In this paper, we have integrated in a GMM based speaker identification system two different techniques: a) Maximum Likelihood Linear Regression (MLLR) transformation which adapts the system to the new environment based on modifying the continuous densities of the GMM mixtures. We apply the MLLR to perform environmental compensation by reducing a mismatch due to channel or additive noise effects, b) Linear Discriminant Analysis (LDA) applied on sequences of acoustic vectors. LDA extracts, from these sequences, a set of discriminant parameters maximizing the class separability by designing a linear transformation. Previous works have shown that application of LDA to speech recognition problem increases performance of speech recognition system. We use this approach to extract features that are more invariant to non-speakers-related conditions such as handset types and channel effects. Experiments are done on 45 speaker's Spidre database.