Steady-State Covariance Analysis for a Forward-Pass Fixed-Interval Smoother

[+] Author and Article Information
Keigo Watanabe

College of Engineering, Shizuoka University, Hamamatsu 432, Japan

J. Dyn. Sys., Meas., Control 108(2), 136-140 (Jun 01, 1986) (5 pages) doi:10.1115/1.3143755 History: Received February 01, 1986; Online July 21, 2009


This paper studies the solution of the steady-state error covariance equation (which is represented by the algebraic Lyapunov equation) associated with a forward-pass fixed-interval smoother for discrete-time linear systems. A necessary and sufficient condition is given to assure the existence of a unique stabilizing solution. A simple algorithm for solving such an equation is also proposed by using four eigenvector matrices, which are generated by a symplectic matrix, corresponding to the algebraic Riccati equation of a backward-pass information filter. Thus the results have application to the important problem of the limiting covariance analysis of smoothing prior to practically dealing with a finite interval of data.

Copyright © 1986 by ASME
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