  We consider estimating the transition probability matrix of a finite-state
finite-observation alphabet hidden Markov model with known observation
probabilities. The main contribution is a two-step algorithm; a method of
moments estimator (formulated as a convex optimization problem) followed by a
single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold
contribution of this letter is, firstly, to theoretically show that the
proposed estimator is consistent and asymptotically efficient, and secondly, to
numerically show that the method is computationally less demanding than
conventional methods - in particular for large data sets.
