2 Data Acquisition System Lab Testing 30 20 10 0.02 0.04 0.06 0.08 Frequency[Hz] 0.1 50 c 40 30 20 10 0 0 0.02 0.04 0.06 0.08 Frequency[Hz] 0.1 PSD Vx gps,HP(Ax),Scaled HP(Ax) 40 0 0 PSD Vx gps,Scaled HP(Ax),Add a 50 b 40 30 20 10 0 0 0.02 0.04 0.06 0.08 Frequency[Hz] 0.1 50 Vx gps,PSD Add,Fused VelX PSD Vx gps,Ax,highpass Ax 50 57 d 40 30 20 10 0 0 0.02 0.04 0.06 0.08 Frequency[Hz] 0.1 Fig. 52 PSD at particular steps of the data fusion process between the DGPS north component velocity and the IMU north component acceleration. Figure 52 shows the Power Spectral Density (PSD) at key steps of the data fusion process between the DGPS north component velocity and the IMU north component acceleration. Figure 52a compares the DGPS north component velocity (blue), the north component of the IMU acceleration (black), and the same signal high-pass filtered (red). Figure 52b shows the DGPS north component velocity (blue) next to the high-pass filtered north component of the IMU acceleration (black), and the same signal scaled using the data fusion frequency (red). Figure 52c shows the DGPS north component velocity (blue), the scaled high-pass filtered IMU acceleration (black) and the addition of the two signals in red. The addition of scaled high-pass filtered IMU acceleration and the DGPS velocity is noted as a preemphasized signal. Finally Figure 52d shows the north component of the merged velocity (red) compare to the DGPS north component velocity (blue) and its addition to the scaled high-pass filtered IMU acceleration. This study shows the high-pass filter applied to the raw acceleration measurement has reduced the region of frequency where the DGPS velocity spectrum has most of its significant spectral content (Figure 52.a) which allows the merged signal to follow the DGPS velocity spectrum before the data fusion frequency (Figure 52.d). Figure 52.b demonstrates the advantage of scaling the 4 Motion Observation and Experimental Results 58 Vx/y GPS,CSAx/y,Fused Vx/y acceleration signal, increasing the significant spectral content of the signal at higher frequencies where the DGPS signal is smothered by the noise. As a result, on Figure 52.c the preemphasized signal for frequencies smaller than the data fusion frequency (0.05Hz) comes predominantly from the DGPS velocity signal, while for frequencies greater than 0.05Hz the signal comes predominately from the IMU acceleration measurement. The enhanced version of the merged velocity is then retrieved by deconvolution using a 1st order Butterworth low-pass filter with a cutoff frequency at the data fusion point, 0.05Hz (Figure 52.d). The Butterworth filter is selected because typical and an Elliptic filter could also have been used. The merged velocity signal is plotted in the time domain and compared to the direct integration of the IMU acceleration signal (Figure 53) to show the importance of the data fusion. 2 0 -2 -4 -6 -8 250 a 300 350 400 2 450 b 0 -2 -4 250 300 350 Time[s] 400 450 Fig. 53 Comparison in the time domain between the merged velocity (red) and the velocity obtained by direct integration of the raw IMU acceleration signal (black). The blue signal is the DGPS velocity measurement. The upper panel shows the north component of the signal (a) and the lower, the east component (b) Now that the merged velocity estimate of the data acquisition system is available, the subsequent data fusion process applied is between the merged velocity and the DGPS position measurement to obtain a full frequency measure of the position estimate. The choice of the data fusion frequency is done in a similar fashion to aforementioned and the same data fusion point at 0.05Hz is selected. Figure 54 shows the diagram of the process of the second data fusion process between the enhanced velocity signal and the DGPS position measurement. 4.2 Data Acquisition System Lab Testing 59 Fig. 54 Data fusion diagram between the DGPS position measurement and the merged velocity estimate obtained by fusing the IMU acceleration data and the DGPS velocity. The enhanced (merged) velocity signals estimated from the previously described first data fusion process have most of their significant spectral content below the data fusion point from the DGPS velocity data. Therefore, the DGPS position signal and the enhanced velocity signal have matching spectra, below the data fusion point, and no pre-processing is needed on the DGPS velocity signal before the data fusion with the DGPS position data. The next step is to verify the agreement between the DGPS position measurement and the merged position, as well as between the DGPS velocity measurement and the merged velocity at frequencies lower than the data fusion point. 4.2.3 Step 3: Low-Pass Filtering of the Merged and DGPS Data at the Data Fusion Frequency and Conclusion on Their Agreement Using the Crosscorrelation Method To verify the agreement between the DGPS position (respectively velocity) measurements and the merged velocity estimates (respectively IMU acceleration) a 1st order Butterworth low-pass filter with a cutoff frequency at the data fusion point, 0.05Hz, is applied to both signals, which are then crosscorrelated. The Butterworth filter is selected because typical and an Elliptic filter could also have been used. During the square maneuver, the first crosscorrelation reveals the DGPS velocity signal and the merged velocity estimate agree by 99.02% for the north component (Figure 55.a) and by 99.01% for the east component (Figure 55.b). The second crosscorrelation reveals that the DGPS position signal and the merged position estimate agree by 99.58% for the north component (Figure 55.c) and by 99.59% for the east component (Figure 55.d). 4 Motion Observation and Experimental Results 60 0 -0.5 2 4 6 8 10 12 14 4 x 10 b 0.5 0 -0.5 % of agreement (1=100%) % of agreement (1=100%) a 0.5 0.8 0.6 0.4 0.2 0 -0.2 -0.4 c 2 4 6 8 10 12 14 4 x 10 d 0.5 0 -0.5 2 4 6 8 10 Sample Number 12 14 2 4 x 10 4 6 8 10 Sample Number 12 14 4 x 10 Fig. 55 Crosscorrelation (a) (respectively (b)) between the north, (respectively east) component of the DGPS velocity and the north (respectively east) component of the merged velocity estimates. Similarly, (c) (respectively (d)) corresponds to the crosscorrelation between the north (respectively east) component of the DGPS position and the north (respectively east) component of the merged position estimates. Since the merged velocity of the data acquisition system is ultimately to be used to correct the ADCP data, it is important to estimate the standard deviation of that signal. 4.2.4 Step 4: High-Pass Filtering of the Merged Signals to Conclude on the Signals Standard Deviation The standard deviation of the merged velocity error is typically determined by subtracting the expected velocity of the cart with the merged velocity estimate. However, since it was not possible to precisely control the motion of the cart, the expected velocity of the cart could not be determined. Instead, the estimation of the signals noise is applied by high-pass filtering the merged velocity signal, removing the motion of the vehicle, and computing the standard deviation of the filtered signal. Using this estimation process, the standard deviation of the merged velocity estimates (Table 8) is calculated for the three trajectories. Table 8 Estimates of the standard deviation of the merged velocity signal for the three trajectories of the on shore data acquisition test. Estimates of the merged velocity standard deviation [cm/s] NORTH COMPONENT EAST COMPONENT Square Path at 0.55m/s 0.77 0.78 Square Path at 0.93m/s 1.16 1.19 Square in zigzag course at 0.39m/s 0.65 0.7 Circle at 0.47m/s 0.66 0.74 The standard deviation of the enhanced velocity signal averages 0.83 cm/s and the signal is used in the subsequent section for the correction of the ADCP data when performing a mission at sea. Chapter 5 At Sea Experiment of Data Acquisition System This chapter presents the mission at sea conducted for the observation of the motion data acquisition system measurements in the field as well as the collection and correction of unreferenced ADCP data. Both the motion data acquisition system and TRDI ADCP are installed on a test vessel, the R/V Oceaneer IV, which performs a series of specifically chosen maneuvers in open sea while the motion data along with the ADCP data are simultaneously collected to be later post-processed. The mission is performed off the southeast coast of Florida where the currents run predominately near shore in a north-south direction with velocity ranging up to 1m/s (Figure 56). The Florida Current receives its water from two main sources, the Loop Current and the Antilles Current. The Loop current is the most significant of these sources and can be considered the upstream extension of the Gulf Stream System [NOAA]. Fig. 56 The Florida Current The ship maneuvers follows two different tracks: an L-shape track (going south then east) and a straight line roundtrip track along the south-north direction. In the first section of this chapter, results of the navigational data fusion for each maneuver are presented. The second section examines the unreferenced ADCP velocity profiles and their correction, by subtracting the vessel motion from the measurements. The correction is performed on both its Beam coordinate frame, C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 61–84. