Discrete-time filtering for linear systems with non-Gaussian initial conditions: asymptotic behavior of the difference between the MMSE and LMSE estimates

Author

Sowers, Richard B. ; Makowski, Armand M.

Author_Institution

Dept. of Electr. Eng., Maryland Univ., College Park, MD, USA

Volume

37

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

114

Lastpage

120

Abstract

The authors consider the one-step prediction problem for discrete-time linear systems in correlated plant and observation Gaussian white noises, with nonGaussian initial conditions. They investigate the large time asymptotics of ε_t, the expected squared difference between the MMSE and LMSE (or Kalman) estimates of the state of time t given past observations. They characterize the limit of their error sequence {ε_t, t=0,1,. . .} and obtain some related rates of convergence; a complete analysis is provided for the scalar case. The discussion is based on explicit representations for the MMSE and LMSE estimates, recently obtained by the authors, which display the dependence of these quantities on the initial distribution

Keywords

discrete time systems; filtering and prediction theory; linear systems; state estimation; Kalman filters; LMSE estimates; MMSE estimates; convergence; discrete-time linear systems; error sequence; filtering; nonGaussian initial conditions; one-step prediction problem; state estimation; Convergence; Covariance matrix; Displays; Filtering; Kalman filters; Linear systems; Nonlinear filters; State estimation; Stochastic systems; White noise;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.109645

Filename

109645