Sea Technology

JUN 2017

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Page 38 of 72

38 st / June 2017 of the oceans. Gravity and gravity gradient disturbances in the world's oceans are gener- ally associated with large terrain features on the seabed. Flat seabed expanses do not en- gender the rich gravity gradient disturbances that rough and mountainous terrains do. In fact, the magnitude of gravity gradient distur- bances above the seabed terrain highly cor- relate 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 vari- ous degrees of accuracy, the gravity gradi- ent disturbance magnitude at any particular height above the seabed. The accuracy of the forward modeling methods is dependent upon the method it- self, the accuracy of the terrain height data- base and the resolution of the data. Bathymetry of the world's oceans is avail- able on the Web as open-source data at a resolution of 1 arc-minute at http://topex. This database was compiled from a variety of sources but is heavily depen- dent upon satellite altimeter-derived measurements. There is also a section of ocean bathymetry around and includ- ing 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 interpo- lation from the generally available 1 arc-minute bathymetry to higher resolution (3 to 6 arc-seconds) data sets. The lat- ter are required for forward modeling of disturbance gravity gradients of sufficient resolution to enable accurate naviga- tion aiding. What is missing in the open literature are comparisons of gravity gradient data, predicted by forward modeling meth- ods, 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. Navigation-Aiding Algorithms Most literature on the subject of gravity aiding of inertial navigation considers the use of either some form of correla- tion method and/or a Kalman-filter-based fusion of the geo- physical measurements with the inertial navigation equa- tions. 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 mea- surements and the predicted measurements (from the stored map) is incorporated. These preprocessing algorithms are re- quired 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 mod- eling methods. The nature of these approximate modeling 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 gradi- ometer concept than previous gradiometers. GREMLIT is small, light and not mechanically complex. Like the Falcon gradiometer, GREMLIT measures three of the five indepen- dent 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 criti- cal to aiding inertial navigation positioning. Strapdown gradiometers using current, high-accuracy, navigation-grade accelerometer sensors have also been de- veloped recently and are being tested for UUV application. Deep-Ocean Gravity Gradient Maps A key requirement to enable gravity gradient map match- ing is the existence of associated maps of disturbance grav- ity gradients in the particular part of the ocean where navi- gation 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 ad- vance 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. gov- ernment. I am not aware of an equivalent archive of distur- bance gravity gradient maps of the world's oceans, although the U.S. government does have such maps for limited areas This figure shows the time evolution of position error of one instance of a Monte Carlo simulation. The initial position er- ror is 750 m.

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