Piecewise optimal trajectories of observer for bearings-only tracking of maneuvering target

Abstract

This paper provides a general framework for optimizing the trajectory of an observer by means of bearings-only tracking (BOT) in the case where the source is maneuvering. The basic problem of target motion analysis (TMA) is to estimate the trajectory of an object from noise corrupted sensor data. In the BOT context, the source state is only partially observed through nonlinear measurements, and the quality of the estimation strongly depends on the observer trajectory. We assume that the source has maneuvering capabilities, which is a case of practical interest though the TMA performance may be dramatically degraded. To characterize more precisely observer-optimal maneuvers, we have to be able to determine the optimal course. To this purpose, the common approach consists in maximizing the determinant of the Fisher information matrix (FIM) by an iterative algorithm to obtain an optimal observer trajectory. In our framework, a cumulative sum of bearing rates and relative distance between the target and observer is used as reward function, and the chosen maneuver will be the one that maximizes the mathematical expectation of the reward function. The target's motion is quantized, and an extended Kalman filter is used to estimate the position and velocity of the target and to provide the initial distribution for each optimization period. The proposed algorithm is a closed-loop control, and by maximizing the reward function, it allows to automatically compute the suboptimal maneuver. The applicability of our approach is demonstrated on realistic scenarios.