A note on Kalman filtering

The purpose of this paper is to point out a confusing phenomenon in the teaching 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 would mean that the DKF is better than CKF since it gives a smaller error covariance. However, simulation results show that CKF gives estimates much closer to the true states. We will provide a simple qualitative argument to explain this phenomenon.