In this paper, we present a framework for a mixed estimationscheme for hidden Markov models (HMM).A robust estimation scheme is first presented using the minimax method thatminimizes a worst case cost for HMMs with bounded uncertainties.Then we present a mixed estimation scheme that minimizes arisk-neutral cost with a constraint on the worst-case cost. Somesimulation results are also presented to compare these different estimationschemes in cases of uncertainties in the noise model.