Automated Tuning of an Extended Kalman Filter Using the Downhill Simplex Algorithm

Abstract

A method of tuning a Kalman filter by means of the downhill simplex numerical optimization algorithm is presented. The problem is defined by a brief description of the Kalman filter and the extended Kalman filter and the sensitivity of filter performance to process noise and measurement noise covariance matrices Q and R. The filter tuning problem for a system processing simulated data is then formulated as a numerical optimization problem by defining a performance index based on state estimate errors. The resulting performance index is then minimized using the downhill simplex algorithm. The technique is then applied to three numerical examples of increasing complexity to demonstrate its practical utility.