首页|Stability and performance analysis of the compressed Kalman filter algorithm for sparse stochastic systems

Stability and performance analysis of the compressed Kalman filter algorithm for sparse stochastic systems

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This paper considers the problem of estimating unknown sparse time-varying signals for stochastic dynamic systems.To deal with the challenges of extensive sparsity,we resort to the compressed sensing method and propose a compressed Kalman filter(KF)algorithm.Our algorithm first compresses the original high-dimensional sparse regression vector via the sensing matrix and then obtains a KF estimate in the compressed low-dimensional space.Subsequently,the original high-dimensional sparse signals can be well recovered by a reconstruction technique.To ensure stability and establish upper bounds on the estimation errors,we introduce a compressed excitation condition without imposing independence or stationarity on the system signal,and therefore suitable for feedback systems.We further present the performance of the compressed KF algorithm.Specifically,we show that the mean square compressed tracking error matrix can be approximately calculated by a linear deterministic difference matrix equation,which can be readily evaluated,analyzed,and optimized.Finally,a numerical example demonstrates that our algorithm outperforms the standard uncompressed KF algorithm and other compressed algorithms for estimating high-dimensional sparse signals.

sparse signalcompressed sensingKalman filter algorithmcompressed excitation conditionstochastic stabilitytracking performance

LI RongJiang、GAN Die、XIE SiYu、Lü JinHu

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Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

Zhongguancun Laboratory,Beijing 100049,China

School of Aeronautics and Astronautics,University of Electronic Science and Technology of China,Chengdu 611731,China

School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China

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National Key Research and Development Program of ChinaNational Natural science Foundation of ChinaNational Natural science Foundation of ChinaChina Postdoctoral Science FoundationMajor Key Project of Peng Cheng Laboratory

2022YFB330560061621003621416042022M722926PCL2023AS1-2

2024

10.1007/s11431-023-2514-6

中国科学:技术科学(英文版)
中国科学院

中国科学:技术科学(英文版)

CSTPCDEI
影响因子：1.056
ISSN：1674-7321
年,卷(期)：2024.67(2)
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