1. A computer implemented method of training a model to characterize coarticulation and reduction in a speech signal using a computer with a processor, comprising: calculating, with the processor, a likelihood function for an observation vector derived from cepstral observation data corresponding to speech as an objective function; using a gradient ascent algorithm, using a frame independent approximation that provides a closed form solution, to estimate, with the processor and based on the calculated objective function, covariance matrices for the model, the covariance matrices being estimated independent of a time frame corresponding to the cepstral observation data, wherein the model gives a probability of a vocal tract resonance (VTR) trajectory as a filtered sequence of VTR target frequencies and a probability of the observation vector, given as a function of the VTR trajectory and an acoustic model having cepstral residuals as acoustic parameters, and wherein the covariance matrices are estimated such that at least one covariance matrix is used for generating the probability for the filtered sequence of vocal tract target frequencies and at least a second covariance matrix is used for the acoustic cepstral residuals used by the acoustic model; and outputting with the processor, the model for use in modeling coarticulation and reduction in the speech signal to recognize speech.