Piecewise Optimal Trajectories of Observer for Bearings-Only Tracking by Quantization

We investigate the problem of determining the trajectory that an observer should follow to be able to accurately track a target in a bearings-only measurements context. We assume that the target's motion is uniform and that the measurements are corrupted by an additive Gaussian white noise. Though, in theory, this process is observable if the observer maneuvers with turns or accelerations, the quality of the resulting estimation strongly depends on the trajectory chosen by the observer. In this paper, we present a numerical method to compute a trajectory of a maneuvering observer with the objective of maximizing the cumulative sum of bearing rates between the target and observer. Our approach is based on the piecewise stochastic control of a finite-horizon Markov process. A quantization method is applied to transform the problem into a discrete domain. We show that this transformation allows for a numerically tractable solution able to accurately track the target in a number of practical scenarios.