Non-Gaussian Pseudolinear Kalman Filtering-Based Target Motion Analysis with State Constraints

For the bearing-only target motion analysis (TMA), the pseudolinear Kalman filter (PLKF) solves the complex nonlinear estimation of the motion model parameters but suffers serious bias problems. The pseudolinear Kalman filter under the minimum mean square error framework (PL-MMSE) has a more accurate tracking ability and higher stability compared to the PLKF. Since the bearing signals are corrupted by non-Gaussian noise in practice, we reconstruct the PL-MMSE under Gaussian mixture noise. If some prior information, such as state constraints, is available, the performance of the PL-MMSE can be further improved by incorporating state constraints in the filtering process. In this paper, the mean square and estimation projection methods are used to incorporate PL-MMSE with linear constraints, respectively. Then, the linear approximation and second-order approximation methods are applied to merge PL-MMSE with nonlinear constraints, respectively. Simulation results demonstrate that the constrained PL-MMSE algorithms result in lower mean square errors and bias norms, which demonstrates the superiority of the constrained algorithms.