Statistical analysis of true and extraneous mode estimates for the TLS-Prony algorithm

The authors present a statistical analysis of the poles and amplitude coefficients estimated using a total least squares (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. The complete covariance matrix for the estimated pole and amplitude coefficient parameters is derived. The statistics of the mode energies for both the true and extraneous modes are developed. 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 chi /sup 2/ distributed. The theory was verified with Monte-Carlo simulations.<>