On the accuracy of the Kumaresan-Tufts method for estimating complex damped exponentials

Abstract

Recently, Kumaresan and Tufts (KT) presented a method for estimating the parameters of damped exponential waveforms in additive white noise. The KT method uses singular value decomposition (SVD) of the data matrix, with truncation and backward prediction to improve the accuracy of the estimates. The KT method was demonstrated to have a very good performance, in comparison to traditional methods used for the same problem (e.g., Prony's method). Kumaresan and Tufts also showed, by numerical simulations, that the variances of the estimates obtained by their method approaches the Cramer-Rao lower bounds for selected test cases. In this correspondence, we provide a quantitative accuracy analysis of the KT method. The analysis is based on first-order Taylor series approximations of the estimated parameters around their true values. No assumptions are made on the number of data points used, but it is assumed that the noise level is small enough for the first-order approximations to be valid. Results of the analysis are illustrated by some numerical examples. These results confirm the good performance of the KT method, and show the effect of the user-chosen parameters on the accuracy of the estimates.