Remarks on the Kalman filtering simulation and verification

The purpose of this paper is to convey the readers several useful remarks for understanding, simulating and verifying the Kalman filter (KF) computer codes. A tutorial, example-based approach is employed to present several KF issues of considerable importance in engineering practice, and to suggest some check points on Kalman filtering verification process. Some illustrative examples are accompanied where necessary to the readers for better understanding the fundamental basis and for enhancing the reliability (correctness) of the self-developed computer codes before larger, complicated KF designs are performed. Notes on two forms of discrete-time Kalman filter loop are pointed out. Methods for determining the process noise covariance matrix are provided. Simulation of the dynamic process is discussed. Guidelines for verification of filtering solutions are provided, which cover (1) the consistency check between the discrete-time to the continuous-time covariance and gain matrices; (2) evaluation of estimator optimality with sensitivity analysis and consistency check between theoretical and simulation results.