Exact Maximum Likelihood Parameter Estimation of Superimposed Exponential Signals in Noise

A unified framework is presented for the exact maximum-likelihood (ML) estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems. An exact expression for the ML criterion is derived in terms of the linear prediction polynomial of the signal, and an iterative algorithm for the maximization of this criterion is presented. The algorithm is equally applicable in the case of signal coherence in the array problem. Simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques. In addition to its practical value, the present formulation is used to interpret previous methods.