Linear optimal full-order estimators for discrete-time stochastic uncertain systems with packet losses
MA Jing
SUN Shu-li
Abstract：We investigate the state estimation problem for discrete-time stochastic linear systems with packet losses and stochastic uncertainties. Packet losses are random with Bernoulli distribution, and the stochastic uncertainties in system matrix are represented by white multiplicative noises. Firstly, the unbiased optimal linear recursive full-order filters in the least-mean-squares (LMS) sense are designed via the method of completing square. The proposed filters employ the measurements received at the present instant and the last instant to guarantee the linear optimality. It is shown that the derived linear filters have less computational burden when compared with polynomial filters and augmented filters. Then, the linear optimal predictor and smoother are also given on the basis of the linear filters. Further, the asymptotic stability of the linear optimal estimators is studied. A sufficient condition to guarantee the steady-state property is obtained. Finally, we use two simulation examples to demonstrate the advantages of the derived estimation algorithms.
Keywords：linear optimal estimatorstochastic uncertain systemmultiplicative noisepacket losssteady-state estima-tor
Publication Date：2014-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：9( 764-772 )