  Vocal tract resonance characteristics in acoustic speech signals are
classically tracked using frame-by-frame point estimates of formant frequencies
followed by candidate selection and smoothing using dynamic programming methods
that minimize ad hoc cost functions. The goal of the current work is to provide
both point estimates and associated uncertainties of center frequencies and
bandwidths in a statistically principled state-space framework. Extended Kalman
(K) algorithms take advantage of a linearized mapping to infer formant and
antiformant parameters from frame-based estimates of autoregressive moving
average (ARMA) cepstral coefficients. Error analysis of KARMA, WaveSurfer, and
Praat is accomplished in the all-pole case using a manually marked formant
database and synthesized speech waveforms. KARMA formant tracks exhibit lower
overall root-mean-square error relative to the two benchmark algorithms, with
third formant tracking more challenging. Antiformant tracking performance of
KARMA is illustrated using synthesized and spoken nasal phonemes. The
simultaneous tracking of uncertainty levels enables practitioners to recognize
time-varying confidence in parameters of interest and adjust algorithmic
settings accordingly.
