A black box method for solving the complex exponentials approximation problem

TL;DR

This paper introduces a black box stochastic perturbation method for estimating the parameters and number of damped sinusoids in noisy data, outperforming traditional maximum likelihood approaches at low signal-to-noise ratios.

Contribution

It proposes a novel black box approach that is robust to noise and independent of application-specific hyperparameters for complex exponentials approximation.

Findings

Better performance than maximum likelihood methods at low SNR

Hyperparameters are application-independent and fixed

Effective in estimating the number and parameters of damped sinusoids

Abstract

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.