Regularized adaptive Kalman filter for non-persistently excited systems

Abstract

Most available methods for joint state-parameter estimation in discrete-time stochastic time-varying systems suffer from severe performance degradation if the system is not persistently excited. We revisit and extend a recently proposed adaptive Kalman filter in order to enhance its robustness against periods of poor excitation. A Levenberg–Marquardt-like regularization algorithm is integrated in the filter to preclude the estimator from becoming unreliable due to wind-up effects. It is proven that, under uniform complete observability–controllability conditions and a persistent excitation condition, the expectations of the state and parameter estimation errors tend to zero exponentially fast. Furthermore, their stability (in the sense of Lyapunov) is guaranteed even if the persistent excitation condition is not satisfied. The effectiveness of the algorithm is demonstrated using real sensor data from a vehicle motion estimation application. Unlike the original algorithm, the proposed regularized adaptive Kalman filter provides accurate and reliable estimates of the states and parameters despite periods of poor excitation.