A note on Kalman filtering

The purpose of this paper is to point out a confusing phenomenon in the tea ching of Kalman filtering. Students are often confused by noting that the a posteriori error covariance of the discrete Kalman filter (DKF) is smaller than the error covariance of the continuous Kalman filter (CKF), which wou ld mean that the DKF is better than CKF since it gives a smaller error cova riance. However, simulation results show that CKF gives estimates much clos er to the true states, We will provide a simple qualitative argument to exp lain this phenomenon.