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 62 5 At Sea Experiment of Data Acquisition System where the data is recorded, and in its Earth Reference frame (North-East-Up frame). The last section summarizes the results of the mission at sea. 5.1 Motion Data Acquisition Measurements and Navigational Data Fusion Results The following analysis presents further details of each maneuver observing motion data acquisition measurements. It concludes on the enhanced velocity measurement of the ship obtained by navigational data fusion, which is used in the subsequent section to correct ADCP data. The first maneuver, L-shape track, is performed by heading south for 623.56m at approximately 1.04m/s and then east for 1274.8m at approximately 2.04m/s (according to the GPS measurements). The trajectory of the boat exhibits a slight drift to the east when heading south and a more noticeable drift to the north when heading east (Figure 57.a). This indicates the presence of a water current, as expected, mainly along shore in the south-north direction with a secondary transverse east component. The water current is quantified when observing the ADCP measurements in the next section. The water currents’ influence on the vessel’s motion can also be observed during the second maneuver (Figure 57.b), where the straight line maneuver goes 687.6m south-east at approximately 1.07m/s, and then goes 1988m north-east at approximately 2.92m/s. The boat drifts off the track (Figure 57) because of the water current. 0 a b 1000 X gps[m]=>North X gps[m]=>North -100 -200 -300 -400 500 0 -500 -600 0 -500 200 400 600 800 Y gps[m]=>East 1000 0 50 100 Y gps[m]=>East 150 Fig. 57 Trajectory perceived by the DGPS during the first (a) and second (b) maneuver at sea. The low frequency component of the velocity measured by the DGPS is merged with acceleration estimates from the IMU. A data fusion point chosen at 0.05Hz is used to obtain an enhanced velocity estimate using a complementary filter. A close up around the data fusion frequency is shown in Figure 58 using the signal’s Power Spectral Density (PSD) on a logarithmic scale. The top (respectively bottom) figures (a) and (c) (respectively (b) and (d)) represent the PSD of the north (respectively east) component of the signals during the L-track maneuver (left) and the straight line maneuver (right).The focus is made before 5.1 Motion Data Acquisition Measurements and Navigational Data Fusion Results 63 a 0 10 Vx GPS Ax IMU Vx Fused -1 10 b 0 10 Vy GPS Ay IMU Vy Fused PSD Vx/y gps,Fused Vx/y,Ax/y PSD Vx/y gps,Fused Vx/y,Ax/y and after the data fusion point to follow the behavior of the merged signal. As predicted, the figures demonstrate how the enhanced estimate of the vessel’s velocity supports the DGPS spectra below the data fusion point and the IMU acceleration measurement above it. c 0 10 Vx GPS Ax IMU Vx Fused -1 10 d 0 10 Vy GPS Ay IMU Vy Fused -1 -1 10 Frequency[Hz] 10 Frequency[Hz] Fig. 58 Close ups around the data fusion frequency, 0.05Hz, of the PSD of the velocity measurement from the DGPS (blue), the acceleration estimate from the IMU (black) and the enhanced estimate of the velocity obtained by data fusion (red). Vx [m/s] 1 0 -1 a 200 0 2 1 0 -1 0 200 400 600 800 1000 1200 b 400 600 800 400 600 800 Time[s] 1000 1200 d 4 2 0 0 1.5 1 0.5 0 -0.5 500 0 500 1000 1200 c 200 Vy [m/s] 0 2 1 0 Vz [m/s] Vz [m/s] Vy [m/s] Vx [m/s] The time series of the three components, north, east and down, of the enhanced velocity estimate for the two maneuvers is plotted in Figure 59. The vessel travels at 1.1m/s when heading south and 2.06m/s when heading east according to the enhanced velocity signal, for the first maneuver (Figure 59 a, b and c). During the second maneuver, (Figure 59 d, e, and f) the boat is traveling at 1.14m/s when heading south and 2.94m/s when heading north. The enhanced velocity estimate, updated every 1/128 s, leads to a more accurate measurement of the vessel’s motion since measured over a larger range of frequency of motion when compared to the GPS velocity measurement updated every 2 s. The enhanced velocity is later removed from the ADCP measurements in order to obtain true current measurements. 1 0 -1 0 1000 e 1000 f 500 Time[s] 1000 Fig. 59 Time series of the vessel’s enhance velocity measurement obtained by data fusion with its north (east, down) component in blue (red, black) for the first maneuver (a, b, c) and second maneuver (d, e, f) 64 5 At Sea Experiment of Data Acquisition System According to the tilt sensor the boat rolled 1.66° and pitched 0.58° during the first maneuver. It rolled 1.9° and pitched 0.56° during the second maneuver. These tilts are taken into account in the navigational data fusion and for the corrections of the ADCP data. Characteristic of the maneuvers at sea, like the distance travelled, the headings and the enhanced velocity measurement of the ship are now available to study and correct the water current measured by the ADCP. 5.2 ADCP Unreferenced and Corrected Measurements The following section presents ADCP current measurements collected during the two maneuvers at sea as well as the correction applied to the data in order to recover water velocity profiles not contaminated by the vessel’s motion. The removal of the ship’s velocity is necessary to quantify the water current measured since the vessel surge, sway and heave account for the majority of the velocity measured by the ADCP [Ray 2002]. Two parts compose the section, illustrating the results of the correction of the ADCP data in two different reference frames for comparison purposes. The first part illustrates the results from correcting the ADCP velocity data in the ADCP radial beam coordinate frame, which allows us to manipulate ADCP data in its rawest form, i.e. no internal ADCP corrections applied. The second part illustrates the results of the ADCP corrected velocity data in the North-East-Up Frame, the Earth coordinate frame of the ADCP. For this mission, the ADCP is a 600 kHz Teledyne RDI Broadband Workhorse Sentinel. Its reference beam, beam 3, is mounted 45o counter-clockwise from the centerline of the ship in order to increase noise rejection and the effective ADCP measured velocity by a factor of 1.4. As a result, beams 2 and 3 are pointing forward, and beams 1 and 4 are pointing aft. The water profile will be composed of 16 bins, each 4m in length. A default blanking distance of 88cm is used in order to avoid measuring currents when the ADCP is ringing; resultantly the center of the first bin is located 5.05m away from the ADCP which puts the center of the last bin 65.05m away from the ADCP. To properly construe the raw ADCP data, it is noted that when the ship moves in a particular direction, with the ADCP mounted looking down, the velocity of the boat creates a relative flow that is opposite in direction of the actual movement of the boat. For example, when looking at the following raw ADCP data, one has to take into account this inverted bias. In addition to looking at the ADCP velocity profiles, the raw velocity at the first bin, where the water current is its strongest in the middle of the bin (~5m depth relative to the ADCP), is compared to the corrected ADCP velocity and the merged ship velocity. All velocities presented are in m/s. Finally the standard deviation of the error velocity, which is also the estimated standard deviation of the measured velocity, is calculated. 5.2 ADCP Unreferenced an nd Corrected Measurements 665 5.2.1 Correction of the t ADCP Data in the Beam Coordinate Frame The water current measurrements resulting from the correction of the ADCP daata in the Beam coordinate frame f is presented here. In this reference frame, wherre beams 2 and 3 are lookin ng forward and beams 1 and 4 are looking aft, the radiial velocity sign is positive when the water is moving towards the transducer. Thhe enhanced vessel’s velociity measured by the data acquisition system is in thhe North-East-Down frame so s it needs to be converted to the ADCP Beam coordinaate frame before being subttracted from the ADCP data. The conversion is donne through three consecutivee transformations (Figure 60). The velocity is transformeed from the North-East-Dow wn vessel coordinates to the ADCP Ship reference fram me (Forward-Starboard-Up). The vessel’s velocity is then converted from the ADC CP o the ADCP instrument coordinate frame, with its x-axxis Ship coordinate system to is pointing from beam 1 to o beam 2, its y-axis from beam 4 to beam 3 and its z-axxis pointing upward. Finally y, the transformation is performed between the ADC CP instrument coordinate fram me and the Beam coordinate Frame. NED • VESSEL • North • East • Down FSU • ADCP Ship • Starboard • Forward • Up XYZ • ADCP Instr. •X •Y •Z Bm1,2 3,4 • ADCP Beam • Bm1 ,Bm4 • Bm2 ,Bm3 Fig. 60 Diagram of the neceessary reference frame transformations to transform the vessell’s enhanced velocity measureed by the data acquisition system into the ADCP Beaam coordinate frame. The results of correctiion of the ADCP data in the beam coordinate frame arre presented for the first maaneuver, then the second maneuver. For each section, thhe currents at the first bin an nd the velocity profiles along the 16 bins are presented. The last two bins of the water w profile were discarded by the ADCP internal qualitty algorithms and are represeented by a white space in the water profile figures. 5.2.1.1 Water Current Measured for the First Maneuver, L-Shape Track Heading South Then T East The following presents, for the L-shape track, an estimate of the water currennt measured at the first bin then observes the 16 bins of the ADCP velocity profille. The ship’s velocity alon ng beams 2 and 3 (looking forward) as well as thhe uncorrected and corrected d water current measure along beam 2 and 3 (Figure 61) are computed, plotted an nd examined. The same procedure is done for the daata along beams 1 and 4, look king aft (Figure 62). 5 At Sea Experiment of Data Acquisition System VShipBm2 66 1.5 1 0.5 0 -0.5 VBm2 bn1 0 VCurrent Bm2 bn1 VShipBm3 400 600 800 1000 1200 b 1 0 0 200 400 600 800 1000 1200 c 200 400 600 Time[s] 800 1000 1200 2 d 1 0 0 VBm3 bn1 200 2 1.5 1 0.5 0 -0.5 0 1.5 1 0.5 0 -0.5 0 VCurrent Bm3 bn1 a 200 400 600 800 1000 1200 e 200 400 600 800 1000 1200 f 1 0 -1 0 200 400 600 Time[s] 800 1000 1200 Fig. 61 Ship velocity, in blue, along beam 2 (a), and 3 (d) compare to the contaminated measurement of the water current, in black, along beam 2 (b) and 3 (e), and to the true water current, in red, along beam 2 (c) and 3 (f) during the first maneuver while the beams 2 and 3 are looking forward. VShipBm1 5.2 ADCP Unreferenced and Corrected Measurements 67 a 1 0 -1 0 200 400 600 800 1000 1200 VBm1 bn1 1 0 -1 0 VCurrent Bm1 bn1 b 200 400 600 800 1000 1200 1 c 0 -1 0 200 400 600 Time[s] 800 1000 1200 VShipBm4 1 d 0 -1 0 200 400 600 800 1000 1200 VBm4 bn1 1 -1 0 VCurrent Bm4 bn1 e 0 200 400 600 800 1000 1200 f 1 0 -1 0 200 400 600 Time[s] 800 1000 1200 Fig. 62 Ship velocity, in blue, along beam 1 (a), and 4 (d) compare to the contaminated measure of the water current, in black, along beam 1 (b) and 4 (e), and to the true water current, in red, along beam 1 (c) and 4 (f) during the first maneuver while the beams 1 and 4 are looking aft. Figure 61 and Figure 62 demonstrates the difficulty interpreting the ADCP recording of current, in black, as it is contaminated by the ship’s motion, in blue, which needs to be subtracted from the latter leading to a true measurement of the water current, in red. The observations of the signals led to estimates which are compiled in Table 9. Table 9 Ship’s enhanced velocity measurement, uncorrected and corrected ADCP water current measurement in beam coordinates, at the first bin, during the first maneuver Beam Coordinates, 1st maneuver, bin 1 L- Shape Track Beam 2 Forward Beam 3 Beam 1 Aft Beam 4 Ship’s velocity, [m/s] ADCP uncorrected Water current, [m/s] Corrected Water current, [m/s] 0.2 then 0.13 0.27 then 0.62 -0.22 then -0.21 -0.29 then -0.71 0.46 then 0.38 0.39 then 0.37 –0.55 then –0.42 –0.48 then –0.41 0.26 then 0.25 0.12 then –0.25 –0.33 then –0.21 –0.19 then 0.30 68 5 At Sea Experiment of Data Acquisition System Using Table 9 and basic trigonometric equations, the water current measured at the first bin during the first maneuver is estimated at 4.74° North, 0.5m/s when the ship is heading south and 7.5° North, 0.72m/s when heading east. The subsequent part studies the ADCP velocity profiles to estimate the water current along all bins. There are a number of options for representing time series water current data depending on the desired analyses. For this investigation of the ADCP velocity profiles and for the two maneuvers, the Matlab ‘colormap plot’ is the tool used to conceptualize the current velocity amplitudes. The direction and magnitude of the water current is then calculated using basic trigonometric equations. Uncorrected (Figure 63 and Figure 65) and corrected (Figure 64 and Figure 66) ADCP velocity profiles along the beams 2 and 3 and uncorrected (Figure 67 and Figure 69) and corrected (Figure 68 and Figure 70) velocity profiles along the beams 1 and 4 are presented below for the 16 bins of the water profile of the first maneuver. The bin 15 and 16 contain only the ADCP flag for ‘bad data’, i.e. -32768, indicating the limits of the ADCP range has been reached. Estimations of the water current are compiled in Table 10. 1 1 .5 3 5 1 Bin 7 0 .5 9 0 11 -0 .5 13 -1 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 63 Uncorrected ADCP velocity profile along beam 2, looking forward, during the first maneuver going south then east 5.2 ADCP Unreferenced and Corrected Measurements 69 1 1 .2 3 1 0 .8 5 Bin 0 .6 7 0 .4 9 0 .2 0 11 -0 .2 13 -0 .4 -0 .6 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 64 Corrected ADCP velocity profile along beam 2, looking forward, during the first maneuver going south then east. Figure 64 show the water current along beam 2 is of positive value across the maneuver with a slight increase in value when the boat is heading east. Peaks in current velocity occur along beam 2 when the boat is heading south. 1 1 .5 3 5 1 Bin 7 0 .5 9 0 11 13 -0 .5 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 65 Uncorrected ADCP velocity profile along beam 3, looking forward, during the first maneuver going south then east 70 5 At Sea Experiment of Data Acquisition System 1 1 3 5 0 .5 Bin 7 0 9 11 -0 .5 13 -1 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 66 Corrected ADCP velocity profile along beam 3, looking forward, during the first maneuver going south then east. Figure 67 shows the water current along beam 3 has approximately the same range of value but of opposite signs when the boat heads south (positive) and east (negative). Peaks in current velocity mostly occur along beam 3 when the boat is heading south. 1 0 .5 3 5 0 Bin 7 9 -0 .5 11 -1 13 15 -1 .5 200 400 600 E n s e m b le 800 1000 1200 Fig. 67 Uncorrected ADCP velocity profile along beam 1, looking aft, during the first maneuver going south then east 5.2 ADCP Unreferenced and Corrected Measurements 71 1 0 .5 3 5 0 Bin 7 -0 .5 9 11 -1 13 -1 .5 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 68 Corrected ADCP velocity profile along beam 1, looking aft, during the first maneuver going south then east. Figure 69 shows the water current along beam 1 is of negative value across the maneuver with a slight increase in value when the boat is heading south. Peaks in current velocity occur sporadically along beam 1 throughout the maneuver. 