Statistical Analysis Of True And Extraneous Mode Estimates For The TLS-Prony Algorithm

In this paper we present a statistical analysis of the poles and amplitude coefficients estimated using a TLS-Prony method where signals consist of arbitrary damped exponential terms in noise. Both the true and extraneous modes are considered in the analysis. The derivation for this procedure is based on a first order perturbation analysis; thus the analysis assumes high SNR. We derive the complete covariance matrix for the estimated pole and amplitude coefficient parameters. We also develop the statistics of the mode energies for both the true and extraneous modes. To first order the distributions of the true mode energies are well approximated by Gaussian distributions, and the energies of the extraneous modes are central Ø 2 distributed. We verify the theory with Monte-Carlo simulations. 1. INTRODUCTION The problem of estimating model parameters of noisy exponential signals has been an area of considerable attention in the past few years. This problem has applications in a number..