In this paper, a new strategy for a fast adaptation of acoustic models is proposed for embedded speech recognition. It relies on a general GMM, which represents the whole acoustic space, associated with a set of HMM state-dependent probability functions modeled as transformations of this GMM. The work presented here takes advantage of this architecture to propose a fast and efficient way to adapt the acoustic models. The adaptation is performed only on the general GMM model, using techniques gathered from the speaker recognition domain. It does not require state-dependent adaptation data and it is very efficient in terms of computational cost. We evaluate our approach in the voice-command task, using a car-based corpus. This adaptation method achieved a relative error-rate decrease of about 10% even if few adaptation data are available. The complete system allows a total relative gain of more than 20% compared to a basic HMM-based system.