Random field modelling of DEM uncertainty and its impact on terrain referenced navigation

Random field modelling of DEM uncertainty and its impact on terrain referenced navigation
Guy Ruckebusch

IC3i, 5 rue de Villequoy, 78610 Auffargis, France (guy.ruckebusch@orange.fr)

Abstract: Terrain Referenced Navigation (TRN) is an integrated navigation solution, where terrain height measurements from a radar altimeter are compared to a Digital Elevation Model (DEM) to filter the errors of the Inertial Navigation System. Most conventional systems incorrectly assume that the DEM errors are Gaussian and uncorrelated, with a standard deviation linearly related to the slope. This is all the more annoying as any departure from these assumptions is known to adversely impact the TRN performance. In this paper, two new random field models of DEM altimetric error are described. The first model is a doubly stochastic random field. The error is Gaussian, conditioned on its standard deviation, modeled as a lognormal random field, whose mean is a logistic function of the DEM slope. This model is statistically learned by analyzing the difference of the DEM with a highquality reference DEM. The second model is limited to Reference3D DEMs, with the availability of the (two) stereoscopic images used to produce the DEM. The approach relies on a Bayesian modelling of the altimetric error, where the prior is precisely the first model. The impact of the DEM uncertainty model on the TRN performance is evaluated through Monte Carlo simulation.

Keywords: DEM uncertainty, random field model, statistical learning, Bayesian stereo modelling, Terrain Referenced Navigation, uncertainty propagation.

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