Stable random variables are often use to model impulsive noise; Recently it has be shown that communication at very high frequency suffer from such a noise. Stable noise cannot however be considered as usual noise in estimation processes because the variance does not usually exists nor an analytic expression for the probability density function. In this work we show how to manage such a problem using a bayesian nonparametric approach. We develop a Sequential Monte Carlo based algorithm to realize the estimation in a non linear dynamical system. The measurement noise is a non-stationnary stable process and it is modeled using a Dirichlet Process Mixture.