Adaptive Robust Extended Kalman Filter

The extended Kalman filter (EKF) is one of the most widely used methods for state estimation with communication and aerospace applications based on its apparent simplicity and tractability (Shi et al., 2002; Bolognani et al., 2003; Wu et al., 2004). However, for an EKF to guarantee satisfactory performance, the system model should be known exactly. Unknown external disturbances may result in the inaccuracy of the state estimate, even cause divergence. This difficulty has been recognized in the literature (Reif & Unbehauen, 1999; Reif et al., 2000), and several schemes have been developed to overcome it. A traditional approach to improve the performance of the filter is the 'covariance setting' technique, where a positive definite estimation error covariance matrix is chosen by the filter designer (Einicke et al., 2003; Bolognani et al., 2003). As it is difficult to manually tune the covariance matrix for dynamic system, adaptive extended Kalman filter (AEKF) approaches for online estimation of the covariance matrix have been adopted (Kim & ILTIS, 2004; Yu et al., 2005; Ahn & Won, 2006). However, only in some special cases, the optimal estimation of the covariance matrix can be obtained. And inaccurate approximation of the covariance matrix may blur the state estimate. Recently, the robust H∞ filter has received considerable attention (Theodor et al., 1994; Shen & Deng, 1999; Zhang et al., 2005; Tseng & Chen, 2001). The robust filters take different forms depending on what kind of disturbances are accounted for, while the general performance criterion of the filters is to guarantee a bounded energy gain from the worst possible disturbance to the estimation error. Although the robust extended Kalman filter (REKF) has been deeply investigated (Einicke & White, 1999; Reif et al., 1999; Seo et al., 2006), how to prescribe the level of disturbances attenuation is still an open problem. In general, the selection of the attenuation level can be seen as a tradeoff between the optimality and the robustness. In other words, the robustness of the REKF is obtained at the expense of optimality. This chapter reviews the adaptive robust extended Kalman filter (AREKF), an effective algorithm which will remain stable in the presence of unknown disturbances, and yield accurate estimates in the absence of disturbances (Xiong et al., 2008). The key idea of the AREKF is to design the estimator based on the stability analysis, and determine whether the error covariance matrix should be reset according to the magnitude of the innovation. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg