A speech recognition method includes receiving a speech input signal in a first noise environment which includes a sequence of observations, determining the likelihood of a sequence of words arising from the sequence of observations using an acoustic model, adapting the model trained in a second noise environment to that of the first environment, wherein adapting the model trained in the second environment to that of the first environment includes using second order or higher order Taylor expansion coefficients derived for a group of probability distributions and the same expansion coefficient is used for the whole group.