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We present in this paper a numerical method which computes the optimaltrajectory of a underwater vehicle subject to some mission objectives. Themethod is applied to a submarine whose goal is to best detect one or severaltargets, or/and to minimize its own detection range perceived by the othertargets. The signal considered is acoustic propagation attenuation. Ourapproach is based on dynamic programming of a finite horizon Markov decisionprocess. A quantization method is applied to fully discretize the problem andallows a numerically tractable solution. Different scenarios are considered. Wesuppose at first that the position and the velocity of the targets are knownand in the second we suppose that they are unknown and estimated by a Kalmantype filter in a context of bearings-only tracking.

Stochastic Control of Observer Trajectories in Bearings-only Tracking with Acoustic Signal Propagation Optimization