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