ESTIMATION OF THE COVARIANCES OF THE PROCESS NOISE AND MEASUREMENT NOISE FOR A LINEAR DISCRETE DYNAMIC SYSTEM

There have been many papers written about tuning Kalman filters. Such tuning usually consists of adjustments to values used for the covarian ces of the model and observation noise. In this paper we described a p rocedure using the observations with a linear process model to develop estimates for the effective values of the covariance matrices of both the process noise (Q) and the measurement noise (R). These are needed for maximum likelihood state estimation in control and optimization. A horizon state estimator is derived that is linearly unbiased and has a constant state estimation error covariance. The process and measure ment models are combined with the state estimates and a constant state estimation error covariance to generate cumulative error covariances that are also constant. A maximum likelihood function and a linear reg ression technique are then utilized to obtain the diagonal elements of covariance matrices of the process noise and the measurement noise. A simulation example for two chemical reactors in series is presented.