Pseudolinear kalman filters for target tracking using hybrid measurements

Abstract

This paper presents new variants of the pseudolinear Kalman filter (PLKF) for target tracking in 2D-plane using angle-of-arrival, time-difference-of-arrival and frequency-difference-of-arrival measurements collected by stationary sensors. Using hybrid measurements can yield performance advantage over the traditional bearings-only estimators, but may involve complex noise vector and correlation between the measurement matrix and the noise vector. A closed-form PLKF is developed by rearranging measurement equations to compensate the non-zero mean of the noise vector. To tackle the bias issue of PLKF, the bias is derived and compensated instantaneously, leading to the proposed BCPLKF estimator. Then a new variant of instrumental variable-based Kalman filter (IVKF) was presented, which alleviates the bias by utilizing BCPLKF estimates instead of noisy measurements to compute the measurement matrix. In addition, the posterior Cramér-Rao lower bound (PCRLB) is derived for the nonlinear filtering problem. Simulation results demonstrate that the proposed estimators outperform the bearings-only estimator significantly and have the mean squared error fairly close to the PCRLB.