{"title":"基于稳定核尺寸自适应的最大熵卡尔曼滤波","authors":"Vahid Azimi , Simona Onori","doi":"10.1016/j.sysconle.2025.106198","DOIUrl":null,"url":null,"abstract":"<div><div>The state-of-the-art maximum correntropy Kalman filter (MCKF) that incorporates Gaussian kernels into its formulation is a powerful estimation technique to robustify the traditional Kalman filter (KF) against non-Gaussian noises. However, improper selection of <em>kernel sizes</em> may either degrade the estimation performance or slow down the convergence rate. This paper extends and encompasses the baseline MCKF through the development of a projection-based adaptive MCKF (PAMCKF) for continuous-time linear systems with a class of non-Gaussian noises: measurement outliers that are mainly due to sensor failures, cyber-attacks, etc We suggest an adaptation mechanism that exploits the innovation signals to update “on-line” the <em>kernel sizes</em>. The proposed adaptive method is then unified with a modified version of MCKF to achieve robust estimation with low computational effort against measurement outliers without the need for knowing their bounds <em>a priori</em>. The main contribution of this paper is that state and <em>kernel size</em> estimation errors are uniformly ultimately bounded which is formally proven using a deterministic Lyapunov stability argument. Simulations and comparisons to KF and MCKF are carried out to validate the theoretical results and demonstrate the benefits of the proposed filter.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106198"},"PeriodicalIF":2.1000,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stable kernel size adaptation-based maximum correntropy Kalman filter\",\"authors\":\"Vahid Azimi , Simona Onori\",\"doi\":\"10.1016/j.sysconle.2025.106198\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The state-of-the-art maximum correntropy Kalman filter (MCKF) that incorporates Gaussian kernels into its formulation is a powerful estimation technique to robustify the traditional Kalman filter (KF) against non-Gaussian noises. However, improper selection of <em>kernel sizes</em> may either degrade the estimation performance or slow down the convergence rate. This paper extends and encompasses the baseline MCKF through the development of a projection-based adaptive MCKF (PAMCKF) for continuous-time linear systems with a class of non-Gaussian noises: measurement outliers that are mainly due to sensor failures, cyber-attacks, etc We suggest an adaptation mechanism that exploits the innovation signals to update “on-line” the <em>kernel sizes</em>. The proposed adaptive method is then unified with a modified version of MCKF to achieve robust estimation with low computational effort against measurement outliers without the need for knowing their bounds <em>a priori</em>. The main contribution of this paper is that state and <em>kernel size</em> estimation errors are uniformly ultimately bounded which is formally proven using a deterministic Lyapunov stability argument. Simulations and comparisons to KF and MCKF are carried out to validate the theoretical results and demonstrate the benefits of the proposed filter.</div></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":\"204 \",\"pages\":\"Article 106198\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-07-16\",\"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/S016769112500180X\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016769112500180X","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}
Stable kernel size adaptation-based maximum correntropy Kalman filter
The state-of-the-art maximum correntropy Kalman filter (MCKF) that incorporates Gaussian kernels into its formulation is a powerful estimation technique to robustify the traditional Kalman filter (KF) against non-Gaussian noises. However, improper selection of kernel sizes may either degrade the estimation performance or slow down the convergence rate. This paper extends and encompasses the baseline MCKF through the development of a projection-based adaptive MCKF (PAMCKF) for continuous-time linear systems with a class of non-Gaussian noises: measurement outliers that are mainly due to sensor failures, cyber-attacks, etc We suggest an adaptation mechanism that exploits the innovation signals to update “on-line” the kernel sizes. The proposed adaptive method is then unified with a modified version of MCKF to achieve robust estimation with low computational effort against measurement outliers without the need for knowing their bounds a priori. The main contribution of this paper is that state and kernel size estimation errors are uniformly ultimately bounded which is formally proven using a deterministic Lyapunov stability argument. Simulations and comparisons to KF and MCKF are carried out to validate the theoretical results and demonstrate the benefits of the proposed filter.
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.