Discrete-Time Filtering for Linear Systems in Correlated Noise with Non-Gaussian Initial Conditions: Asymptotic Behavior of the Difference Between the MMSE and LMSE Estimates

Abstract

We consider the one-step prediction problem for discrete-time linear systems in correlated plant and observation noises, and non-Gaussian initial conditions. We investigate the asymptotic behavior of the expected square Et of the difference between the MMSE and LMMSE (or Kalman) estimates of the state given past observations. We characterize the hrnit of the error seqnence {Et, t = 0,1,...) and obtain some related rates of convergence, with complete analysis being provided for the scalar case. The discussion is based on the explicit representations which were obtained by the authors in [ , ] for the MMSE and LMMSE estimates, and which explicitly display the dependence of these quantities on the initial distribution.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1989
Accession Number
ADA454737

Entities

People

  • Armand M. Makowski
  • Richard B. Sowers

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  • University of Maryland

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  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.