Although hidden Markov models (HMMs) provide a relatively efficient modeling framework for speech recognition, they suffer from several shortcomings which set upper bounds in the performance that can be achieved. Alternatively, linear dynamic models (LDM) can be used to model speech segments. Several implementations of LDM have been proposed in the literature. However, all had a restricted structure to satisfy identifiability constraints. In this paper, we relax all these constraints and use a general, canonical form for a linear state-space system that guarantees identifiability for arbitrary state and observation vector dimensions. For this system, we present a novel, element-wise maximum likelihood (ML) estimation method. Classification experiments on the AURORA2 speech database show performance gains compared to HMMs, particularly on highly noisy conditions.