Modeling and estimation of discrete-time Gaussian reciprocal processes

Author

Levy, Bernard C. ; Frezza, Ruggero ; Krener, Arthur J.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Davis, CA, USA

Volume

35

Issue

9

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

1013

Lastpage

1023

Abstract

Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process

Keywords

Markov processes; boundary-value problems; state-space methods; Markov processes; correlation; discrete-time Gaussian reciprocal processes; modelling; second-order model; smoothing problem; state-space models; two-point boundary-value nearest-neighbor model; Context modeling; Differential equations; Gaussian noise; Gaussian processes; Markov processes; Markov random fields; Mathematics; Random processes; Smoothing methods; Stochastic processes;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.58529

Filename

58529