Online EM estimation of the Dirichlet process mixtures scale parameter to model the GPS multipath error

The performance of GPS is strongly degraded in a multipath environment. The multipath impact the distribution of the additive noise corrupting the distance measurements between the satellites and the GPS receiver. In this paper, this distribution is assumed unknown and modeled in a flexible way by using the Bayesian non parametric framework and more precisely the Dirichlet process mixtures. Nevertheless, these latter depend on the so-called scale parameter which can be difficult to tune a priori. The originality of our approach consists in adapting a recent version of the online EM algorithm, developed by Cappé for hidden Markov models, to compute a maximum a posteriori estimate of the scale parameter. Then, as the proposed model is non linear and non Gaussian, the EM-based scale parameter estimation is coupled with a Rao-Blackwellized particle filter for the joint estimation of the mobile location and the distance measurement noise distribution.