In previous work, we proposed a new speech recognition technique that generates a smooth speech trajectory from hidden Markov models (HMMs) by maximizing likelihood subject to the constraints that exist between static and dynamic speech features. This paper presents a theoretical analysis of this method. We show that the approach used to generate the smoothed trajectory is equivalent to a Kalman filter. This result demonstrates that there is a strong relationship between the dynamics of delta features (and delta-delta features) in HMM-based speech recognition and Kalman filter dynamics.