Continuous-discrete filters for bearings-only underwater target tracking problems

In this work, we develop a continuous-discrete shifted Rayleigh filter (CD-SRF) and a continuous-discrete sparse-grid Gauss-Hermite filter (CD-SGHF) for a real-life passive underwater bearings-only target tracking problem. The stochastic difference equation describing the process model is derived from its continuous equivalent using Ito-Taylor expansion of order 1.5. The performance of the proposed filters is compared in terms of root mean square error (RMSE), track divergence and computational time. For a fair comparison, popular filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) and Gauss-Hermite filter (GHF) are implemented. The effect of initial uncertainty, measurement noise covariance and sampling time on filtering accuracy is also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer-Rao lower bound (CRLB). From simulation results, it was observed that CD filters performed with higher accuracy than their discrete equivalents, with CD-SRF proving to be the most accurate among all the filters.