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Type: Journal article
Title: Convergence of optimal linear estimator with multiplicative and time-correlated additive measurement noises
Author: Liu, W.
Shi, P.
Citation: IEEE Transactions on Automatic Control, 2019; 64(5):2190-2197
Publisher: IEEE
Issue Date: 2019
ISSN: 0018-9286
Statement of
Wei Liu, Peng Shi
Abstract: In this paper, the problem of convergence for the optimal linear estimator of discrete-time linear systems with multiplicative and time-correlated additive measurement noises is studied. By defining a new random vector that consists of the innovation, error, and part of the noise in the new measurement obtained from the measurement differencing method, we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose. It is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and, moreover, this fixed point can be obtained by solving a set of matrix equations.
Keywords: Convergence; multiplicative noises; optimal linear estimator; state error covariance matrix; time correlated
Rights: © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
DOI: 10.1109/TAC.2018.2869467
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Electrical and Electronic Engineering publications

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