Joint segmentation of a set of piecewise stationary processes

We present in this article a Bayesian estimation model for the joint segmentation of a set of piecewise stationary process. The estimate we propose is based on the maximization of the posterior distribution of the change instants conditionally to the process parameter estimation. It is defined as a penalized contrast function with a first term related to the fit to the observation and a second term of penalization. In the case of joint segmentation the term of penalization is deduced from the prior law of the change instants. It is composed of parameters that guide the number and the position of the change and of parameters that will bring prior information on the mutual behavior of the processes. This work is applied to the estimation of the wind statistic parameters. The contrast function is deduced from the log-likelihood of circular Von Mises distribution for the wind direction and the log-normal distribution for the speed. The feasibility and the contribution of our method are shown on synthetic data