Linear minimum mean square error estimation for discrete-time Markovian jump linear systems

The linear minimum mean square error estimator (LMMSE) for discrete-time linear systems subject to abrupt changes in the parameters modeled by a Markov chain /spl theta/(k)/spl epsiv/{1...,N} is considered. The filter equations are derived from geometric arguments in a recursive form, resulting in a...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 39; no. 8; pp. 1685 - 1689
Main Author: Costa, O.L.V.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.1994
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Brazil Council
Computer science; control theory; systems
Control theory. Systems
Equations
Estimation error
Exact sciences and technology
Linear systems
Mean square error methods
Modelling and identification
Noise reduction
Nonlinear filters
State estimation
Uncertainty
Vectors
Markov chain
Linear system
Least squares method
Jump process
Discrete system
Linear estimation
State estimation
Recursive filtering
ISSN:0018-9286
Online Access:Get full text
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Summary:The linear minimum mean square error estimator (LMMSE) for discrete-time linear systems subject to abrupt changes in the parameters modeled by a Markov chain /spl theta/(k)/spl epsiv/{1...,N} is considered. The filter equations are derived from geometric arguments in a recursive form, resulting in an on-line algorithm suitable for computer implementation. The author's approach is based on estimating x(k)1/sub {/spl theta/(k/=i}) instead of estimating directly x(k). The uncertainty introduced by the Markovian jumps increases the dimension of the filter to N(n+1), where n is the dimension of the state variable. An example where the dimension of the filter can be reduced to n is presented, as well as a numerical comparison with the IMM filter.< >
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ISSN:0018-9286
DOI:10.1109/9.310052