Evolutionary programming Kalman filter

Abstract A robust Kalman filtering (KF) algorithm based on the evolutionary programming (EP) technique is proposed in this paper, for uncertain systems with unknown-but-bounded uncertain parameters which are described by interval systems. This algorithm takes advantage of the global optima-searching capability of EP to find the optimal KF results at every iteration, which include both the upper–lower boundaries and the nominal trajectory of the optimal estimates of the system state vectors. One prominent feature of this EP filtering algorithm is that it assumes the same statistical conditions and provides the same optimal estimates as the conventional KF scheme. Both linear and nonlinear systems are studied. Two typical computer simulation examples are given with comparison, which verify the merits of the new method – it yields more accurate estimation results and is less conservative as compared to the existing interval Kalman filtering (IKF).

[1]  Guanrong Chen,et al.  Interval Kalman filtering , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Lang Hong.  Distributed Filtering Using Set Models for Systems with Non-Gaussian Noise , 1993 .

[3]  Guanrong Chen.  Approximate Kalman filtering , 1993 .

[4]  Guanrong Chen,et al.  Linear Stochastic Control Systems , 1995 .

[5]  Arnold W. Heemink,et al.  Performance robustness analysis of Kalman filter for linear discrete-time systems under plant and noise uncertainty , 1995 .

[6]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[7]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

[8]  Guanrong Chen,et al.  Fuzzy Kalman filtering , 1998, Inf. Sci..

[9]  Hyun Myung,et al.  Evolutionary programming techniques for constrained optimization problems , 1997, IEEE Trans. Evol. Comput..

[10]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[11]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

[12]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .

[13]  Yijia Cao.  Eigenvalue optimisation problems via evolutionary programming , 1997 .

[14]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[15]  Lihua Xie,et al.  H∞ estimation for discrete-time linear uncertain systems , 1991 .