The Stability Analysis of the Adaptive Fading Extended Kalman Filter

The well-known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. Thus, the Kalman filter with incomplete information may be degraded or even diverged. In a number of practical situations, the system model and the stochastic information are incomplete. To solve this problem, a new adaptive fading Kalman filter (AFKF) using the forgetting factor has recently been proposed. This paper extends the AFKF to nonlinear system models to obtain an adaptive fading extended Kalman filter (AFEKF). The forgetting factor is generated from the ratio between the calculated innovation covariance and the estimated innovation covariance. Based on the analysis result of Reif for the EKF, the stability of the AFEKF is also analyzed.

[1]  M. Netto,et al.  On the optimal and suboptimal nonlinear filtering problem for discrete-time systems , 1977 .

[2]  T. Tarn,et al.  Observers for nonlinear stochastic systems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[3]  Konrad Reif,et al.  Stochastic stability of the discrete-time extended Kalman filter , 1999, IEEE Trans. Autom. Control..

[4]  T. Moore,et al.  Adaptive Kalman filtering algorithms for integrating GPS and low cost INS , 2004, PLANS 2004. Position Location and Navigation Symposium (IEEE Cat. No.04CH37556).

[5]  T. Westerlund,et al.  Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems" , 1980 .

[6]  L. Gimeno,et al.  On the optimal and suboptimal nonlinear filtering problem for discrete time systems , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[7]  Chris Hide,et al.  Adaptive Kalman Filtering for Low-cost INS/GPS , 2002, Journal of Navigation.

[8]  김광훈.  An)Adaptive filter design for a fault tolerant navigation system , 2006 .

[9]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

[10]  L. Schwartz,et al.  A computational comparison of several nonlinear filters , 1968 .

[11]  A. H. Mohamed,et al.  Adaptive Kalman Filtering for INS/GPS , 1999 .

[12]  Raman K. Mehra,et al.  Approaches to adaptive filtering , 1970 .

[13]  M. Rao,et al.  A new state estimation algorithm-adaptive fading Kalman filter , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[14]  Xuemin Shen,et al.  Adaptive fading Kalman filter with an application , 1994, Autom..