1 3 0 .5 5 0 Bin 7 -0 .5 9 11 -1 13 -1 .5 15 200 400 600 E n s e m b le 800 1000 1200 Fig. 69 Uncorrected ADCP velocity profile along beam 4, looking aft, during the first maneuver going south then east 72 5 At Sea Experiment of Data Acquisition System 1 1 3 5 0 .5 Bin 7 9 0 11 -0 .5 13 15 -1 200 400 600 E n s e m b le 800 1000 1200 Fig. 70 Corrected ADCP velocity profile along beam 4, looking aft, during the first maneuver going south then east. Figure 70 shows the water current along beam 4 has a negative value when the boat is heading south and a positive value when the boat heads east. Peaks in current velocity mostly occur along beam 3 when the boat is heading east. Looking at both of the corrected velocity profiles of the beams 2 and 3, looking forward, the peaks in current velocity appears in dark red and mostly occurs when the boat is heading south, i.e. when the water current is coming towards the beams. Plotting the time series using the colormap method reveals the variations in current magnitude according to direction and depth. Along the four beams, the water current is found to be homogeneously distributed over the water column, i.e. the coloring is mostly the same from the surface to the limit of the ADCP range. Quantifications of the uncorrected and corrected water current along the four beams and all bins are summarized in Table 10. In the table the abbreviation ‘Bm’ stands for ‘beam’. 5.2 ADCP Unreferenced and Corrected Measurements 73 Table 10 Estimates of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in beam coordinates during the first maneuver. Beam Coordinates, 1st maneuver, all bins L- Shape Track Bm 2 Forward Bm 3 Bm 1 Aft Bm 4 Uncorrected ADCP Water Profile, [m/s] Going South: between 0.3 and 0.7 Going East: between 0.2 and 0.5 Going South: between 0.3 and 0.5 Going East: between 0.3 and 0.5 Going South: between -0.7 and -0.5 Going East: between -0.5 and -0.3 Going South: between -0.6 and -0.2 Going East: between -0.5 and -0.3 Corrected Water profile, [m/s] Going South: between 0.1 and 0.5 Going East: between 0.1 and 0.3 Going South: between 0.1 and 0.3 Going East: between –0.3 and -0.1 Going South: between -0.5 and -0.2 Going East: between -0.3 and -0.1 Going South: between -0.3 and -0.1 Going East: between 0.2 and 0.4 The water current is estimated averaging the water current measurements along each beam (Table 10) and using basic trigonometric equations. For the first maneuver, the water current is estimated at 13° north, 0.72m/s when the ship is heading south and 8.8° north, 0.64m/s when the vessel’s heading east. The following section presents estimates of the water current during the second maneuver, using the same method as the study of the first maneuver. 5.2.1.2 Water Current Measured for the Second Maneuver, Linear Track Heading South Then North The following presents, for the linear track, an estimate of the water current measured at the first bin then observes the 16 bins of the ADCP velocity profile. The ship’s velocity along beams 2 and 3 (looking forward) is computed, plotted and examined as well as the uncorrected and corrected water current measure along beam 2 and 3 (Figure 71). The same procedure is done for the data along beams 1 and 4, looking aft (Figure 72). 5 At Sea Experiment of Data Acquisition System VShipBm2 74 1 0 VBm2 bn1 0 200 400 600 800 1000 1200 b 1 0 -1 0 VCurrent Bm2 bn1 a 2 200 400 600 800 1000 1200 1 c 0 -1 0 200 400 600 Time[s] 800 1000 1200 VShipBm3 2 0 VBm3 bn1 0 200 400 600 800 1000 1200 e 1 0 -1 0 VCurrent Bm3 bn1 d 1 200 400 600 800 1000 1200 1 f 0 -1 0 200 400 600 Time[s] 800 1000 1200 Fig. 71 Ship velocity, in blue, along beam 2 (a), and 3 (d) compare to the contaminated measure of the water current, in black, along beam 2 (b) and 3 (e), and to the true water current, in red, along beam 2 (c) and34 (f) during the second maneuver while the beams 2 and 3 are looking forward. 5.2 ADCP Unreferenced and Corrected Measurements 75 VShipBm1 1 a 0 -1 -2 0 200 400 600 800 1000 1200 -1 -1.5 0 VShipBm4 VBm4 bn1 200 400 600 800 1000 1200 1 c 0 -1 0 200 400 600 Time[s] 800 1000 1200 d 1 0 -1 -2 0 VCurrent Bm4 bn1 b 0 -0.5 VCurrent Bm1 bn1 VBm1 bn1 0.5 0.5 0 -0.5 -1 -1.5 0 200 400 600 800 1000 1200 e 200 400 600 800 1000 1200 f 0.5 0 -0.5 0 200 400 600 Time[s] 800 1000 1200 Fig. 72 Ship velocity, in blue, along beam 1 (a), and 4 (d) compare to the contaminated measure of the water current, in black, along beam 1 (b) and 4 (e), and to the true water current, in red, along beam 1 (c) and 4 (f) during the second maneuver while the beams 1 and 4 are looking aft. Figure 71 and Figure 72 demonstrate the influence of the ships’ motion (blue) on the ADCP measurement of the current (black) and it is only when this contamination is eliminated that one can interpret the water current measurement (red). Table 11 compiles the data estimates. Table 11 Ship’s velocity, uncorrected and corrected ADCP water current measurement in beam coordinates, for the first bin, during the second maneuver Beam Coordinates, 2nd maneuver, bin 1 Straight Line Track Bm 2 Forward Bm 3 Bm 1 Aft Bm 4 Ship’s velocity, ADCP uncorrected Corrected Water [m/s] Water current, [m/s] current, [m/s] 0.25 then 0.75 0.26 then 0.75 -0.24 then -0.65 -0.24 then –0.66 0.48 then 0.36 0.39 then 0.42 -0.59 then –0.48 -0.51 then -0.53 0.22 then –0.36 0.12 then -0.32 -0.32 then 0.16 -0.25 then 0.12 76 5 At Sea Experiment of Data Acquisition System Using Table 11 and basic trigonometric equations, the water current measured at the first bin during the second maneuver is estimated at 5.49° north, 0.65m/s when the ship is heading south and 4.8° north, 0.68m/s when heading north. The subsequent part studies the ADCP velocity profiles to estimate the water current along all bins. As for the first maneuver, the Matlab ‘colormap plot’ is the tool used to conceptualize the current velocity amplitudes. The uncorrected and corrected ADCP velocity profiles along the beams 2 and 3 and the uncorrected and corrected ADCP velocity profiles along the beams 1 and 4 are observed for the second maneuvers. The bin 15 and 16 contain only the ADCP flag for ‘bad data’(-32768), indicating that the limits of the ADCP water profile range have been reached. The estimation of the water current is compiled in Table 12. The corrected velocity profiles of the beams 2 and 3, looking forward, shows peaks in current velocity (dark red) mostly occurring when the boat is heading south, i.e. when the water current is coming towards the beams while peaks in current velocity appear on the beams 1 and 4, looking aft, when the boat is heading north. Along the four beams, the water current is considered homogeneously distributed over the water column although one can note slight changes in the colors, compare to the first maneuver profiles, showing the water current amplitude reducing with depth. The estimations of the uncorrected and corrected water current along the four beams and all bins are summarized in Table 12 where the abbreviation ‘Bm’ stands for beam. Table 12 Estimation of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in beam coordinates during the second maneuver. Beam Coordinates, 2nd maneuver, all bin Straight Line Track Bm 2 Forward Bm 3 Bm 1 Aft Bm 4 Uncorrected ADCP Water Profile, [m/s] Going South: between 0.35 and 0.6 Going North: between 0.25 and 0.6 Going South: between 0.35 and 0.5 Going North: between 0.3 and 0.65 Going South: between -0.65 and -0.5 Going North: between -0.55 and -0.45 Going South: between -0.65 and -0.35 Going North: between -0.55 and -0.4 Corrected Water profile, [m/s] Going South: between 0.1 and 0.3 Going North between -0.5 and -0.2 Going South: between 0.1 and 0.2 Going North between -0.5 and -0.1 Going South: between -0.4 and -0.2 Going North: between 0.1 and 0.2 Going South: between -0.4 and -0.1 Going North: between 0.1 and 0.2 5.2 ADCP Unreferenced an nd Corrected Measurements 777 The water current is esstimated averaging the water current measurements alonng each beam (Table 12) an nd using basic trigonometric equations. For the seconnd maneuver, the water currrent is estimated 1.25° north, 0.64m/s when the ship is heading south and 3.2° no orth, 0.67m/s when the vessel’s heading north. The following section presents the ADCP data correction in the North-East-U Up parison purposes. Frame, this time for comp 5.2.2 Correction of the t ADCP Data in the North-East-Up Frame, the ADCP’s Ea arth Reference Frame The water current measurrements resulting from the correction of the ADCP daata in the North-East-Up fram me, for the 2 maneuvers, are presented here. The nortth and east component off the corrected water current measurement are firrst quantified separately. Forr each component of the water current, the currents at thhe first bin and the velocity profiles p along the 16 bins are presented. The last two binns of the water profile were discarded by the ADCP internal quality algorithms annd are represented by a whitte space in the water profile figures. Finally, the resullts are combined to conclud de on the direction and