Sea Technology

JUN 2017

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Page 39 of 72 June 2017 / st 39 methods and the finite resolution of the underlying bathy- metric 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 con- cern for the special processing that mainly minimizes the effects of scale-factor, bias and other errors. The preprocessing algorithms were adapted for the navi- gation map-matching application from similar algorithms developed and mainly used in the image and video pro- cessing 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 ba- thymetry 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 interpo- lation algorithm was used to increase the gravity gradient map resolution to a grid size of 3 arc-seconds (approximate- ly 90 m). A simulation of the aided navigation algorithms was per- formed while the notional UUV traversed a mainly North- South track (moving gradually to the East) over the middle- third 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 (as- suming typical sensor errors) were processed every 5 sec- onds; INS map-matching and gradiometer sensor measure- ments 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-sec- onds; 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 sen- sor errors assumed in the simulation are believed to be rep- resentative of what is possible with today's sensor technol- ogy and the associated navigation processing algorithms. Predicted Gravity-Aided Navigation Performance Simulation of gravity-aided navigation predicts position- ing performance of about 50 percent of the map grid size (1-sigma). This was true for both map-matching methods in- vestigated and for gravity gradient map grid sizes of 3 and

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