{"title":"非线性系统的广义正则变量分析","authors":"W. Larimore","doi":"10.1109/CDC.1988.194622","DOIUrl":null,"url":null,"abstract":"The canonical variate analysis (CVA) is extended to general nonlinear systems. Nonlinear canonical variables are shown to determine the optimum nonlinear transformation of the past maximizing the mutual information between the true and an approximating normal distribution. A sequential procedure for selection of the canonical variables is described. Nonlinear CVA is applied to nonlinear controlled Markov processes to obtain approximating nonlinear filters. A recursive innovations representation is given for the nonlinear filter that also yields an innovations representation for the Markov process model.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"744 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Generalized canonical variate analysis of nonlinear systems\",\"authors\":\"W. Larimore\",\"doi\":\"10.1109/CDC.1988.194622\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The canonical variate analysis (CVA) is extended to general nonlinear systems. Nonlinear canonical variables are shown to determine the optimum nonlinear transformation of the past maximizing the mutual information between the true and an approximating normal distribution. A sequential procedure for selection of the canonical variables is described. Nonlinear CVA is applied to nonlinear controlled Markov processes to obtain approximating nonlinear filters. A recursive innovations representation is given for the nonlinear filter that also yields an innovations representation for the Markov process model.<<ETX>>\",\"PeriodicalId\":113534,\"journal\":{\"name\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"volume\":\"744 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1988.194622\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 27th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1988.194622","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalized canonical variate analysis of nonlinear systems
The canonical variate analysis (CVA) is extended to general nonlinear systems. Nonlinear canonical variables are shown to determine the optimum nonlinear transformation of the past maximizing the mutual information between the true and an approximating normal distribution. A sequential procedure for selection of the canonical variables is described. Nonlinear CVA is applied to nonlinear controlled Markov processes to obtain approximating nonlinear filters. A recursive innovations representation is given for the nonlinear filter that also yields an innovations representation for the Markov process model.<>
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