{"title":"Steady state analysis for Kalman filters with Poisson-sampled observations","authors":"Anubhab Dasgupta , Aneel Tanwani","doi":"10.1016/j.sysconle.2025.106209","DOIUrl":null,"url":null,"abstract":"<div><div>We study optimal filtering for continuous-time linear stochastic systems with Poisson-sampled observation processes. For each realization of the sampled observation process, the posterior distribution is a Gaussian process whose mean and covariance are described by continuous-discrete process. We are particularly interested in analyzing the expectation of the first and second moment of the estimation error with respect to the sampling process. Using the system-theoretic properties like observability and controllability, our results provide tractable conditions on the mean sampling rate for convergence of the expected error covariance, its boundedness and convergence of expected estimation error to zero. Some comparisons are also drawn with the solution of Riccati differential equation associated with the continuous-observation process.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106209"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125001914","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
We study optimal filtering for continuous-time linear stochastic systems with Poisson-sampled observation processes. For each realization of the sampled observation process, the posterior distribution is a Gaussian process whose mean and covariance are described by continuous-discrete process. We are particularly interested in analyzing the expectation of the first and second moment of the estimation error with respect to the sampling process. Using the system-theoretic properties like observability and controllability, our results provide tractable conditions on the mean sampling rate for convergence of the expected error covariance, its boundedness and convergence of expected estimation error to zero. Some comparisons are also drawn with the solution of Riccati differential equation associated with the continuous-observation process.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.