Optimal observer trajectory in bearings-only tracking for manoeuvring sources

In the bearings-only tracking context, the source state is only partially observed through nonlinear measurements which are the estimated bearings. For a manoeuvring Markovian source, the source trajectory is estimated by means of classical dynamic programming. However, the quality of the estimation is strongly dependent of the observer trajectory, thus mixing estimation and control. But, in this context, the separation principle (for estimation and control) does not hold. In fact, the problem consists in controlling a partially observable Markov decision process. Application of this framework to search theory is mentioned. However, even if the problem presents strong similarities with an approach used in the optimisation of the search effort for a (Markovian) moving source, it is focused on the estimation of the whole source trajectory instead of its detection at the end of the scenario. To this intrinsic difficulty, the observation is richer. Consequently also, the optimisation problem presents important difficulties, i.e. memory and computation requirements. Thus the authors aim to develop a feasible framework, based on the Smallwood and Sondik (1973) approach, capable of handling real problems. To attain this objective, a specific algorithm is developed and the dimension of the bearings-only tracking is drastically reduced. The applicability of the approach is demonstrated on realistic sonar scenarios.