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Abstract and Applied Analysis
Volume 2014, Article ID 716716, 10 pages
Research Article

Optimal Kalman Filtering for a Class of State Delay Systems with Randomly Multiple Sensor Delays

Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received 17 March 2014; Accepted 29 March 2014; Published 24 April 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 Dongyan Chen and Long Xu. 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.


The optimal Kalman filtering problem is investigated for a class of discrete state delay stochastic systems with randomly multiple sensor delays. The phenomenon of measurement delay occurs in a random way and the delay rate for each sensor is described by a Bernoulli distributed random variable with known conditional probability. Based on the innovative analysis approach and recursive projection formula, a new linear optimal filter is designed such that, for the state delay and randomly multiple sensor delays with different delay rates, the filtering error is minimized in the sense of mean square and the filter gain is designed by solving the recursive matrix equation. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed filtering scheme.