{"title":"Analysis of the Compressed Distributed Kalman Filter Over Markovian Switching Topology","authors":"Rongjiang Li;Die Gan;Siyu Xie;Haibo Gu;Jinhu Lü","doi":"10.1109/TCYB.2024.3507275","DOIUrl":null,"url":null,"abstract":"This article investigates the distributed estimation problem of an unknown high-dimensional sparse state vector for a stochastic dynamic system. The communication topology randomly switches, and the switching law is governed by a time-homogeneous Markovian chain. By means of the compressed sensing (CS) theory and a diffusion strategy, we propose a compressed distributed Kalman filter (CDKF). That is, each sensor first compresses the original high-dimensional regression data. Then, the covariance intersection fusion rule is utilized to obtain a distributed Kalman filter (DKF) estimate in the compressed low-dimensional space. Afterward, the original high-dimensional sparse state vector can be well recovered by a reconstruction technique. In terms of stability analysis, one of the main difficulties lies in analyzing the product of nonindependent and nonstationary random matrices in the context of time-varying communication topologies. Relying on the stochastic stability theory, the Markov chain theory, and the CS theory, we establish the upper bound for the estimation error under the compressed cooperative excitation condition, which is much weaker than the traditional uncompressed collective observability conditions used in the existing literature. Finally, we provide a simulation example to illustrate the performance of the proposed algorithm.","PeriodicalId":13112,"journal":{"name":"IEEE Transactions on Cybernetics","volume":"55 3","pages":"1372-1384"},"PeriodicalIF":9.4000,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Cybernetics","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10804850/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This article investigates the distributed estimation problem of an unknown high-dimensional sparse state vector for a stochastic dynamic system. The communication topology randomly switches, and the switching law is governed by a time-homogeneous Markovian chain. By means of the compressed sensing (CS) theory and a diffusion strategy, we propose a compressed distributed Kalman filter (CDKF). That is, each sensor first compresses the original high-dimensional regression data. Then, the covariance intersection fusion rule is utilized to obtain a distributed Kalman filter (DKF) estimate in the compressed low-dimensional space. Afterward, the original high-dimensional sparse state vector can be well recovered by a reconstruction technique. In terms of stability analysis, one of the main difficulties lies in analyzing the product of nonindependent and nonstationary random matrices in the context of time-varying communication topologies. Relying on the stochastic stability theory, the Markov chain theory, and the CS theory, we establish the upper bound for the estimation error under the compressed cooperative excitation condition, which is much weaker than the traditional uncompressed collective observability conditions used in the existing literature. Finally, we provide a simulation example to illustrate the performance of the proposed algorithm.
期刊介绍:
The scope of the IEEE Transactions on Cybernetics includes computational approaches to the field of cybernetics. Specifically, the transactions welcomes papers on communication and control across machines or machine, human, and organizations. The scope includes such areas as computational intelligence, computer vision, neural networks, genetic algorithms, machine learning, fuzzy systems, cognitive systems, decision making, and robotics, to the extent that they contribute to the theme of cybernetics or demonstrate an application of cybernetics principles.