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

## TL;DR

This paper introduces a numerical method using dynamic programming and quantization to optimize the trajectory of an underwater vehicle for target detection and stealth, considering acoustic signal propagation and target tracking uncertainties.

## Contribution

It develops a finite horizon Markov decision process approach with quantization for trajectory optimization in underwater acoustic tracking scenarios, including unknown target states.

## Key findings

- Effective trajectory optimization under known target states.
- Robustness of the method with target state estimation.
- Applicability to various underwater tracking scenarios.

## Abstract

We present in this paper a numerical method which computes the optimal trajectory of a underwater vehicle subject to some mission objectives. The method is applied to a submarine whose goal is to best detect one or several targets, or/and to minimize its own detection range perceived by the other targets. The signal considered is acoustic propagation attenuation. Our approach is based on dynamic programming of a finite horizon Markov decision process. A quantization method is applied to fully discretize the problem and allows a numerically tractable solution. Different scenarios are considered. We suppose at first that the position and the velocity of the targets are known and in the second we suppose that they are unknown and estimated by a Kalman type filter in a context of bearings-only tracking.