magnitude of the water currennt during the two maneuverss. The ADCP data are reccorded in the Beam coordinate frame, its rawest form, sso it needs to first be converrted to the North-East-Up frame before the measuremennt correction can occur. Th his is done through three consecutive transformationns (Figure 73). The ADCP data d are transformed from the Beam coordinate frame tto the ADCP instrument coo ordinate frame, with its x-axis pointing from beam 1 tto beam 2, its y-axis from beeam 4 to beam 3 and its z-axis pointing upward. The daata are then converted to the ADCP Ship reference frame (Forward-Starboard-Up) tto finally be converted to thee ADCP Earth frame (North-East-Up). Bm1,2 3,4 • ADCP Beam • Bm1 ,Bm4 • Bm2 ,Bm3 XY YZ • ADCP Instr. •X •Y •Z FSU • ADCP Ship • Starboard • Forward • Up NEU • ADCP Earth • North • East • Up Fig. 73 Diagram of the neceessary reference frame transformations to transform the ADC CP data into the North-East-Up coordinate frame where the enhanced velocity measurement of the vessel is available. The enhanced velocity y measurement of the ship is also transformed to thhe North-East-Up coordinate frame since it is measured in the North-East-Dow wn bsequent sections covers the study of the water currennt reference frame. The sub measured for the first bin during the two maneuvers. 78 5 At Sea Experiment of Data Acquisition System 5.2.2.1 Water Current Measured, at the First Bin, in the NEU Frame for the L-Shape Track and the Linear Track VCurrent N bn1 VN bn1 0 a 200 400 600 800 1000 1200 b 2 1 0 0 2 1 0 0 VShipN 1 0 -1 200 400 600 800 1000 1200 c 200 400 600 800 Time[s] 1000 1200 VCurrent N bn1 VN bn1 VShipN This section quantifies the north and east component of the corrected water current measurement at the first bin in the North-East-Up reference frame for the two maneuvers. The north (respectively east) component of the ship’s velocity is shown in Figure 74.a (Figure 75.a) for L-shape track and in Figure 74.d (Figure 75.d) for the linear track. The north (east) component of the uncorrected and corrected currents, at the first bin, is presented in Figure 74.b (Figure 75.b) and Figure 74.c (Figure 75.c) for the L-shape track and in Figure 74.e (Figure 75.e) and Figure 74.f (Figure 75.f) for the linear track. 4 2 0 d 0 4 2 0 -2 0 6 4 2 0 -2 0 200 400 600 800 1000 1200 e 200 400 600 800 1000 1200 f 200 400 600 800 1000 1200 Time[s] 0 1 0 -1 -2 0 1 0 -1 0 a 200 400 600 800 1000 1200 b 200 400 600 800 1000 1200 c 200 400 600 800 Time[s] 1000 1200 VShipE 2 1 0 1.5 1 0.5 0 -0.5 0 2 1 0 -1 VCurrent E bn1 VE bn1 VCurrent E bn1 VE bn1 VShipE Fig. 74 Time series of the north component of the ship (blue), of the contaminated water current measured by the ADCP in the middle of the first bin (black) and of the water current resulting from its correction (red) in the NEU during the first (a, b an c) and the second maneuver (d, e, and f). 0 2 1 0 -1 0 d 500 1000 e 500 1000 f 500 Time[s] 1000 Fig. 75 Time series of the east component of the ship (blue), of the contaminated water current measured by the ADCP in the middle of the first bin (black) and of the water current resulting from its correction (red) during the first (a, b an c) and the second maneuver (d, e, and f). 5.2 ADCP Unreferenced and Corrected Measurements 79 The boat changes direction after 600s for the first maneuver and 630s for the second maneuver. The impact can be seen on the east component of the data (Figure 75a and Figure 75b) where there is a temporary inversion in the velocity sign. These brief reversals are due to the ship’s dynamic response to waves. Another perturbation on the ADCP data can be noted after 950s on the second maneuver (Figure 74 and Figure 75 d, e and f). Each figure is accounted for and the data estimations are presented in Table 13 for the first and second maneuver. Table 13 Ship’s velocity, uncorrected and corrected ADCP water current measurement in North-East-Up coordinates, for the first bin, during the first and second maneuver NEU Coordinates, 1st bin L- Shape Track Linear Shape Track North Component East Component North Component East Component Ship’s velocity,[m/s] ADCP uncorrected Water current, bin 1 [m/s] Corrected Water current, bin 1 [m/s] –1.038 then 0.927 1.959 then 0.048 0.9 0.069 then 1.79 0.14 then – 1.65 0.16 -1 then 2.9 1.99 then –1.88 0.96 0.075 then 0.15 –0.17 then 0.02 0.12 The water current measured has an estimated 0.93m/s north component and a 0.14m/s east component (Table 13). Hence the water current measured, at the first bin, in the NEU frame and on average over the two maneuvers, is estimated at 8.6° north, 0.94m/s. The next part examines the ADCP velocity profiles to estimate the water current along all bins. 5.2.2.2 Water Current Measured Observing the ADCP Velocity Profiles in the NEU Frame for the L-Shape Track and the Linear Track The next step is to observe and quantify the north and east component of the uncorrected (Figure 76, Figure 78, Figure 80 and Figure 82) and corrected (Figure 77, Figure 79, Figure 81 and Figure 83) ADCP velocity profiles along all bins for the two maneuvers. There are a number of options for representing time series water column current data, depending on the desired analyses. For this investigation of the ADCP velocity profiles and for the two maneuvers, the Matlab ‘colormap plot’ is the tool used to conceptualize the current velocity amplitudes. The direction of the water current is then calculated using basic trigonometric equations. Bin 15 and 16 contain only the ADCP flag for ‘bad data’, i.e. -32678, indicating that the limits of the ADCP range have been reached. 80 5 At Sea Experiment of Data Acquisition System 2 2.5 Bin 4 2 6 1.5 8 1 0.5 10 0 12 -0.5 14 -1 16 200 400 600 Ensemble 800 1000 1200 -1.5 Fig. 76 Uncorrected north component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. Bin 2 2.5 4 2 6 1.5 8 1 0.5 10 0 12 -0.5 14 -1 16 200 400 600 Ensemble 800 1000 1200 -1.5 Fig. 77 Corrected north component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. Figure 77 shows the north component of the water current is of positive value across the maneuver with a peak in current velocity when the boat changes directions. 5.2 ADCP Unreferenced and Corrected Measurements 81 2 1 4 0.5 6 0 Bin 8 -0.5 10 -1 12 -1.5 14 -2 16 200 400 600 Ensemble 800 1000 1200 Fig. 78 Uncorrected east component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. 2 1 4 0.5 6 0 Bin 8 -0.5 10 -1 12 -1.5 14 -2 16 200 400 600 Ensemble 800 1000 1200 Fig. 79 Corrected east component of the ADCP velocity profile during the first maneuver of the mission at sea, creating an L-shape track going south then east. 82 5 At Sea Experiment of Data Acquisition System 2 4 4 3 6 2 Bin 8 1 10 0 12 -1 14 -2 16 200 400 600 Ensemble 800 1000 1200 Fig. 80 Uncorrected north component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. 2 4 4 3 6 2 Bin 8 1 10 0 12 -1 14 -2 16 200 400 600 Ensemble 800 1000 1200 Fig. 81 Corrected north component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. Figure 81 shows the water current is of positive value across the maneuver with a decrease in value when the boat is changing direction. 5.2 ADCP Unreferenced and Corrected Measurements 83 2 2 4 1.5 6 1 Bin 8 0.5 10 0 12 -0.5 14 -1 16 -1.5 200 400 600 Ensemble 800 1000 1200 Fig. 82 Uncorrected east component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. A drop in velocity is visible on Figure 82 when the boat changes direction. 2 2 4 1.5 6 1 Bin 8 0.5 10 0 12 -0.5 14 -1 16 -1.5 200 400 600 Ensemble 800 1000 1200 Fig. 83 Corrected east component of the ADCP velocity profile during the second maneuver of the mission at sea, following a straight line track going south then north. The figures are analysed individually and estimations of the water current measurements are presented in Table 14. 84 5 At Sea Experiment of Data Acquisition System Table 14 Estimation of uncorrected and corrected ADCP water current measurement looking at the velocity profiles in NEU coordinates during the first and second maneuver. NEU Frame, all bins L-shape track going south then east Straight line track going south then north Component North East North East Uncorrected ADCP Water Profile, [m/s] Going South: between 1 and 1.7 Going East: between -0.7 and 0.5 Going South: between -0.1 and 0.6 Going East: between -1.7 and -1.3 Going South: between 1.5 and 2.2 Going North: between -2.5 and -2 Going South: between -0.7 and 0.5 Going North: between -0.4 and 0.5 Corrected Water profile, [m/s] between 0 and 1.8 [average 0.9] between -0.3 and 0.5 [average 0.1] between 1 and 1.5 [average 1.25] between -0.2 and 0.3 [average 0.1] The average water current measured from the two maneuvers is composed of a longshore current in the northerly direction, estimated at 1.07m/s and a weaker offshore current of 0.1m/s (Table 14). The water current measured, observing all bins and averaging the two maneuvers, is estimated at 5.3° north, 1.07m/s in the NEU frame. 5.3 Conclusion on the At-Sea Mission The mission at sea was conducted for the observation of the motion data acquisition system measurements in the field as well as the collection and correction of unreferenced ADCP data. The ship maneuvers followed two different tracks, an L-shape track, going south then east, and a straight line roundtrip track along the south-north direction. The mission was performed off the southeast coast of Florida where the currents run predominately near shore in a north-south direction with magnitudes ranging up to 1m/s. The unreferenced ADCP velocity profiles collected during the mission were corrected by subtracting the vessel motion from the measurements. The correction of the ADCP data was obtained in the ADCP beam coordinate frame, where the data are recorded, and in its Earth Reference frame, North-East-Up frame, for comparison purposes. Chapter 6 Conclusion Conclusio n Unmanned Surface Vehicles (USVs) are self contained unmanned untethered vessels that can transit on the surface of the water autonomously or through remote control. FAU has designed a multi-purpose oceanographic and GATEWAY USV that is a low cost mobile surface platform. Since standard GPS receivers are unable to provide the rate (0.5Hz) or precision required when used on a small vessel, a high rate (128Hz) and high precision position and orientation measurement system is developed. The system integrates a motion measurement package (the focus of this work) to aid in navigation, control, and enhances acoustic performance. The onboard sensors, including an Acoustic Doppler Current Profiler (ADCP), provide oceanographic measurements. ADCPs measure the relative velocity between its sensor heads and the water using the Doppler shift and time dilation of an acoustic pulse. By transmitting acoustic pulses at a fixed frequency and listening to the Doppler shift of echoes returning from sound scatterers in the water, water velocity estimates can be made. While ADCPs non-intrusively measure water flow, they suffer from the inability to discriminate between motions in the water column and self-motion. When mounted on a moving platform, the measured velocity is the sum of the platform velocity and the water velocity. Thus, the vessel motion contamination needs to be removed to analyze the data and avoid long average times. The motion measurement system is used to control the ADCP by commanding it to ping at a set rate (1Hz) and decoding the measurements returned by the instrument. The single ping water velocity measurements are decoded, motion corrected, and converted into an earth fixed frame. The motion measurement system of the USV consists of an Inertial Measurement Unit (IMU) with accelerometers and rate gyros, a GPS receiver, a flux-gate compass , a roll and tilt sensor, and an ADCP. While the sensors cannot be used independently to measure the position of the vehicle, they have complimentary characteristics that can be used to reduce or eliminate their individual errors when they are combined. Thus, integration and data fusion methods are used to combine the measurements from the sensors to estimate the position of the vehicle (Driscoll et al., 2000), in real-time. Using these techniques, a software package is developed where useful sensor measurements are preserved and erroneous data is rejected at all frequencies and the resulting, merged signal is drift free. C. Gelin: A Low-Cost, High Rate Motion Measurement System, NAMESS 1, pp. 85–92. © Springer-Verlag Berlin Heidelberg 2013 springerlink.com 86 6 Conclusion The data fusion techniques developed in this work combine the complementary outputs of sensors measuring a related state to eliminate the drift of integrating the measurement , while increasing the rate and resolution of where are measurements of some state and output by two distinct sensors (position sensor and velocity sensor for example). The pre-emphasized signal, , is obtained by summing the signal with the derivative signal , such that (Mudge and Lueck 1994): Ω , (38) where the scaling factor Ω , denoting the cutoff frequency, is a real positive constant. The choice of Ω is determined by the characteristics of the complementary region of the two sensors. For frequencies that are small compared to the cutoff frequency (Ω Ω , the signal portion of the spectrum comes , while for Ω Ω , the signal is predominately from predominantly from . The enhanced version of the signal is then obtained by with a single-pole, low-pass filter. The enhanced signal of convolving the signal contains low-frequency information from the sensor measuring , and the high-frequency information from the sensor measuring . The first data fusion method is applied in finding the Euler angles. Considering the characteristics of each instrument, a data acquisition system is developed that synchronously decodes data from all the instruments and converts them into a consistent format using the Euler angles, which are not directly measured. The Euler angles, , are obtained by fusing the low-frequency Euler angles, , and , calculated from the tilt measurements and , and the compass heading, , with the high-frequency IMU angular rates, , , T. Fig. 84 Diagram of the data fusion IMU / TCM2/ Tilt sensor to obtain Euler angles, . The experiment applied to find a suitable data fusion frequency between the IMU, TCM2 and tilt sensor to calculate the Euler angles consists in mounting the sensors on the same rigid plate and turning the sensor system simultaneously Conclusion 87 about multiple axes and rotation at different speed. The IMU rate gyros are found to have a low drift rate and the data fusion point is chosen to be at 1/30Hz. This data fusion frequency is selected so that at frequencies lower than the cutoff frequency, the tilt sensors and compass heading, provide accurate and stable measures of the Euler angles, , and and at frequencies above the cutoff frequency, the rate gyros in the IMU provide accurate measures of the Euler rates, , and . The estimated Euler angles are then used to convert the IMU acceleration from body-fixed frame, , , T , to the NED frame, , , T , where gravity is removed. The enhanced velocity of the ship, , is obtained by directly fusing the high frequency (128Hz) acceleration measurement from the IMU, , and the low frequency (0.5Hz) velocity obtained from the speed and course T , , . The position is then overground output from the GPS, T obtained by fusing the enhanced velocity, , , , with the latitude and longitude measured with the GPS. Two experiments are conducted to choose the best data fusion point (Ω ) to be later used to obtain the full frequency measure of the ships velocity, , and its position, . The first experiment investigates the properties of the vertical NED acceleration and the different methods available to obtain the merged vertical and the merged position, . The experiment takes place in a machine velocity, shop and consists of mounting the IMU, the tilt sensor and the TCM2 compass on a level plate. The plate is leveled and tethered to the extremity of a 1.03m rigid lever. The middle of the lever is attached to a gearbox that is attached to a rotating engine. The extremity of the lever describes circular trajectories of 0.515m radius at different speeds. The test consists of six sets of vertical roundtrip periods of approximately 5, 10, 15, 20, 25 and 35 s, each lasting about 10 minutes. The speeds are manually set using the speed variator of the rotating engine. The IMU, which is assumed accurate only at high frequencies, is merged with a null signal at low frequency and a data fusion point at 1/100Hz is found to be the best compromise to obtain a full frequency measure of the vertical velocity. The vertical velocity is then merge with a null signal to obtain the full frequency measure of the vertical position signal and a cutoff frequency of 1/50Hz is found to be the best choice for that data fusion method. The second experiment investigates the properties of the data acquisition system on shore, without the ADCP in order to find the best data fusion points of the horizontal velocity and position signals. The experiments takes place in an open parking lot to ensure the GPS system has a clear and unimpeded signal. The experimental setup consists in mounting the IMU, the tilt sensor and the compass on a rigid plate that is fixed to a cart where the rest of the data acquisition system (without the ADCP) is mounted. Because of the lack of automatic motion control, the cart is moved manually between four spots on the ground that mark the corners of a square with 7.88m legs with the corners pointing towards the four cardinal points. Three trajectories are selected: a square path, a zigzag course and a circle. These trajectories are each repeated at least three times at different speeds. The path of the trajectories, speed and periodicity are selected to test the system’s ability to accurately measure the cart motion. 