Improved Pseudolinear Kalman Filter Algorithms for Bearings-Only Target Tracking

Despite its stability and computational complexity advantages, the pseudolinear Kalman filter (PLKF) suffers from severe bias problems in bearings-only target tracking applications. This paper develops new variants of the PLKF with significant performance improvement. First, a detailed analysis of the PLKF bias is provided for nearly constant-velocity target dynamics. This analysis uncovers the specific reasons of bias in state estimation and leads to a new bias-compensated PLKF (BC-PLKF) algorithm with the improved bias performance. The bias arising from the correlation between the measurement vector and pseudolinear noise is tackled by a novel instrumental-variable Kalman filter (IVKF). While the method of instrumental variables has been successfully applied to batch pseudolinear estimation algorithms, its extension to the PLKF is new. The IVKF embeds the method of recursive IV estimation into the BC-PLKF and employs the BC-PLKF to construct instrumental variable vectors with desired properties. The IVKF is further improved by adopting the method of selective angle measurements (SAM), which ensures that the performance of the IVKF is not degraded by a weak correlation between the instrumental variable vector and measurement vector in low signal-to-noise ratio (SNR) situations. Comparative simulation examples are presented to demonstrate the performance improvement of the proposed recursive estimators (the BC-PLKF, IVKF and SAM-IVKF) over the conventional PLKF and the extended Kalman filter. The SAM-IVKF is observed to provide the best estimation performance among the proposed estimators by producing a negligible estimation bias and mean squared error close to the posterior Cramér-Rao lower bound at moderate noise levels.