Recursive approach of optimal Kalman filtering problem for multiparameter singularly perturbed systems

Authors:
H. Mukaidani
Affiliations:
Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan
Venue:
International Journal of Systems Science
Year:
2005

Citing 4
Cited 0

The existence of a unique and bounded solution of the algebraic Riccati equation of multimodel estimation and control problems

Systems & Control Letters
Singular perturbation methods in control: analysis and design

Singular perturbation methods in control: analysis and design
Singularly Perturbed and Weakly Coupled Linear Control Systems: A Recursive Approach

Singularly Perturbed and Weakly Coupled Linear Control Systems: A Recursive Approach
Brief New results for near-optimal control of linear multiparameter singularly perturbed systems

Automatica (Journal of IFAC)

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Abstract

In this paper, the optimal Kalman filtering problem for multiparameter singularly perturbed systems is considered. In order to obtain the filter gain, the solution of the multiparameter algebraic Riccati equations (MAREs) is needed. The main contributions in this paper are to propose a new recursive algorithm for solving the MARE and to establish sufficient conditions related to the convergence property of the proposed algorithm. Using the recursive algorithm, it is shown that the solution of the MARE converges to a positive semidefinite stabilizing solution with the rate of convergence of O(||µ||i). Moreover, it is proved that the mean square error via the proposed high-order filter attain, the O(||µ||2i+1) approximation compared with the optimal filter.