88 6 Conclusion The first data fusion process, involving the IMU acceleration and the GPS velocity measurement leads to a full frequency measure of the velocity measurement. Pre-filtering of IMU data are found to be necessary before the data fusion process (Figure 85) and the experiment observations suggest the complementary region of the sensors intersect around 0.05Hz, which is used as the data fusion point. This data fusion point is selected so that at frequencies lower than 0.05Hz the GPS provide an accurate measure of the velocity of the system, and at frequencies above 0.05Hz the IMU provides an accurate estimation of the velocity. Fig. 85 Diagram of the data fusion between the IMU acceleration data and the DGPS velocity measurements in order to obtain the enhanced velocity estimate. The subsequent data fusion process applied is between the merged velocity and the DGPS position measurement to obtain a full frequency measure of the position estimate. The choice of the data fusion frequency is done in a similar fashion to aforementioned and the same data fusion point at 0.05Hz is selected. Figure 86 shows the diagram of the process of the second data fusion process between the enhanced velocity signal and the DGPS position measurement. Fig. 86 Diagram of the data fusion process between the DGPS position measurement and the merged velocity estimate obtained by fusing the IMU acceleration data and the DGPS velocity. Conclusion 89 The enhanced (merged) velocity signals estimated from the previously described first data fusion process have most of their significant spectral content below the data fusion point from the DGPS velocity data. Therefore, the DGPS position signal and the enhanced velocity signal have matching spectra, below the data fusion point, and no pre-processing is needed on the DGPS velocity signal before the data fusion with the DGPS position data. Since the enhanced velocity signals are used to correct the ADCP unreferenced data it is important to quantify their standard deviation so that it is lower than the ADCP velocity standard deviation. A value of less than 1 cm/s is desired for velocity measurements, which is about one half the value of the lowest single ping standard deviation (with an 8m bin size). Following the experiment conducted onshore, the standard deviation of the merged velocity error could have been determined by subtracting the expected velocity of the cart with the merged velocity estimate. However, since it was not possible to precisely control the motion of the cart, the expected velocity of the cart could not be determined. Instead, the estimation of the signals noise is applied by high-pass filtering the merged velocity signal, removing the motion of the vehicle, and computing the standard deviation of the filtered signal. Using this estimation process, the standard deviation of the merged velocity estimates (Table 15) is calculated for the three trajectories. Table 15 Estimates of the standard deviation of the merged velocity signal for the three trajectories of the on shore data acquisition test. Estimates of the merged velocity standard deviation [cm/s] NORTH COMPONENT EAST COMPONENT Square Path at 0.55m/s Square Path at 0.93m/s 0.77 0.78 1.16 1.19 Square in zigzag course at 0.39m/s 0.65 0.7 Circle at 0.47m/s 0.66 0.74 The standard deviation of the enhanced velocity signal averages 0.83 cm/s (< 1cm/s) and the signal is used for the correction of the ADCP data when performing a mission at sea. The mission at sea is conducted for the observation of the motion data acquisition system measurements in the field as well as the collection and correction of unreferenced ADCP data. Both the motion data acquisition system and TRDI ADCP are installed on a test vessel, the R/V Oceaneer IV, which performs a series of specifically chosen maneuvers in open sea while the motion data along with the ADCP data are simultaneously collected to be later post-processed. The mission is performed off the southeast coast of Florida where the currents run predominately near shore in a north-south direction with magnitudes ranging up to 1m/s. The ship maneuvers follows two different tracks: an L-shape track (going south then east) and a straight line roundtrip track along the south-north direction. For this mission, the ADCP is a 600 kHz Teledyne RDI Broadband Workhorse Sentinel. Its reference beam, beam 3, is mounted 45o counter-clockwise from the 90 6 Conclusion centerline of the ship in order to increase noise rejection and the effective ADCP measured velocity by a factor of 1.4. As a result, beams 2 and 3 are pointing forward, and beams 1 and 4 are pointing aft. The water profile will be composed of 16 bins, each 4m in length. A default blanking distance of 88cm is used in order to avoid measuring currents when the ADCP is ringing; resultantly the center of the first bin is located 5.05m away from the ADCP which puts the center of the last bin 65.05m away from the ADCP. The first maneuver, L-shape track, is performed by heading south for 623.56m at approximately 1.04m/s and then east for 1274.8m at approximately 2.04m/s (according to the GPS measurements). The trajectory of the boat exhibits a slight drift to the east when heading south and a more noticeable drift to the north when heading east. This indicates the presence of a water current, as expected, mainly along shore in the south-north direction with a secondary transverse east component. The water currents’ influence on the vessel’s motion can also be observed during the second maneuver, where the straight line maneuver goes 687.6m south-east at approximately 1.07m/s, and then goes 1988m north-east at approximately 2.92m/s. The water current is quantified when observing the corrected ADCP measurements. The correction of the ADCP data is performed in two different reference frames for comparison purposes. The first correction occurs in the ADCP radial beam coordinate frame, which allows us to manipulate ADCP data in its rawest form, i.e. no internal ADCP corrections applied. The second correction occurs in the North-East-Up Frame, the Earth coordinate frame of the ADCP. In addition to looking at the ADCP velocity profiles, the raw velocity at the first bin, where the water current is its strongest in the middle of the bin (~5m depth relative to the ADCP), is compared to the corrected ADCP velocity and the merged ship velocity. The estimates of the water current for the all missions are compiled in Table 16 and represented using Google earth in Figure 87. Table 16 Summary of water current estimates obtain by correcting the ADCP data during the two maneuvers at sea. Maneuver L-shape track going south then east Straight line track going south then north Reference frame Bin Beam Bin 1 All Bins Water current direction [°N] 4.74° then 7.5° 13° then 8.8° Bin 1 8.6° 0.94 All Bins Bin 1 All Bins 5.3° 5.49° then 4.8° 1.25° then 3.2° 1.07 0.65 then 0.68 0.64 then 0.67 Earth Beam Water current magnitude [m/s] 0.5 then 0.72 0.72 then 0.64 Conclusion 91 Fig. 87 Google Earth visualization of the mission at sea with the two maneuvers, first goes south-east then south-north The correction of the ADCP data can occur accurately since the standard deviation of the enhanced velocity of the ship (0.83 cm/s) is lower than the standard deviation of the water current measurement from the ADCP (Table 15). Table 17 Estimated standard deviation of the ADCP velocity during the first and second maneuver at sea in correlation to the bin size, using the standard deviation of the error velocity 1st Maneuver Bin 1-4 : 4 to 20 m Bin 5-8 : 20 to 36 m Bin 9-12 : 36 to 52 m 2nd Maneuver Bin 1-4 : 4 to 20 m Bin 5-8 : 20 to 36 m Bin 9-12 : 36 to 52 m Estimated standard deviation of the ADCP measured corrected current velocity [cm/s] 2.6 3.3 4.4 2.4 3 3.75 This book has presented a low-cost, high rate motion measurement system developed for an unmanned surface vehicle with underwater navigation and oceanographic applications. The system integrates a motion measurement package to aid in navigation and control while correcting data from an Acoustic Doppler Current Profiler (ADCP), providing oceanographic measurements. 