Robust Bayesian Pitch Tracking Based on the Harmonic Model

Liming Shi, Jesper Kjaer Nielsen, Jesper Rindom Jensen, Max A. Little, Mads Graesboll Christensen

Research output: Contribution to journalArticlepeer-review


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 nonparametric approaches, the proposed fundamental frequency tracking algorithm has superior performance in almost all investigated scenarios, especially in noisy conditions. For example, under 0 dB white Gaussian noise, the proposed 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. A MATLAB version of the proposed algorithm is made freely available for reproduction of the results. 1 1An implementation of the proposed algorithm using MATLAB may be found in

Original languageEnglish
Article number8771212
Pages (from-to)1737-1751
Number of pages15
JournalIEEE/ACM Transactions on Audio, Speech, and Language Processing
Issue number11
Early online date24 Jul 2019
Publication statusPublished - 1 Nov 2019

Bibliographical note

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Funding: Danish Council for Independent Research, grant ID: DFF 4184-00056.


  • Fundamental frequency or pitch tracking
  • Markov process
  • harmonic model
  • harmonic order
  • voiced-unvoiced detection


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