Optimal linear filtering under parameter uncertainty
The author considers the linear time-invariant matrix system of the form NEWLINE\[NEWLINE\dot{x}=Ax+Bw,\quad y=Cx+Dw, \quad z=LxNEWLINE\]NEWLINE with white noise \(w\). It is supposed that the total matrix consisting of \(A\), \(B\), \(C\), \(D\) is unknown, but it belongs to a given convex bounded polyhedral domain. The problem of designing a guaranteed minimum error variance robust filter is solved, and a complete design methodology of robust filters is proposed. The results generalize the previous ones in several directions. Namely, all system matrices can be corrupted by parameter uncertainty, and also the admissible uncertainty may be structured. A comparison with previous results [\textit{I. R. Petersen} and \textit{D. C. MacFarlane}, ``Robust estimation for uncertain system'' in Proc. 30th IEEE Conf. Decision Contr., Brighton, U.K. (1991)] demonstrates that the author's method provides a robust filter with better or at least equal performance. Moreover, it applies to more general models of parametric uncertainties, and no unidimensional search (with respect to the parameter \(\varepsilon\)) is needed. Some numerical results are presented.
scientific article; zbMATH DE number 1632201