Kalman filtering through the feedback adaption of prior error covariance

For Kalman filtering problems with inaccurate or mismatched process noise statistics, through proposing the feedback excavation based covariance adaption scheme, this paper elaborates a new adaptive Kalman filter for linear time-invariant systems. To relief Kalman theory's requirement on the accurate and a priori knowledge about process noise statistics, the original covariance prediction step of Kalman filter is removed in the new approach; instead, with proposed covariance adaption scheme, the prior error covariance is directly reconstructed through online excavating posterior sequence, which is also the main innovation of this work. Since the process noise covariance is not used in the new adaption scheme, the negative influence of mismatched noise statistics can be significantly reduced in proposed adaptive Kalman filter. In addition, the positive semi-definiteness of the online adapted prior error covariance is mathematically guaranteed in the new adaption scheme without imposing extra computational cost. The new approach's advantages in filtering adaptability, accuracy and simplicity are demonstrated using numerical simulations of an object tracking scenario.