Use of particle filtering and MCMC for inference in Probabilistic Acoustic Tube model

The Probabilistic Acoustic Tube (PAT) model is a probabilistic generative model of speech. By associating every generative parameter with a probability distribution, it becomes possible to convert every standard speech analysis task into a probabilistic inference task, thereby grounding every such task with quantifiable measures of bias and consistency. The previously published PAT model did not adequately model AM-FM and therefore phase of the voice source. In this paper, we model the AM-FM of the voice source using an autoregressive process. The resulting model is a non-linear state-space model and thus has no closed-form inference algorithm, but effective inference can be achieved by using Auxiliary Particle Filtering (APF) and Taylor expansion assisted Markov Chain Monte Carlo (MCMC). Results demonstrate that, unlike previous speech models, this model is able to account for the phase of the voice source, achieving signal reconstruction with 8.79dB SNR.