Statistically consistent frequency estimation using linear prediction

Abstract

A new statistically consistent frequency estimation method has been developed and presented using linear prediction (LP) method. The observed signal is assumed to be a sum of complex exponentials with white random noise process. The number of complex exponentials is assumed to be known. A statistically consistent estimator is an estimator that converges to the true value as the number of observations increases to infinite. It is shown that conventional LP-based estimation methods such as Prony's method are not consistent statistically. It is also proved that the new estimation method provides statistically consistent estimates and performs better than Prony's estimation method. Numerical simulation is provided to confirm the performance of the new estimation method and its statistical consistency. >