{"title":"子空间估计的渐近方差","authors":"A. Chiuso, G. Picci","doi":"10.1109/CDC.2001.980485","DOIUrl":null,"url":null,"abstract":"We provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices /spl Sigma/(xx|u/sup +/), /spl Sigma/(u/sup +/u/sup +/|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc.","PeriodicalId":131411,"journal":{"name":"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Asymptotic variances of subspace estimates\",\"authors\":\"A. Chiuso, G. Picci\",\"doi\":\"10.1109/CDC.2001.980485\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices /spl Sigma/(xx|u/sup +/), /spl Sigma/(u/sup +/u/sup +/|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc.\",\"PeriodicalId\":131411,\"journal\":{\"name\":\"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2001.980485\",\"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 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2001.980485","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices /spl Sigma/(xx|u/sup +/), /spl Sigma/(u/sup +/u/sup +/|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc.
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