Modified Kalman filter without covariance matrices for one kinetic linear model

The covariance matrices of measurement and process noise are essential for standard Kalman filter algorithm in practice. In this paper, we will focus on the fundamental estimating problem that there is no priori knowledge about covariance matrices of measurement and process noise for a kind of kinetic system model. To cope with this challenging problem, a modified Kalman filter, terms as MKF-RCE, is proposed based on the basic statistical approach under the framework of Kalman filter. Finally, the stability are verified by simulation experiments to demonstrate that MKF-RCE is optimal in sense that estimate sequence from MKF-RCE is asymptotically convergent with the ideal sequence from Kalman filter with exact covariance matrices.