Passive Autonomous Navigation For Exploration, Defense Using Gravity to Aid INS on UUVs By Paul Madden G ravity has been used as a means to passively aid inertial navigation systems of both submarine and surface ships of the U.S. Navy. Most of this work was first done in the 1990s on an experimental basis using gravimeter and the gradiometer sensors. The modern gradiometer, which measures the gradients of the gravity vector, has been in existence for decades. A version was developed in the 1980s to provide covert aid to submarine navigation as an independent position sensor. The navigation-aiding performance of the gradiometer was completely successful, but the technique is not used operationally in U.S. Navy ships, submarines or UUVs because the gradiometer used in the Navy experiments was large and relatively complex. Versions were subsequently developed for geophysical prospecting. The most recent development of the geophysical gradiometer is the Falcon-Plus version, which is mechanically less complex than the original Bell Aerospace full-tensor gradiometer (FTG) from which it was derived. It measures a subset of the full-tensor set of gravity gradients but is still a large, heavy, complicated sensor system unlikely to be considered practical in a UUV, although it could be useful in a conventional manned submarine. To the best of my knowledge, there is no current operational implementation of a gradiometer-aided navigation system in a submarine vehicle, either manned or unmanned. Most likely, this is because current operational gradiometers are still complex, large and expensive instruments, and the need for navigation covertness by the military has been met by near-covert acoustic fathometer sensors. However, This figure shows the bathymetry north of Palau in the Pacific and the UUV track. Only a short section is required for a position fix. new gravity gradient sensor concepts, gravity gradient map generation methods and navigation algorithms will provide new passive navigation options for deep-ocean UUV exploration and defense missions. New Gradiometers France’s space agency, ONERA, developed the hugely successful electrostatic-accelerometer-based gradiometers used in the European Space Agency missions GRACE and GOCE, Earth-orbiting satellites that have been measuring the Earth’s gravity field and its gradients since 1999. www.sea-technology.com June 2017 / st 37 ONERA is developing a version of the gradiometer that can operate in the 1-g Earth environment, GREMLIT, based on the use of four, planar (two axes) electrostatic silicon accelerometers. As such, it is an entirely different gradiometer concept than previous gradiometers. GREMLIT is small, light and not mechanically complex. Like the Falcon gradiometer, GREMLIT measures three of the five independent tensor components, in contrast with the more complex FTG sensors, and these three components represent the key along-track and cross-track gradient components most critical to aiding inertial navigation positioning. Strapdown gradiometers using current, high-accuracy, navigation-grade accelerometer sensors have also been developed recently and are being tested for UUV application. of the oceans. Gravity and gravity gradient disturbances in the world’s oceans are generally associated with large terrain features on the seabed. Flat seabed expanses do not engender the rich gravity gradient disturbances that rough and mountainous terrains do. In fact, the magnitude of gravity gradient disturbances above the seabed terrain highly correlate with the terrain features, in particular, the terrain height above the seabed. Given a bathymetric map of an extent of the ocean seabed, it is possible to estimate, with various degrees of accuracy, the gravity gradient disturbance magnitude at any particular height above the seabed. The accuracy of the forward modeling methods is dependent upon the method itself, the accuracy of the terrain height database and the resolution of the data. Bathymetry of the world’s oceans is available on the Web as open-source data at a resolution of 1 arc-minute at http://topex. ucsd.edu/cgi-bin/get_data.cgi. This database was compiled from a variety of sources but is heavily dependent upon satellite altimeter-derived measurements. There is also a section of ocean bathymetry around and including the Marianas Trench that is available open source at a resolution of 6.5 arc-seconds; this high resolution is very useful to gauge the loss of accuracy associated with interpolation from the generally available 1 arc-minute bathymetry to higher resolution (3 to 6 arc-seconds) data sets. The latter are required for forward modeling of disturbance gravity gradients of sufficient resolution to enable accurate navigation aiding. What is missing in the open literature are comparisons of gravity gradient data, predicted by forward modeling methods, with actual measurements of gravity gradients taken at ocean depths above the bathymetry used to model the gradients. Similar comparisons of predicted and measured gradients have been made by the geophysical community; however, the comparisons were made at altitudes above ground terrain, as opposed to bathymetry. Deep-Ocean Gravity Gradient Maps A key requirement to enable gravity gradient map matching is the existence of associated maps of disturbance gravity gradients in the particular part of the ocean where navigation fixes are desired. However, not all ocean regions are characterized by gravity gradients of sufficient magnitude and spatial extent to be good candidates for navigation fixes. Such regions must be identified and selected in advance as part of the mission-planning process. Planning for gravity-aided navigation is similar to the process required to identify locations suitable for acoustic terrain map matching by the U.S. Navy submarine fleet and the subsequent preparation of digital terrain maps for the onboard navigation system. This process was substantially aided and hastened by the existence of previously generated bathymetric maps of the world’s oceans by the U.S. government. I am not aware of an equivalent archive of disturbance gravity gradient maps of the world’s oceans, although the U.S. government does have such maps for limited areas Navigation-Aiding Algorithms Most literature on the subject of gravity aiding of inertial navigation considers the use of either some form of correlation method and/or a Kalman-filter-based fusion of the geophysical measurements with the inertial navigation equations. The latter method might be considered conventional, although a hybrid of the two methods has been routinely used for decades as the standard position updating method for airborne cruise missiles. For the gravity-aided navigation described in this article, I used both a modified correlation method and the extended Kalman filter (EKF). Both methods work well provided that