Comparison of several ballistic target tracking filters

In this paper, we compare several nonlinear filtering methods, namely, extended Kalman filter (EKF), unscented filter (UF), particle filter (PF), and linear minimum mean square error (LMMSE) filter for a ballistic target tracking problem. We cast EKF and UF into a general linear recursive estimation framework and reveal their pros and cons. We pinpoint using the LMMSE filter for possible analytical solutions rather than starting with approximations such as system linearization or unscented transform. We compare the performance of EKF, UF, LMMSE filter and Gaussian PF for a ballistic target tracking problem. The estimation accuracy is also compared with the posterior Cramer-Rao lower bound (PCRLB). Our simulation results confirm that the LMMSE filter outperforms EKF and UF in terms of tracking accuracy, filter credibility and robustness against the sensitivity to filter initial condition. Its accuracy is slightly worse than that of Gaussian PF but with much lower computational load. We conclude that the LMMSE filter is preferred for the ballistic target tracking problem being studied.