Notes on M-Estimation in Exponential Signal Models

An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam (IEEE Trans Signal Process 49(2):373–380, 2001), and the estimation was shown to be consistent under mild assumptions. In this paper, the limiting distributions of the M-estimators are investigated. It is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam (IEEE Trans Signal Process 49(2):373–380, 2001). In addition, a recursive algorithm for computing the M-estimators of frequencies is proposed, and the strong consistency of these estimators is established. Monte Carlo simulation studies using Huber’s ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} function are also provided.