Pitch estimation and tracking with harmonic emphasis on the acoustic spectrum

In this paper, we use unconstrained frequency estimates (UFEs) from a noisy harmonic signal and propose two methods to estimate and track the pitch over time. We assume that the UFEs are multivariate-normally-distributed random variables, and derive a maximum likelihood (ML) pitch estimator by maximizing the likelihood of the UFEs over short time-intervals. As the main contribution of this paper, we propose two state-space representations to model the pitch continuity, and, accordingly, we propose two Bayesian methods, namely a hidden Markov model and a Kalman filter. These methods are designed to optimally use the correlations in the consecutive pitch values, where the past pitch estimates are used to recursively update the prior distribution for the pitch variable. We perform experiments using synthetic data as well as a noisy speech recording, and show that the Bayesian methods provide more accurate estimates than the corresponding ML methods.