# Steady-state covariance analysis for a forward-pass fixed-interval smoother

Research output: Contribution to journalArticle

### Abstract

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.

Original language English 136-140 5 Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 108 2 https://doi.org/10.1115/1.3143755 Published - Jun 1986 Yes

### ASJC Scopus subject areas

• Control and Systems Engineering
• Information Systems
• Instrumentation
• Mechanical Engineering
• Computer Science Applications
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