用于块导向系统识别的非参数工具变量

G. Mzyk
{"title":"用于块导向系统识别的非参数工具变量","authors":"G. Mzyk","doi":"10.2478/amcs-2013-0040","DOIUrl":null,"url":null,"abstract":"Abstract A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.","PeriodicalId":253470,"journal":{"name":"International Journal of Applied Mathematics and Computer Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Nonparametric instrumental variables for identification of block-oriented systems\",\"authors\":\"G. Mzyk\",\"doi\":\"10.2478/amcs-2013-0040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.\",\"PeriodicalId\":253470,\"journal\":{\"name\":\"International Journal of Applied Mathematics and Computer Sciences\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Mathematics and Computer Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/amcs-2013-0040\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics and Computer Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/amcs-2013-0040","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5

摘要

摘要针对NARMAX系统的一种特殊情况,提出了一种参数-非参数联合辨识算法。将各个块的参数聚合在一个矩阵中(包括参数的混合积)。利用非参数核方法生成的仪器,采用工具变量技术对矩阵进行估计。最后对结果进行分解,得到系统元素的参数。证明了所提估计的一致性,并分析了其收敛速度。建立了最优工具变量的形式,并提出了最优工具变量的近似生成方法。非参数生成工具变量的思想保证了ivv估计的良好定义,改善了最小二乘法的行为,并允许减少估计误差。该方法实现简单,对相关噪声具有较强的鲁棒性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonparametric instrumental variables for identification of block-oriented systems
Abstract A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信