Optimal Filtering for Linear Discrete State Delay Systems Under Uncertain Observations

CHEN Bo;YU Li;ZHANG Wen'an

Journal of Systems Science and Mathematical Sciences ›› 2010, Vol. 30 ›› Issue (6) : 782-791.

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中国科学院数学与系统科学研究院期刊网
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Journal of Systems Science and Mathematical Sciences ›› 2010, Vol. 30 ›› Issue (6) : 782-791. DOI: 10.12341/jssms08996
论文

Optimal Filtering for Linear Discrete State Delay Systems Under Uncertain Observations

  • CHEN Bo, YU Li, ZHANG Wen'an
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Abstract

The optimal filtering problem is investigated for linear discrete state delay systems under uncertain observations. The uncertainty in the observations
is described by a binary distributed random variable and the probability
of the occurrence of missing data is assumed to be known. Generally, this problem can be solved by using the state augmentation and the standard Kalman filtering methods. However, it will result in higher state dimensions and expensive computational cost, especially when the delay is large. Therefore, based on the minimum mean square error (MMSE) estimation principle, a new filter design method is proposed by using the projection theory and recursive projection formula in Hilbert space. The dimension of the designed filter is the same as the original systems. A simulation example illustrates the effectiveness of the proposed approach.

Key words

Optimal filtering / uncertain observations / discrete state delay systems / projection formula.

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CHEN Bo , YU Li , ZHANG Wen'an. Optimal Filtering for Linear Discrete State Delay Systems Under Uncertain Observations. Journal of Systems Science and Mathematical Sciences, 2010, 30(6): 782-791 https://doi.org/10.12341/jssms08996
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