Notes on M-estimation in exponential signal models
Consider the undamped exponential signal model \[ y_n=\sum_{j=1}^p\alpha_je^{\sqrt{-1}\omega_jn}+w_n\,, \] for \(n=1,\ldots,N\), where the \(y_n\) are observed data, the \(\omega_j\) are unknown frequencies, the \(\alpha_j\) are unknown amplitudes and the \(w_n\) are noise terms. The present paper focuses on maximum likelihood-type estimators of the \(\omega_j\), in particular proving asymptotic normality for such estimators under some mild assumptions. The authors also provide a recursive algorithm for the computation of these estimators which gives consistent estimates under mild conditions, and investigate their results using a numerical study.
scientific article; zbMATH DE number 7383346