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Abstract-This paper focuses on obtaining submerged position fixes for underwater vehicles from comparing bathymetric measurements with a bathymetric map. Our algorithms are tested on real data, collected by a HUGIN AUV equipped with a multibeam echo sounder (MBE). Due to our strongly non-linear and non-Gaussian problem, local linearization methods such as the extended Kalman filter (EKF), has proven unsuitable in many terrain types. We therefore focus on two different recursive Bayesian methods, namely the point mass filter (PMF) and a Bayesian bootstrap particle filter (PF). The PMF is a gridbased approximation method, whereas the PF is a sequential Monte Carlo method, based on sampling from the underlying distributions. The two methods are first compared using a 2-dimensional state-space model, only estimating the horizontal position of the vehicle. A problem with this approach is that uncertainty in the estimation of tidal levels may lead to large errors in the depth measurements. To counter this, one may extend the state vector to three dimensions, and this is investigated in the paper. Characteristics such as accuracy, convergence time, terrain dependency, and computational demands for the two methods are compared. In suited terrain both methods yield a horizontal accuracy comparable to the resolution of the map. The results from the PMF are slightly better, but the PMF is also more computationally demanding than the PF. Extending the methods from 2D to 3D makes them significally more robust to depth errors. The computational demands for the PMF increases dramatically in 3D, whereas they are virtually unchanged for the PF. Previous problems of overconfidence in these methods are effectively reduced through sub-sampling of the MBE data.

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