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; with the processor, using the cepstral observation data to solve a set of equations to estimate covariance matrices for a hidden trajectory model, the set of equations including a gradient ascent algorithm; and outputting, with the processor, the hidden trajectory model to characterize a received speech signal to recognize speech in the received speech signal.