Underwater terrain matching navigation based on Gaussian process regression with a multi-beam sonar

Terrain matching navigation estimates the position of underwater vehicle by matching measured terrain against a prior map, which is attractive to fix the drift inherent to inertial navigation system. With a multibeam bathymetric sonar, a local terrain is usually reconstructed from a prior map by deterministic interpolation methods such as the nearest, linear and spline interpolations, to match the multiple measurements. However, these deterministic interpolation methods can easily lead to terrain under and over-fitting and change the statistical properties of the terrain, which will reduce the positioning accuracy. To address this, a probabilistic interpolation method based on Gaussian process regression is proposed to reconstruct the terrain in this paper. Different from the deterministic interpolation, Gaussian process regression can not only maintain the statistical properties as far as possible, but also give the uncertainty of a interpolated depth. The uncertainty can then be fused into the measurement error in the maximum likelihood estimation method to improve the positioning accuracy. Simulation experiments in a real underwater map demonstrate that the proposed method is feasible and more accurate than the traditional deterministic interpolation for underwater terrain matching navigation.