A modified prony algorithm for estimating sinusoidal frequencies

Abstract

We investigate the modified Prony algorithm of Osborne and Smyth (1991, 1993) applied to the estimation of the frequency of oscillation of a sinusoidal signal with added white noise. and compare it with the algorithms usually associated with the names of Prony and Pisarenko. We show that the Pisarenko algorithm returns O(N-1/2) consistent estimates and that the modified Prnoy algorithm returns the least squares estimates which are O(N-3/2) consistent. The transfer function parameter estimates that are retured by these algorithms converge to the true values at the same rate as the frequency estimates in each case. A concise expression for the asymptotic covariance matrix of these estimates is..