Bias-compensated Pseudolinear Kalman Filter for Acoustic Sensor Tracking with Colored Measurement Noise

The bias-compensated pseudolinear Kalman filter (BC-PLKF) has the advantages of closed form and low computational complexity for bearing-only target tracking. However, it is challenging to directly apply it to acoustic tracking with colored measurement noise. First, in acoustic tracking, the unknown propagation delay included in measurement is highly coupled with the target state, preventing the bearing measurements from being represented as pseudolinear measurement equations. Second, the augmented process noise is correlated with the measurement matrix that includes an unknown delay. In this paper, a recursive BC-PLKF algorithm for delayed measurement with colored noise (BC-PLKF-DC), using a two-stage estimator is proposed. The first stage employs colored noise augmented BC-PLKF (BC-PLKF-C) by neglecting delay to produce a coarse estimate. The second stage estimates the target state considering the effects caused by the delayed measurements. In this stage, a new pseudolinear measurement model with a special measurement error is built by approximating delay time as a linear function using the first stage estimate. But when the colored measurement noise is augmented onto the target state, the new bias arises from two sources. Then a new bias estimate is obtained, and we develop the closed-form BC-PLKF-DC algorithm by compensating the bias for the PLKF estimate. Illustrative examples demonstrate that the proposed algorithm outperforms BC-PLKF and BC-PLKF-C.