An iterated fuzzy extended Kalman filter for nonlinear systems

The fuzzy extended Kalman filter (FEKF) for state estimation can be used to deal with fuzzy uncertainty effectively. However, the linearisation processing of the FEKF introduces truncation error, which degrades the estimation precision. In order to reduce the error, a new iterated fuzzy extended Kalman filter (IFEKF), based on the FEKF and the maximum a posteriori estimation, is proposed in this article. Compared with the FEKF, the proposed algorithm can be used not only to deal with the fuzzy uncertainty, but also to reduce the truncation error and to estimate the states more accurately. With an algebraic example and a passive location simulation, it is shown that the IFEKF has better estimation precision than that of the FEKF.

[1]  P Wach,et al.  Fuzzy filter for state estimation of a glucoregulatory system. , 1996, Computer methods and programs in biomedicine.

[2]  Dan Simon.  Kalman filtering for fuzzy discrete time dynamic systems , 2003, Appl. Soft Comput..

[3]  R. Mehra.  On the identification of variances and adaptive Kalman filtering , 1970 .

[4]  Salim Labiod,et al.  Direct adaptive fuzzy control for a class of MIMO nonlinear systems , 2007, Int. J. Syst. Sci..

[5]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[6]  Ramón Galán,et al.  The fuzzy Kalman filter: State estimation using possibilistic techniques , 2006, Fuzzy Sets Syst..

[7]  Chaio-Shiung Chen.  Adaptive fuzzy control systems with dynamic structure , 2008, Int. J. Syst. Sci..

[8]  Guang-ren Duan,et al.  An Adaptive Iterated Kalman Filter , 2006, The Proceedings of the Multiconference on "Computational Engineering in Systems Applications".

[9]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[10]  Lingzhong Guo,et al.  A fast convergent extended Kalman observer for nonlinear discrete-time systems , 2002, Int. J. Syst. Sci..

[11]  F. W. Cathey,et al.  The iterated Kalman filter update as a Gauss-Newton method , 1993, IEEE Trans. Autom. Control..

[12]  Stephen A. Billings,et al.  Identification and analysis of spatio-temporal dynamical systems using wavelets , 2008, Int. J. Syst. Sci..

[13]  Z-J Zhou,et al.  An improved fuzzy Kalman filter for state estimation of nonlinear systems , 2008 .

[14]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[15]  Mehmt Sunar,et al.  Substructural control of fuzzy nonlinear flexible structures , 2007, J. Frankl. Inst..

[16]  Chang-Hua Hu,et al.  An improved fuzzy Kalman filter for state estimation of non-linear systems , 2010, Int. J. Syst. Sci..