additional real-time processing of the true gradiometer measurements and the predicted measurements (from the stored map) is incorporated. These preprocessing algorithms are required because the stored gravity map is a priori generated using an imperfect representation of the disturbance gravity gradients based upon the use of one of the forward modeling methods. The nature of these approximate modeling This figure shows the time evolution of position error of one instance of a Monte Carlo simulation. The initial position error is 750 m. 38 st / June 2017 www.sea-technology.com methods and the finite resolution of the underlying bathymetric data result in gravity gradient estimates that contain various degrees of random noise and scale-factor-like errors. Navigation algorithms that do not consider the inherent imperfection of the stored map may quickly result in large positioning errors or even filter instability. If the stored map is derived from previously measured disturbance gravity gradients, rather than modeled gradients, there is less concern for the special processing that mainly minimizes the effects of scale-factor, bias and other errors. The preprocessing algorithms were adapted for the navigation map-matching application from similar algorithms developed and mainly used in the image and video processing fields. Gravity-Aided Navigation Simulation To investigate the methods and performance of gravity gradient aiding of inertial navigation, I chose an area of bathymetric terrain north of Palau in the Pacific Ocean as a basis for the navigation analysis. The area is between 12 and 15° North latitude and 133 to 136° East longitude. One of the forward modeling methods was used to generate maps of the five independent gravity gradient tensor components. Sets of maps were generated for a number of ocean depths, all higher (that is, closer to sea level) than the highest bathymetry in the chosen seabed area. The bathymetry data sets are generally available from NOAA at a 1-arc-minute grid size. For the simulation analysis, a tight spline interpolation algorithm was used to increase the gravity gradient map resolution to a grid size of 3 arc-seconds (approximately 90 m). A simulation of the aided navigation algorithms was performed while the notional UUV traversed a mainly NorthSouth track (moving gradually to the East) over the middlethird of the bathymetric terrain at an altitude of about 1,000 m above the highest bathymetry. Each North-South leg of the track was 85 km in length, and the UUV traversed the track at approximately 4 kt. (2 m/s). Each leg of the track takes nearly 12 hours to traverse. Simulation parameters for both the correlation and EKF map-matching methods were as follows: a navigation-grade INS was modeled assuming typical sensor errors for this class of navigation system; velocity log measurements (assuming typical sensor errors) were processed every 5 seconds; INS map-matching and gradiometer sensor measurements were processed every 60 seconds; and initial position errors (latitude and longitude) were 750 m. Assumed gravity-gradient map and gradiometer errors were as follows: interpolated map grid size was 3 arc-seconds; gradiometer measurement root-mean-square (RMS) noise was 3 E; and gradient map scale factor error was 5 percent, and the random noise was 5 E (RMS). The synthetic gravity gradient map and gradiometer sensor errors assumed in the simulation are believed to be representative of what is possible with today’s sensor technology and the associated navigation processing algorithms. Predicted Gravity-Aided Navigation Performance Simulation of gravity-aided navigation predicts positioning performance of about 50 percent of the map grid size (1-sigma). This was true for both map-matching methods investigated and for gravity gradient map grid sizes of 3 and www.sea-technology.com June 2017 / st 39 “Vast improvements in technology and navigation techniques have been made since the first demonstrations of gravity-aided inertial navigation of undersea vehicles two decades ago.” 6 arc-seconds, that is, 90 and 180 m, respectively. A good position fix was achieved in 6 hours, while little improvement was seen after 24 hours. After leaving a position fix location, the UUV navigation performance is entirely dependent upon the intrinsic performance of the velocity-aided INS that, in turn, depends upon the navigation capability of the particular INS employed and the mode of operation of the velocity aiding (either bottomtracking or water-tracking). The particular mission of the UUV or manned submersible most likely will specify the maximum allowable navigation position error. When this error threshold is approached, the vehicle will either have to seek out a new (or previously used) position fix location or surface momentarily to obtain a GPS position fix. The simulation results demonstrate that gravity-aided navigation algorithms have improved significantly and promise new flexibility for the source of the critical onboard gravity-gradient maps required for the map-matching navigation task. The maps can derive from original gradiometer measurement data, or they can be generated using forward modeling methods based upon new ocean bathymetric databases. Use of the latter techniques for navigation aiding must still be demonstrated in practice, but simulation of new algorithms show tolerance to significant inherent map errors of certain types. What is unknown is the complete nature of map error types to be expected using the synthetic map-generation methods. Vast improvements in technology and navigation techniques have been made since the first demonstrations of gravity-aided inertial navigation of undersea vehicles two decades ago. New gravity gradiometer sensors are in the experimental stage and promise to demonstrate equivalent sensitivity to the original gradiometers but with much reduced complexity and bulk. They will be suitable for military submarines and UUVs, as well as the new deep-ocean class of UUVs for geophysical applications. References For a list of references, contact Paul Madden at pmad den@alum.mit.edu. ST Paul Madden spent much of his career at the Draper Laboratory (formerly the MIT Instrumentation Laboratory). He participated in diverse projects involving missile, submarine and aerospace vehicle guidance, navigation and control. Those projects included the Deep Submergence Rescue Vehicle, the NASA Space Shuttle and the first fly-by-wire aircraft. He is presently a navigation consultant based in the Boston area. 7 COMING SOON: More powerful, yet easier to use • Full support for swath bathymetry • Advanced seabed characterization • New faster, integrated 3D viewer • Powerful visualization tools www.chesapeaketech.com 40 st / June 2017 www.sea-technology.com Reproduced with permission of copyright owner. Further reproduction prohibited without permission.
