Strong tracking square-root modified sliding-window variational adaptive Kalman filtering with unknown noise covariance matrices

The Kalman filter’s performance deteriorates in the existence of slowly time-varying and unknown measurement and process noise covariances. A simplified strong tracking square-root modified sliding window variational adaptive Kalman filter is proposed for the aforementioned challenges in this paper. A modified slidingwindow variational adaptive Kalman filtering is designed in the proposed algorithm capable of correcting and smoothing the previous states in accordance with the latter states and reducing the number of backward iterations to improve the filtering accuracy and computational efficiency of the algorithm. The multiple fading factors have been constructed to correct the one-step predicted error covariance matrix. Moreover, the square root decomposition approach is developed for decomposing the error covariance matrices to eliminate numerical rounding errors. The simulation results demonstrate that the proposed algorithm exhibits superior tracking capacity of the one-step predicted error covariance matrix and filtering accuracy compared with the existing filters.