{"title":"高斯输入Volterra核估计器的性能分析","authors":"A. Redfern, G.T. Zhou","doi":"10.1109/HOST.1997.613508","DOIUrl":null,"url":null,"abstract":"The focus of this paper is on Volterra nonlinear system identification from input-output data. When the system is linear-quadratic and the input is Gaussian, closed-form expressions for the kernels were derived by Tick (1961) based on input-output cross-cumulants. However, there have been no known variance expressions for the kernel estimates. In this paper, we analyze the performance of the first- and second-order kernel estimates when the input is zero-mean white Gaussian, and the additive noise has unknown color and distribution. Closed-form variance expressions are presented and verified by simulations.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Performance analysis of Volterra kernel estimators with Gaussian inputs\",\"authors\":\"A. Redfern, G.T. Zhou\",\"doi\":\"10.1109/HOST.1997.613508\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The focus of this paper is on Volterra nonlinear system identification from input-output data. When the system is linear-quadratic and the input is Gaussian, closed-form expressions for the kernels were derived by Tick (1961) based on input-output cross-cumulants. However, there have been no known variance expressions for the kernel estimates. In this paper, we analyze the performance of the first- and second-order kernel estimates when the input is zero-mean white Gaussian, and the additive noise has unknown color and distribution. Closed-form variance expressions are presented and verified by simulations.\",\"PeriodicalId\":305928,\"journal\":{\"name\":\"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/HOST.1997.613508\",\"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 IEEE Signal Processing Workshop on Higher-Order Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/HOST.1997.613508","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Performance analysis of Volterra kernel estimators with Gaussian inputs
The focus of this paper is on Volterra nonlinear system identification from input-output data. When the system is linear-quadratic and the input is Gaussian, closed-form expressions for the kernels were derived by Tick (1961) based on input-output cross-cumulants. However, there have been no known variance expressions for the kernel estimates. In this paper, we analyze the performance of the first- and second-order kernel estimates when the input is zero-mean white Gaussian, and the additive noise has unknown color and distribution. Closed-form variance expressions are presented and verified by simulations.
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