Stochastic approximation for optimal observer trajectory planning

A maneuvering target is to be tracked based on noise corrupted measurements of the target´s state that are received by a moving observer. Additionally, the quality of the target state observations can be improved by the appropriate positioning of the observer relative to the target during tracking. The bearings-only tracking problem is an example of this scenario. The question of optimal observer trajectory planning naturally arises, i.e. how should the observer maneuver relative to the target in order to optimise the tracking performance? In this paper, we formulate this problem as a discrete-time stochastic optimal control problem and present a novel stochastic approximation algorithm for designing the observer trajectory. Numerical examples are presented to demonstrate the utility of the proposed methodology.