A fast algorithm for maximum likelihood-based fundamental frequency estimation

Periodic signals are encountered in many applications. Such signals can be modelled by a weighted sum of sinusoidal components whose frequencies are integer multiples of a fundamental frequency. Given a data set, the fundamental frequency can be estimated in many ways including a maximum likelihood (ML) approach. Unfortunately, the ML estimator has a very high computational complexity, and the more inaccurate, but faster correlation-based estimators are therefore often used instead. In this paper, we propose a fast algorithm for the evaluation of the ML cost function for complex-valued data over all frequencies on a Fourier grid and up to a maximum model order. The proposed algorithm significantly reduces the computational complexity to a level not far from the complexity of the popular harmonic summation method which is an approximate ML estimator.