A black box method for solving the complex exponentials approximation problem
This work addresses the problem of parameter estimation for damped sinusoids in low SNR conditions, offering an alternative to Maximum Likelihood methods for practitioners in signal processing.
The paper proposes a stochastic perturbation method for estimating the number and parameters of exponentially damped sinusoids from noisy data, achieving better results than Maximum Likelihood methods at low signal-to-noise ratios. The method is designed as a black box with fixed hyperparameters.
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.