Exact maximum likelihood estimation of superimposed exponential signals in noise

Abstract

A unified framework for the exact Maximum Likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the single and the multiexperiment cases (respectively the time series and the array problems), is presented. An exact expression for the ML criterion is derived in terms of the prediction polynomial of the noiseless signal, and an iterative algorithm for the maximization of this criterion is presented. A simulation example shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques.