Toward an automatic method of modal analysis

A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which is then estimated by an order selection procedure. It turns out that Maximum Likelihood estimators are biased in this specific case. The idea pursued here is to cope with the bias, by a stochastic perturbation method, in order to get an estimator with smaller Mean Squared Error than the Maximum Likelihood one. Moreover the problem of estimating the number of damped sinusoids and the problem of estimating their parameters are solved jointly. The method is automatic, provided that a few hyperparameters have been chosen, and faster than standard best alternatives. MSC: 30E10, 65C60