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We introduce an enhanced dynamic time warping model (EDTW) which, unlike conventional dynamic time warping (DTW), considers all possible alignment paths for recognition as well as for parameter estimation. The model, for which DTW and the hidden Markov model (HMM) are special cases, is based on a well-defined quality measure. We extend the derivation of the Forward and Viterbi algorithms for HMMs, in order to obtain efficient solutions for the problems of recognition and optimal path alignment in the new proposed model. We then extend the Baum-Welch (1972) estimation algorithm for HMMs and obtain an iterative method for estimating the model parameters of the new model based on the Baum inequality. This estimation method efficiently considers all possible alignment paths between the training data and the current model. A standard segmental K-means estimation algorithm is also derived for EDTW. We compare the performance of the two training algorithms, with various path movement constraints, in two isolated letter recognition tasks. The new estimation algorithm was found to improve performance over segmental K-means in most experiments.