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

Zihao Huang,Chengpeng Hao,Danilo Orlando,Shijin Chen

doi:10.3390/rs13152915

Abstract

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.

Highlights

Bearings-only tracking (BOT) comprises estimating a target’s state from bearing measurements received by an observer [1]
The proposed UB–pseudo-linear Kalman filter (PLKF) and velocityconstrained PLKF (VC–PLKF) are compared with the BC
We find that the velocity root mean square error (RMSE) of unbiased PLKF (UB–PLKF) and VC–PLKF decrease after the manoeuvring, which means that the proposed algorithms are more adaptable to abrupt changes in the velocity

Summary

Introduction

Bearings-only tracking (BOT) comprises estimating a target’s state from bearing measurements received by an observer [1]. It plays an important role in both military and civil applications, for example, underwater surveillance [2,3], 3-D passive target tracking [4,5,6,7]. The nonlinear relationship between the bearing measurements and the target state vector makes BOT a typical nonlinear filtering problem [12]. There are two common ways to deal with the nonlinearity in the BOT problem. The extended Kalman filter uses the first-order Taylor expansion to replace the corresponding nonlinear function, which will certainly lead to truncation errors.

Methods

Discussion

Conclusion