Kalman-based autoregressive moving average modeling and inference for formant and antiformant tracking

Area of Science:

• Acoustic Phonetics
• Speech Signal Processing
• Statistical Modeling

Background:

• Classical formant tracking relies on point estimates and dynamic programming, lacking uncertainty quantification.
• Existing methods often use ad hoc cost functions for smoothing formant trajectories.

Purpose of the Study:

• To develop a statistically principled state-space framework for estimating vocal tract resonance parameters (center frequencies and bandwidths) with associated uncertainties.
• To improve the accuracy and reliability of formant and antiformant tracking in acoustic speech signals.

Main Methods:

• Utilized Extended Kalman (K) algorithms within a state-space framework to infer formant and antiformant parameters.
• Employed autoregressive moving average (ARMA) cepstral coefficients for parameter estimation.
• Conducted error analysis comparing the KARMA algorithm against Wavesurfer and Praat using a manually marked formant database and synthesized speech.

Main Results:

• The KARMA algorithm demonstrated lower overall root-mean-square error compared to benchmark algorithms in formant tracking.
• KARMA showed effective antiformant tracking for nasal phonemes using synthesized and spoken data.
• The framework allows controlled trade-offs between bias and variance in parameter estimation.

Conclusions:

• The proposed state-space framework provides statistically principled estimates of vocal tract resonance parameters with uncertainty quantification.
• KARMA offers improved accuracy and flexibility for formant and antiformant tracking in speech analysis.
• Simultaneous tracking of uncertainty levels enhances user confidence and allows for adaptive algorithmic adjustments.