Gaussian Sum Shifted Rayleigh Filter for Underwater Bearings-Only Target Tracking Problems

Abstract

In this paper, a new Gaussian sum (GS) filter with shifted Rayleigh filter (SRF) as proposal has been developed for the bearings-only tracking (BOT) problem. The proposed filter estimates the prior and posterior probability density functions as weighted sum of several Gaussian densities, where the individual Gaussian densities are generated from the SRF. Performance of the proposed filter on the BOT problem is compared with the SRF, the GS sparse-grid Gauss-Hermite filter, and other available GS and quadrature-based filters. Performance of filters is compared in terms of a root-mean-square error (RMSE), track divergence, and computational time. The effect of initial uncertainty, measurement noise covariance, and sampling time on filtering accuracy are also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer-Rao lower bound. From simulation results, it is observed that the performance of the proposed GS-SRF is superior to all other nonlinear filters considered.