92 6 Conclusion Recommendations Another test at sea as well as a complete calibration of the data acquisition system are the first two recommendations. An integration of the system for different control system is also preferable as well as a formal design method for the data fusion process so we can determine the optimal filter shape. Finally a fuzzification of the data fusion process is suggested. References [1] Leonessa, A., Beaujean, P.-P., Driscoll, F.R.: Development of a small, multi-purpose, autonomous surface vessel. Florida Atlantic University, Department of Ocean Engineering (2002) [2] Sousa, J., Cruz, N., Matos, A., Lobo Pereira, F.: Multiple AUVS for coastal oceanography. In: OCEANS 1997, MTS/IEEE Conference Proceedings, October 6-9, vol. 1, pp. 409–414 (1997) [3] Bane, G., Ferguson, J.: The evolutionary development of the military autonomous underwater vehicle. In: Proceedings of the 5th International Symposium on Unmanned Untethered Submersible Technology, vol. 5, pp. 60–88 (June 1987) [4] Grenon, G., An, E., Smith, S., Healey, A.: Enhancement of the Inertial Navigation System for the Morpheus Autonomous Underwater Vehicles. IEEE, Journal of Oceanic Engineering 26(4) (October 2001) [5] Vickery, K., Sonardyne, Inc.: Acoustic Positioning Systems, a practical overview of current system. In: IEEE, Proceedings of the Autonomous Underwater Vehicle (1998) [6] Babb, R.J.: Navigation of unmanned underwater vehicles for scientific surveys. In: Proceedings of the Symposium on Autonomous Underwater Vehicle Technology, AUV 1990, June 5-6, pp. 194–198 (1990) [7] Rayes, R.: Characterization study of the Florida current at 26.11 North latitude, 79.50 West longitude for ocean current power generation. Thesis submitted to the faculty of the College of Engineering, Florida Atlantic University, Boca Raton (May 2002) [8] BEI MotionPak Low Cost Multi-Axis Inertial Sensing System technical manual. Systron Donner Inertial Division (1998) [9] TCM2 Electronic Compass Module – User’s Manual. Precision Navigation, Inc. (July 2003) [10] Garmin GPS 76 owner’s manual and reference guide, GARMIN Corporation (2001) [11] Navigator ADCP/DVL Technical Manual. RD Instruments, Second Edition for Broadband ADCPs, P/N 951-6069-00 (1996) [12] Shafer, S.A., Stentz, A.: An Architecture for Sensor Fusion in a Mobile Robot. IEEE (1986) [13] Luo, R.C., Kay, M.G.: Multisensor Integration and Fusion in Intelligent Systems. IEEE SMC-19(5) (1989) [14] Cvetanovs, J.K.: Autonomous Submersible Robot: Sensor Characterization and Testing. RSL Australian National University (2000) [15] Gustafson, E.I.: A Post-Processing Kalman smoother for Underwater Vehicle Navigation. FAU Ocean Engineering Dept. (2001) [16] Welch, G., Bishop, G.: An Introduction to the Kalman Filter. University of North Carolina, Department of Computer Science (2001), http://www.cs.unc.edu/~welch/kalman/ 94 References [17] Chaumet-Lagrange, M., Loeb, H., Ygorra, S.: Design of an Autonomous Surface Vehicle (ASV). University of Bordeaux I, France, Automatic and production Laboratory, IEEE (1994) [18] Manley, J.E.: Development of the Autonomous Surface Craft ‘ACES’. Massachusetts Institute of Technology, Department of Ocean Engineering, Sea Grant College Program, Cambridge MA 02139, IEEE (1997) [19] CARAVELA Development of a Long-Range Autonomous Oceanographic Vessel, Dynamic Systems and Ocean Robotics lab (DSOR) (1998-2000) [20] Advanced System Integration for Managing the Coordinated Operation of Robotic Ocean Vehicles (ASIMOV). ISR-IST, Lisbon, Portugal, ORCA Instrumentation, France; System Technologies, United Kingdom; ENSIETA, France (1998-1999-2000) [21] Oliveira, P., Pascoal, A., Rufino, M., Sebastiao, L., Silvestre, C.: The DELFIM Autonomous Surface Craft. Report (December 1999) [22] Oliveira, P., Pascoal, A., Kaminer, I.: A Nonlinear Vision Based Tracking System for Coordinated Control of Marine Vehicles. IST/DEEC, Lisbon, Portugal, Naval Postgraduate School, Monterey, USA (2002) [23] Mudge, T.D., Lueck, R.G.: Digital Signal Processing to Enhance Oceanographic Observations. Journal of Atmospheric and Oceanic Technology 11(3) (June 1994) [24] Fossen, T., Lane, B.: Guidance and Control of Ocean Vehicles. John Wiley and Sons, Ins., England (1994) [25] Etkin, B.: Dynamics of Atmospheric Flight. Wiley, New York (1972) [26] Driscoll, F.R., Lueck, R.G., Nahon Retkin, M.: The motion of a deep-sea remotely operated vehicle system, Part 1: Motion observations. Ocean Engineering 27, 29–56 (2000) Appendix A - Native Output of the Instruments Appe ndix A - Native Out put of the I nstrume nts 1. GPS The native representation of the GPS is of NMEA output format with the following NMEA messages available: $GPGGA - Global Positioning System Fix Data $GPGLL - Geographic Position, Latitude/Longitude $GPGSA – GNSS (Global Navigation Satellite System) DOP and Active Satellites $GPGST - GNSS Pseudorange Error Statistics $GPGSV - GNSS Satellites in View $GPRMC - Recommended Minimum Specific GNSS Data $GPRRE – Range Residual Message $GPVTG – Course over ground and Ground Speed $GPZDA - UTC Date / Time and Local Time Zone Offset The GPGGA message contains detailed GPS position information, and is the most frequently used NMEA message, this message takes the following form: $GPGGA,hhmmss.ss,ddmm.mmm,a,dddmm.mmm,b,q,xx,p.p,a.b,M,c.d,M,x.x,nnnn hhmmss.ss = UTC of position ddmm.mmm = latitude of position a = N or S, latitude hemisphere dddmm.mmm = longitude of position b = E or W, longitude hemisphere q = GPS Quality indicator (0=No fix, 1=Non-differential GPS fix, 2=Differential GPS fix, 6=Estimated fix) xx = number of satellites in use p.p = horizontal dilution of precision a.b = Antenna altitude above mean-sea-level M = units of antenna altitude, meters Appendix A - Native Output of the Instruments 96 c.d = Geoidal height M = units of geoidal height, meters x.x = Age of Differential GPS data (seconds since last valid RTCM transmission) nnnn = Differential reference station ID, 0000 to 1023 2. COMPASS The TCM2 standard output format is of NMEA format: $C<compass>P<pitch>R<roll> Appendix B Setup and Acquisition of the ADCP THE SERIAL BREAK The serial break which is used to wake up the ADCP is sent by changing the 6th bit (sets break enable) of the Line Control Register (LCR) that controls the data going on the Transmit Data (TD) and Receive Data (RD) lines. When active, the TD line goes into "Spacing" state which causes a break in the receiving UART. Setting this bit to '0' disables the Break. Table 18 RS232 Registers Base Address +0 +1 +2 DLAB Read/Write Abr. Register Name =0 Write - Transmitter Holding Buffer =0 Read - Receiver Buffer =1 Read/Write - Divisor Latch Low Byte =0 Read/Write IER Interrupt Enable Register =1 Read/Write - Divisor Latch High Byte - Read IIR Interrupt Identification Register - Write FCR FIFO Control Register +3 - Read/Write LCR Line Control Register +4 - Read/Write MCR Modem Control Register +5 - Read LSR Line Status Register +6 - Read MSR Modem Status Register +7 - Read/Write - Scratch Register 98 Appendix B Setup and Acquisition of the ADCP DOWNLOAD THE ADCP DATA The data, preceded by the ID code 7F7F, contains header data. The fixed and variable leader data is preceded by ID codes 0000 and 8000. Table 19 PD0 standard output data buffer format Header: 6 Bytes + [2*Number of Data Types] Always Output Fixed Leader Data: 53 Bytes Variable Leader Data: 65 Bytes Velocity: 2 Bytes + 8 Bytes per Depth Cell WP – Command Correlation Magnitude: 2 Bytes + 4 Bytes per Depth Cell WD - Command Echo Intensity: 2 Bytes + 4 Bytes per Depth Cell Percent Good: 2 Bytes + 4 Bytes per Depth Cell BP - Command Bottom Track Data: 85 Bytes Always Output Reserved: 2 Bytes Checksum: 2 Bytes Knowing the necessary binary address offsets, it is possible to directly access to the desired data, which are pitch, roll and heading information, as well as, the four velocities (each beam) for each one of the 16 depth cell.