# American Institute of Mathematical Sciences

January  2011, 7(1): 79-85. doi: 10.3934/jimo.2011.7.79

## State estimation for discrete linear systems with observation time-delayed noise

 1 School of Control Science and Engineering, Shandong University, Jinan 250000, China 2 Department of Information Science and Technology, Taishan University, Taian 271021, China 3 School of Mathematics, Shandong University, Jinan 250000, China

Received  July 2010 Revised  September 2010 Published  January 2011

State estimation problem is discussed for discrete-time systems with delays in measurement noise sequence, which is usually seen in network control and geophysical prospecting systems. An optimal recursive filter is derived via state augmentation. Dimensions of the optimal filter just are the sum of dimensions of state and observation vector. Therefore, they are not related to the size of delay. Besides, a sub-optimal recursive filter with same dimension as the original state is designed. The sub-optimal filter realizes instant optimization at current time. One example shows the effectiveness of the proposed approach.
Citation: Peng Cui, Hongguo Zhao, Jun-e Feng. State estimation for discrete linear systems with observation time-delayed noise. Journal of Industrial & Management Optimization, 2011, 7 (1) : 79-85. doi: 10.3934/jimo.2011.7.79
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