Integrated Pseudolinear Kalman Filter for Target Tracking With Nonlinear Measurements

To address the nonlinear measurement problem of maneuvering target tracking with active sensors, an instrumental variable-based integrated pseudolinear Kalman filter (IV-IPLKF) is developed in this article. First, a pseudolinear measurement equation for range measurements is proposed, and the first and second-order statistical characteristics of the pseudolinear noise are derived. Following that, an integrated pseudolinear Kalman filter (IPLKF) is formulated to process mixed nonlinear range and bearing measurements. A thorough analysis of the IPLKF bias indicates that it primarily originates from the correlation between pseudolinear noise and the observation matrix, which has led to the development of the bias-compensated IPLKF (BC-IPLKF). Moreover, inspired by the asymptotically unbiased property of a closed-form instrumental variable estimator, an IV-IPLKF is proposed based on the recursive least square (RLS) method and BC-IPLKF. Finally, the stability and convergence of the proposed algorithm are proved based on the Lyapunov theory. Simulation results indicate that the IV-IPLKF enjoys better filtering accuracy and efficiency than state-of-the-art algorithms. It achieves performance closer to the posterior Cramér-Rao lower bound (PCRLB) while taking only one-third of the cubature Kalman filter (CKF) runtime.