Suboptimal filter for continuous‐time linear systems with unknown parameters

The filtering problem for continuous-time linear systems with unknown parameters is considered. A new suboptimal filter is herein proposed. It is based on the optimal mean-square linear combination of the local Kalman filters. In contrast to the optimal weights, the suboptimal weights do not depend on current observations; thus, the proposed filter can easily be implemented in real-time. Examples demonstrate high accuracy and efficiency of the suboptimal filter.

[1]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[2]  Peter S. Maybeck,et al.  Reducing lag in virtual displays using multiple model adaptive estimation , 1998 .

[3]  Peter S. Maybeck,et al.  Interrelationship of single-filter and multiple-model adaptive algorithms , 1998 .

[4]  V. Balakrishnan,et al.  Robust adaptive Kalman filters for linear time-varying systems with stochastic parametric uncertainties , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[5]  Lennart Ljung,et al.  The Extended Kalman Filter as a Parameter Estimator for Linear Systems , 1979 .

[6]  J. R. Vasquez,et al.  Enhanced motion and sizing of bank in moving-bank MMAE , 2004 .

[7]  Feng Ding,et al.  Brief paper Hierarchical gradient-based identification of multivariable discrete-time systems , 2005 .

[8]  Feng Ding,et al.  Hierarchical gradient-based identification of multivariable discrete-time systems , 2005, Autom..

[9]  Feng Ding,et al.  Hierarchical least squares identification methods for multivariable systems , 2005, IEEE Trans. Autom. Control..

[10]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

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

[12]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

[13]  Yaakov Bar-Shalom,et al.  The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[14]  渡辺 桂吾,et al.  Adaptive estimation and control : partitioning approach , 1991 .

[15]  D. Lainiotis,et al.  Partitioning: A unifying framework for adaptive systems, I: Estimation , 1976, Proceedings of the IEEE.

[16]  Fan Wang,et al.  Robust Kalman filters for linear time-varying systems with stochastic parametric uncertainties , 2002, IEEE Trans. Signal Process..

[17]  Feng Ding,et al.  Hierarchical identification of lifted state-space models for general dual-rate systems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[19]  F. Lewis.  Optimal Estimation: With an Introduction to Stochastic Control Theory , 1986 .

[20]  Richard M. Stanley.  Optimal Estimation With an Introduction to Stochastic Control , 1988 .

[21]  Demetrios G. Lainiotis,et al.  Partitioned linear estimation algorithms: Discrete case , 1975 .

[22]  M. E. Welch,et al.  Bayesian analysis of time series and dynamic models , 1990 .