Derivative-free filters for target motion analysis with bearings-only measurement

Nonlinear filtering for state and parameter estimation in both defence and civil applications has been recently advanced to accurate, computationally efficient and stable alternatives. The conventional nonlinear estimation technique is the extended Kalman filters (EKF) that uses first order derivative. For chancy and practical applications, the EKF may lead to inaccurate and unstable. In nineties, derivative- free filters such as the central difference filter (CDF) and the unscented Kalman filters (UKF) has been developed to provide accurate and stable estimation. The CDF algorithm for posterior state estimation has been presented in literature [7]. Main contribution of this paper is formulation of the CDF algorithm for prior state estimation and applied that to tracking problem. In this work, target motion analysis (TMA) using angle or bearings-only measurement has been studied with both prior and posterior state estimation. The considered tracking problem is highly nonlinear and has uncertainly in initial conditions. Particular focus in this work is to assess the robustness of the CDF in comparison with other nonlinear filters. The frequency of track-loss due to initial condition uncertainly has been studied. The robustness of CDF algorithm is studied with both prior and posterior estimation approach. First, the EKF, UKF and CDF algorithms for posterior estimation are applied to examine the tracking performance. Relative merits of the CDF vis-a-vis EKF and UKF are explored. Secondly, the EKF and CDF algorithm for prior estimation are applied for TMA. With large Monte Carlo simulation runs the tracking performance of EKF and CDF are compared by studying the root mean square error (RMSE) and robustness against initial uncertainly. As the tracking performance of CDF is superior to the EKF and close to the UKF and the computational efficiency of CDF is very close to the EKF, the CDF is one of the candidate for TMA with bearings-only measurement.