A Prony method for noisy data: Choosing the signal components and selecting the order in exponential signal models

Abstract

Prony's method is a simple procedure for determining the values of parameters of a linear combination of exponential functions. Until recently, even the modern variants of this method have performed poorly in the presence of noise. We have discovered improvements to Prony's method which are based on low-rank approximations to data matrices or estimated correlation matrices [6]-[8], [15]-[27], [34]. Here we present a different, often simpler procedure for estimation of the signal parameters in the presence of noise. This procedure has received only limited dissemination [35]. It is very close in form and assumptions to Prony's method. However, in preliminary tests, the performance of the method is close to that of the best available, more complicated, approaches which are based on maximum likelihood or on the use of eigenvector or singular value decompositions.