The shifted Rayleigh filter for 3D bearings-only measurements with clutter

Bearings-only tracking concerns the estimation of the position of a moving target from noisy measurements of the direction of the target relative to the sensor platform. We present an algorithm for bearings-only tracking, in which the measurements are in 3D space and are corrupted by clutter. In common with the earlier proposed shifted Rayleigh filter (SRF), the algorithm is based on exact calculations of the updated conditional mean and covariance of the state variable, under the assumption of a Gaussian prior. The presence of clutter on bearings measurements in 3D space adds considerably to the difficulty of performing these exact calculations. We report on simulations in a challenging scenario, aimed at comparing the performance of various trackers. In these simulations, the proposed tracking algorithm consistently outperforms other moment matching filters and the mean square tracking error compares favorably with the posterior Cramér-Rao lower bound (CRLB).