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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 809734, 11 pages
http://dx.doi.org/10.1155/2015/809734
Research Article

Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays

1Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China
2Department of Computer Science, Brunel University London, Uxbridge, Middlesex UB8 3PH, UK
3Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 4 January 2015; Accepted 25 January 2015

Academic Editor: Zidong Wang

Copyright © 2015 Dongyan Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.