Bias-compensation Kalman Filter Algorithm for AoA-ToA Target Tracking

In target tracking with angle-of-arrival (AoA) and time-of-arrival (ToA) measurements, existing nonlinear Kalman filter algorithms cannot achieve both low computational complexity and high tracking accuracy. To address this problem, in this paper, we propose a simple and effective algorithm called the bias-compensation Kalman filter (BCKF). First, nonlinear measurement equations are pseudo-linearized by utilizing the equivalent geometric relationship between the AoA and ToA, which yields a pseudo-linear Kalman filter (PLKF). To overcome the bias associated with the PLKF, a detailed theoretical bias expression is derived, and the effect of each bias term is analyzed. Then, the BCKF compensates for the bias caused by the correlation of the pseudo-linear measurement of the noise vector and the measurement matrix to achieve more accurate state estimation. A theoretical analysis of the complexity and the simulation results of the filter performance show that BCKF achieves higher tracking accuracy with lower computational overhead compared with other filter algorithms, and attains the posterior Cramér-Rao lower bound over the mild noise region. Furthermore, BCKF enables fast convergence and is not susceptible to initial errors.