# Bayesian Pitch Tracking Based on the Harmonic Model

## TL;DR

This paper introduces a Bayesian fundamental frequency tracking method using the harmonic model and Markov processes, improving robustness and accuracy over existing methods, especially in noisy conditions.

## Contribution

It proposes a novel Bayesian algorithm that incorporates temporal smoothness priors for fundamental frequency, model order, and voicing, enhancing estimation accuracy and noise robustness.

## Key findings

- Reduces mean absolute errors by 15-36% compared to state-of-the-art methods.
- Decreases gross errors by 20-26% in noisy conditions.
- Achieves superior performance on speech and voice datasets, including Parkinson's disease voices.

## Abstract

Fundamental frequency is one of the most important characteristics of speech and audio signals. Harmonic model-based fundamental frequency estimators offer a higher estimation accuracy and robustness against noise than the widely used autocorrelation-based methods. However, the traditional harmonic model-based estimators do not take the temporal smoothness of the fundamental frequency, the model order, and the voicing into account as they process each data segment independently. In this paper, a fully Bayesian fundamental frequency tracking algorithm based on the harmonic model and a first-order Markov process model is proposed. Smoothness priors are imposed on the fundamental frequencies, model orders, and voicing using first-order Markov process models. Using these Markov models, fundamental frequency estimation and voicing detection errors can be reduced. Using the harmonic model, the proposed fundamental frequency tracker has an improved robustness to noise. An analytical form of the likelihood function, which can be computed efficiently, is derived. Compared to the state-of-the-art neural network and non-parametric approaches, the proposed fundamental frequency tracking algorithm reduces the mean absolute errors and gross errors by 15\% and 20\% on the Keele pitch database and 36\% and 26\% on sustained /a/ sounds from a database of Parkinson's disease voices under 0 dB white Gaussian noise. A MATLAB version of the proposed algorithm is made freely available for reproduction of the results\footnote{An implementation of the proposed algorithm using MATLAB may be found in \url{https://tinyurl.com/yxn4a543}