Bearings-Only Target Tracking with an Unbiased Pseudo-Linear Kalman Filter

In bearings-only target tracking, the pseudo-linear Kalman filter (PLKF) attracts much attention because of its stability and its low computational burden. However, the PLKF’s measurement vector and the pseudo-linear noise are correlated, which makes it suffer from bias problems. Although the bias-compensated PLKF (BC–PLKF) and the instrumental variable-based PLKF (IV–PLKF) can eliminate the bias, they only work well when the target behaves with non-manoeuvring movement. To extend the PLKF to the manoeuvring target tracking scenario, an unbiased PLKF (UB–PLKF) algorithm, which splits the noise away from the measurement vector directly, is proposed. Based on the results of the UB–PLKF, we also propose its velocity-constrained version (VC–PLKF) to further improve the performance. Simulations show that the UB–PLKF and VC–PLKF outperform the BC–PLKF and IV–PLKF both in non-manoeuvring and manoeuvring scenarios.