## 1 Introduction  
Parametric representation of speech often implies a fundamental frequency (also referred to as F0 or pitch) contour as a part of the text-to-speech (TTS) synthesis. During voiced speech, such as vowels, pitch values can be successfully estimated over a short time period (e.g., a speech frame of 25 ms). Pitch observations are continuous and usually range from 60 Hz to 300 Hz for human speech [1]. However, in unvoiced speech, such as unvoiced consonants, the long-term spectrum of turbulent airflow tends to be a weak function of frequency [2], which suggests that the identification of a single reliable F0 value in unvoiced regions is not possible. Thus, a commonly accepted assumption is that F0 values in unvoiced speech frames are undefined and must instead be represented by a sequence of discrete unvoiced symbols [3]. In other words, F0 is a discontinuous function of time and voicing classification is made through pitch estimation. In standard TTS with the mixed-excitation system, frames classified as voiced will be excited with a combination of glottal pulses and noise while frames classified as unvoiced will just be excited with noise. Consequently, any hard voiced/unvoiced (V/UV) classification gives two categories of errors: false voiced, i.e., setting frames to voiced that should be unvoiced, and false unvoiced, i.e., setting frames to unvoiced that are voiced. Perceptually, the synthesized speech with false voiced produces buzziness, mostly in the higher frequencies, while false unvoiced introduces a hoarse quality in the speech signal. Generally, both of them sound unnatural [4]. One solution is to directly model the discontinuous F0 observation with multi-space probability distribution using hidden Markov models (MSD-HMM) [5]. However, MSD-HMM has some restrictions with dynamic features that cannot be easily calculated due to the discontinuity at the boundary between V/UV regions. Hence, separate streams are normally used to model static and dynamic features [6]. However, this also limits the model's ability to correctly capture F0 trajectories. An alternative solution, random values generated from a probability density with a large variance have been used for unvoiced F0 observations [7], while setting all unvoiced F0 to be zero has been investigated in [8]. Once again, both of these techniques are inappropriate for the TTS system, since it would lead to a synthesis of random or meaningless F0 [9]. In recent years, there has been a rising trend of assuming that continuous F0 observations are similarly present in unvoiced regions, and there have been various modeling schemes along these lines. It was found in [3] that a continuous F0 creates more expressive F0 contours with HMM-based TTS than one based on the MSD-HMM system. [PERSON] et al. [10] introduced a new approach to improve piece-wise modeling of the continuous F0 trajectory with voicing strength and V/UV decision for HMM-based TTS. [PERSON] et al. [9], whose baseline method is used in this study, proposed a simple continuous F0 tracker, where the measurement distribution is determined from the autocorrelation coefficients. This algorithm is better suited to the Bayesian pitch estimation of [PERSON] et al. [11]. [PERSON] and [PERSON] [12] have shown that continuous F0 contour can be better approximated with HMM and deep neural network (DNN) than traditional discontinuous F0. In [13], an excitation model has been proposed which combines continuous F0 modeling with Maximum Voiced Frequency (MVF). This model has been shown to produce more natural synthesized speech for voiced sounds than traditional vocoders based on standard pitch tracking, whereas it was also found that there is a room for improvement in modeling unvoiced sounds. Recently, [PERSON] et al. [14] developed a robust method for adaptively weighting the estimates of F0 values using an adaptive Kalman filter framework, while [PERSON] et al. [15] proposed an F0 method by applying a time warp on the input speech signal in each step.