This paper addresses the problem of temporal data clustering using a dynamic Gaussian mixture model whose means are considered as latent variables distributed according to random walks. Its final objective is to track the dynamic evolution of some critical railway components using data acquired through embedded sensors. The parameters of the proposed algorithm are estimated by maximum likelihood via the Expectation-Maximization algorithm. In contrast to other approaches as the maximum a posteriori estimation in which the covariance matrices of the random walks have to be fixed by the user, the results of the simulations show the ability of the proposed algorithm to correctly estimate these covariances while keeping a low clustering error rate.