  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}
