Quadratic constraint Kalman filter algorithm for three dimensional AoA target tracking

In the three-dimensional target tracking with angle of arrival (AoA) measurements, pseudo-linear Kalman filter has the advantages of high stability and low computational complexity. However, PLKF suffers from severe bias problem which causes its tracking accuracy to degrade rapidly. In view of this problem, a quadratic constraint Kalman filter (QCKF) is proposed. Firstly, an augmented matrix involving all measurement noise terms is introduced. Then, an objective function equivalent to linear Kalman filter is established, and a constraint containing quadratic terms on the objective function is imposed to reduce the bias effect and achieve more accurate state update. QCKF algorithm solves the constraint optimization problem by generalized eigenvalue decomposition, and its covariance matrix cannot be derived directly through the state update expression. Thus, the covariance matrix is updated by utilizing the constraint conditions and the matrix perturbation method. Simulation analysis shows that QCKF algorithm achieves better tracking performance than other nonlinear filter algorithms. QCKF attains the posterior Cramer Rao lower bound over the mild noise region and significantly reduces the tracking error under heavy noise. Moreover, its computational overhead is relatively low. © 2021, Editorial Office of Systems Engineering and Electronics. All right reserved.