A New Adaptive Extended Kalman Filter for a Class of Nonlinear Systems

This paper proposes a new adaptive extended Kalman filter (AEKF) for a class of nonlinear systems perturbed by noise which is not necessarily additive. The proposed filter is adaptive against the uncertainty in the process and measurement noise covariances. This is accomplished by deriving two recursive updating rules for the noise covariances, these rules are easy to implement and reduce the number of noise parameters that need to be tuned in the extended Kalman filter (EKF). Furthermore, the AEKF updates the noise covariances to enhance filter stability. Most importantly, in the worst case, the AEKF converges to the conventional EKF. The AEKF performance is determined based on the mean square error (MSE) performance measure and the stability is proven. The results illustrate that the proposed AEKF has a dramatic improved performance over the conventional EKF, the estimates are more stable with less noise.