Statistical modeling of speech feature vector trajectories based on a piecewise continuous mean path

One of the key tasks in speech recognition based on statistical methods is the calculation of the class conditional probability density. This paper presents a new statistical model of the trajectories of speech feature vectors. In this model each vector is assumed to correspond to a point on a mean path that consists of a number of concatenated straight line segments. The model characterizes both the deviation of the trajectory from the mean path and the deviation from the mean rate at which the vectors move through the vector space in a way that avoids the conditional independence assumption implicit in hidden Markov modeling. The model is formulated using a state space approach in which the state vector consists of only two elements. These represent the position on the mean path corresponding to the present observation vector and the rate at which points on the mean path are moving through the vector space. A method for estimating the parameters of the model using the Expectation Maximization algorithm is presented.