Model based feature enhancement techniques are constructed from acoustic models for speech and noise, together with a model of how the speech and noise produce the noisy observations. Most techniques incorporate either Gaussian mixture models (GMM) or hidden Markov models (HMM). This paper explores using a switching linear dynamic model (LDM) for the clean speech. The linear dynamics of the model capture the smooth time evolution of speech. The switching states of the model capture the piecewise stationary characteristics of speech. However, incorporating a switching LDM causes the enhancement problem to become intractable. With a GMM or an HMM, the enhancement running time is proportional to the length of the utterance. The switching LDM causes the running time to become exponential in the length of the utterance. To overcome this drawback, the standard generalized pseudo-Bayesian technique is used to provide an approximate solution of the enhancement problem. We present preliminary results demonstrating that, even with relatively small model sizes, substantial word error rate improvement can be achieved.