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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
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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).
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ƌĂǁĚĂƚĂ
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ƚŚĞĨƵƐŝŽŶ
ĨƌĞƋƵĞŶĐLJ
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ͻsĂůŝĚĂƚĞƚŚĞ
ĐŚŽŝĐĞĨŽƌƚŚĞ
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ͻƌŽƐƐĐŽƌƌĞůĂƚĞ
>W'W^ĂŶĚ>W
ĨƵƐĞĚƐŝŐŶĂů
ͻƐƚŝŵĂƚĞƚŚĞ
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ĚĞǀŝĂƚŝŽŶŽĨ
ƚŚĞǀĞůŽĐŝƚLJ
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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.
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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.