{"title":"The solution to the Lyapunov equation in constant gain filtering and some of its applications","authors":"John E. Gray, A. S. Smith-Carroll, L. A. Jordan","doi":"10.1109/SSST.2004.1295612","DOIUrl":null,"url":null,"abstract":"Presented in this paper is a solution to the Lyapunov equation in constant gain filtering. A specific method for deriving the noise reduction ratios for the alpha-beta and alpha-beta-gamma filters are explored using the Lyapunov equation. This enables us to simplify the computation drastically. For a 2 /spl times/ 2 matrix, one has to solve for one unknown instead of two. For a 3 /spl times/ 3 matrix, one has to solve for three unknowns instead of six and so on. Thus reduction in the number of variables has considerable advantage for higher dimensional filters such as the alpha-beta-gamma filter.","PeriodicalId":309617,"journal":{"name":"Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SSST.2004.1295612","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
Presented in this paper is a solution to the Lyapunov equation in constant gain filtering. A specific method for deriving the noise reduction ratios for the alpha-beta and alpha-beta-gamma filters are explored using the Lyapunov equation. This enables us to simplify the computation drastically. For a 2 /spl times/ 2 matrix, one has to solve for one unknown instead of two. For a 3 /spl times/ 3 matrix, one has to solve for three unknowns instead of six and so on. Thus reduction in the number of variables has considerable advantage for higher dimensional filters such as the alpha-beta-gamma filter.
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