On the Effects of the Initial Condition in State Estimation for Discrete-Time Linear Systems

Richard B. Sowers, Armand M. Makowski

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider the one-step prediction problem for discrete-time linear systems in correlated Gaussian white plant and observation noises, and non-Gaussian initial conditions. Explicit representations are obtained for the MMSE and LLSE (or Kaiman) estimates of the state given past observations, as well as for the expected square of their difference. These formulae are obtained with the help of the Girsanov transformation for Gaussian white noise sequences, and explicitly display the effects of the distribution of the initial condition. With the help of these formulae, we investigate the large-time asymptotics of Et, the expected squared difference between the MMSE and LLSE estimates at time t. We characterize the limit of the error sequence {Et, t = 1,2,…} and obtain some related rates of convergence. A complete large-time analysis is provided for the scalar case.

Original languageEnglish (US)
Title of host publicationControl and Dynamic Systems
Pages325-393
Number of pages69
DOIs
StatePublished - Jan 1 1993

Publication series

NameControl and Dynamic Systems
Volume56
ISSN (Print)0090-5267

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems

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    Sowers, R. B., & Makowski, A. M. (1993). On the Effects of the Initial Condition in State Estimation for Discrete-Time Linear Systems. In Control and Dynamic Systems (pp. 325-393). (Control and Dynamic Systems; Vol. 56). https://doi.org/10.1016/B978-0-12-012756-6.50014-1