An adaptive robust Kalman filter based on influence function

To solve the engineering application problems of the Kalman filter, the existing methods often enhance the robustness at the cost of excessive performance loss, which leads to performance degradation. To improve the filtering accuracy, this paper constructs the adaptive robust Kalman filter (ARKF) algorithm based on the Riccati equation with the influence function to minimize the performance loss while reducing uncertainty. First, the influence function is used to perceive and quantify the uncertainty influence in real time; second, the observation deviation caused by uncertainty is inverted according to the quantification; then, the priori covariance matrix of the Riccati equation is adjusted according to the observation deviation, thus realizing the adaptive tuning of the robustness and minimizing the performance loss; lastly, the effectiveness and superiority of the proposed algorithm are demonstrated by numerical simulation and application in the quadruple-capacity water tank experiments.