A Bayesian non parametric time-switching autoregressive model for multipath errors in GPS navigation

Multipath is one of the most penalizing error sources in GPS navigation. It occurs when the satellite signals are reflected on obstacles before reaching the GPS receiver, corrupting the satellite-receiver distance measurements. In recent works, Bayesian non parametric (BNP) models of the measurement errors in the presence of multipath were considered. The latter were assumed to be distributed according to an a priori infinite mixture of Gaussian probability density functions. However, the errors were considered temporally white. This assumption does not hold in practice. In this paper, we extend the proposed BNP formalism to the case of time-correlated errors. For this purpose, we model the correlated measurement errors as an infinite mixture of autoregressive processes. Then, the on-line joint estimation of the navigation variables, the correlated measurement errors and their parameters from the GPS measurements is performed by particle filtering.