Optimal linear estimation for continuous stochastic systems with random observation delays

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)359-380
Journal / PublicationInternational Journal of Robust and Nonlinear Control
Issue number4
Publication statusPublished - 10 Mar 2013


This paper is concerned with the linear minimum mean square error estimation for Itô-type differential equation systems with random delays, where the delay process is modeled as a finite-state Markov chain. By first introducing a set of equivalent delay-free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay-free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady-state optimal estimator are studied for time-invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time-invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.

Research Area(s)

  • continuous-time systems, convergence analysis, innovation analysis method, linear estimation, random jump delays, Riccati differential equations