Bias compensation Kalman filter for 3D angle-only measurements target traking

Some sensors can only measure the angle of arrival of the signal, but the real position of the signal source is usually interesting. To obtain an accurate target position estimate, this paper studies the target tracking problem based on angle-only measurements in 3-Dimensional (3D) space. Firstly, the target position estimate is obtained by using weighted least-squares (WLS) algorithm, and the covariance matrix of the position estimate is calculated. Although this algorithm has low computational complexity, there is a bias problem due to the transformation of angle measurement equation from nonlinear to linear. To counter the bias, a bias compensation step is considered by estimating the correlation between the measurement matrix and noise vector. The classical Kalman filter (KF) is applied to the target position estimates before and after compensation. In numerical results, the performance advantages of the proposed bias compensation KF over the uncompensated algorithm and extended Kalman filter are verified. In addition, the impacts of angle measurement accuracy and sensor self-positioning accuracy are analyzed, indicating that the bias compensation Kalman filter can achieve high positioning performance with low computational cost.