Adaptive Unscented Kalman Filter for Target Tracking in the Presence of Nonlinear Systems Involving Model Mismatches

In order to improve filtering precision and restrain divergence caused by sensor faults or model mismatches for target tracking, a new adaptive unscented Kalman filter (N-AUKF) algorithm is proposed. First of all, the unscented Kalman filter (UKF) problem to be solved for systems involving model mismatches is described, after that, the necessary and sufficient condition with third order accuracy of the standard UKF is given and proven by using the matrix theory. In the filtering process of N-AUKF, an adaptive matrix gene is introduced to the standard UKF to adjust the covariance matrixes of the state vector and innovation vector in real time, which makes full use of normal innovations. Then, a covariance matching criterion is designed to judge the filtering divergence. On this basis, an adaptive weighted coefficient is applied to restrain the divergence. Compared with the standard UKF and existing adaptive UKF, the proposed UKF algorithm improves the filtering accuracy, rapidity and numerical stability remarkably, moreover, it has a good adaptive capability to deal with sensor faults or model mismatches. The performance and effectiveness of the proposed UKF is verified in a target tracking mission.