{"title":"恒定增益滤波中李雅普诺夫方程的解及其一些应用","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":"{\"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}","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}
The solution to the Lyapunov equation in constant gain filtering and some of its applications
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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