1. A computer-implemented method for performing steps with a computer having a processor, the method comprising: accessing, with the processor, cepstral observation data representing acoustic data from a speech signal; estimating covariance parameters for distributions of a hidden trajectory model that gives a probability of a vocal tract resonance (VTR) trajectory, by using the cepstral observation data to solve a set of equations, with the processor, to estimate covariance matrices for a residual model that forms part of a probabilistic mapping from hidden trajectory for the vocal tract resonance to an observed trajectory in the hidden trajectory model, the mapping providing a probability of an observed feature vector from the speech signal given a hidden trajectory value, the set of equations including a gradient ascent algorithm that uses a gradient of a log-likelihood of a sequence of cepstral observation values in the cepstral observation data given a speech unit, wherein the gradient ascent algorithm is constrained such that the estimated covariances of the covariance matrices are constrained to always be positive; and outputting, with the processor, the hidden trajectory model to characterize a received speech signal to recognize speech in the received speech signal.