On the use of Dirichlet process mixtures for the modelling of pseudorange errors in multi-constellation based localisation

In Global Navigation Satellite Systems (GNSS) positioning, the receiver measures the pseudoranges with respect to each observable navigation satellite and determines the user position. The use of many constellations should lead to highly available, highly accurate navigation anywhere. However, it is important to notice that even if modern receivers achieve high position accuracy in line-of-sight (LOS) conditions, multipath propagation highly degrades positioning performances even in multi-constellation based localisation (¿GPS + Galileo¿ for instance). In urban area, some obstacles (cars, pedestrians, etc) can appear suddenly and thus can induce a random error in the pseudorange measure. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Hence, the paper will contain two main parts. The first part focuses on the modelling of the pseudorange noises using DPMs and its suitability in the estimation problem handled by an efficient particle filter. The other part contains interesting validation schemes.