  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 can then be estimated by an order selection procedure.
As the problem can be severely ill posed, a stochastic perturbation method is
proposed which provides better results than Maximum Likelihood based methods
when the signal-to-noise ratio is low. The method depends on some
hyperparameters which turn out to be essentially independent of the
application. Therefore they can be fixed once and for all, giving rise to a
black box method.
