A method of producing at least one possible sequence of vocal tract resonance (VTR) for a fixed sequence of phonetic units, and producing the acoustic observation probability by integrating over such distributions is provided. The method includes identifying a sequence of target distributions for a VTR sequence corresponding to a phone sequence with a given segmentation. The sequence of target distributions is applied to a finite impulse response filter to produce distributions for possible VTR trajectories. Then these distributions are applied to a linearized nonlinear function to produce the acoustic observation probability for the given sequence of phonetic units. This acoustic observation probability is used for phonetic recognition.
Acoustic models with structured hidden dynamics with integration over many possible hidden trajectories