  We address the issue of context tree estimation in variable length hidden
Markov models. We propose an estimator of the context tree of the hidden Markov
process which needs no prior upper bound on the depth of the context tree. We
prove that the estimator is strongly consistent. This uses
information-theoretic mixture inequalities in the spirit of Finesso and
Lorenzo(Consistent estimation of the order for Markov and hidden Markov
chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exponents in hidden
Markov model order estimation(2003)). We propose an algorithm to efficiently
compute the estimator and provide simulation studies to support our result.
