Sub-optimal gain schedules for the discrete Kalman filter.

Abstract

The object of this study is to find an approximation to the discrete optimal Kalman filter gain schedule by closed-form analytic expressions. In doing so, required table storage and/or on-line computation time can be reduced at little expense in terms of filter performance degradation. The method of least squares was used to determine the closed-form solution which was the best fit to the discrete Kalman filter gain schedule. The criterion for performance degradation was the difference between the values of the diagonal elements of the estimation covariance matrix, P, ,, , obtained by using the Kalman gain schedule, and the corresponding values obtained by using the closed-form analytic expressions for the elements of" the gain matrix. Examples are presented to show that near-optimal results were obtained utilizing this method. A comparison of the results of this study with another near-optimal estimation scheme is also included.