指数信号模型中参数的稳健估计

 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。

Robust Estimation of the Parameters in Damped Exponential Signal Model

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.