航空学报 > 2003, Vol. 24 Issue (5): 439-442

指数信号模型中参数的稳健估计

温显斌1,3, 田铮2,3, 林伟2   

  1. 1. 西北工业大学计算机科学与工程系, 陕西西安?? 710072;2. 西北工业大学数学与信息科学系, 陕西西安?? 710072;3. 中科院自动化所模式识别国家重点实验室, 北京?? 100080
  • 收稿日期:2003-06-03 修回日期:2003-07-18 出版日期:2003-10-25 发布日期:2003-10-25

Robust Estimation of the Parameters in Damped Exponential Signal Model

WEN Xian-bin1,3, TIAN Zheng2,3, LIN Wei2   

  1. 1. Department of computer Science and Technology; Northwestern Polytechnical University; Xi'an 710072; China;2. Department of Mathematics and Information Science; Northwestern Polytechnical University; Xi'an 710072; ChinaChinese Academy of Sciences; Beijing 100080; China
  • Received:2003-06-03 Revised:2003-07-18 Online:2003-10-25 Published:2003-10-25

摘要: 给出了阻尼指数信号模型中参数的M 估计和Bootstrap M 估计; 基于Prony 方法给出估计的重新定义和新算法; 并且在较弱的条件下证明了这些估计的相容性; 最后利用Huber 函数给出了两种估计的模拟结果, 结果表明这两种估计的稳健性和精度都比传统的最小二乘估计好。

关键词: 阻尼指数信号模型, Bootstrap, M估计, 强相容性, 稳健

Abstract: Robust estimations o f the parameters in damped ex ponential signals are consider ed when t he no ise distribution is unknown. Two kinds of robust estimation metho ds of the par ameters have been proposed: M-estimationand Bootstrap M estimation. In or der to avo id difficulty of solv ing nonlinear equatio n w ith exponential terms, thelinear par ameters are separated from the nonlinear parameters based on the Prony method, and all the parameters estimation ar e tr anslated into linear parameters estimat ion with no ex ponential terms. Then their asymptot ic performance is investigated. Under mild conditions, strong consistence of the estimations is pro ved. Finally, simulationsof the performance of the est imatio ns using Huber s function are provided w hen the sample size is small, and compar isons among the performances o f the least squares ( LS) estimation, Mestimatio n and the Bootstrap Mestimationare also presented. The results of simulat ion indicate that algor ithms we proposed are better than LS approach.

Key words: damped exponential signal, Bootstrap, M-estimation, strong consistency, Robust

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