This paper proposes a formant tracker capable of computing the maximum a posteriori probability formant frequencies (eigenfrequencies of the vocal tract) during periods of consonant closure. Two specific novel algorithms are proposed. First, an exponentially weighted autoregressive (EWAR) spectral model is proposed. The EWAR model is capable of modeling the peak amplitudes, bandwidths, and frequencies in an ARMA spectral model without any explicit model of the spectral zeros. Instead of explicit zero models, the amplitudes of spectral peaks are adjusted by exponential coupling weights. It is demonstrated that the parameters of the EWAR model may be efficiently computed from the observed speech cepstrum. Second, the smoothness of formant frequency trajectories is modeled using a linear dynamic systems model with a nonlinear output map, and maximum a posteriori probability tracking of dynamic formant frequencies is demonstrated using a particle filtering approach.