Using Dirichlet Process Mixtures for the Modelling of GNSS Pseudorange Errors in Urban Canyon
Asma Rabaoui, Nicolas Viandier, Juliette Marais, Emmanuel Duflos · 2009
In Global Navigation Satellite Systems (GNSS) positioning, when the signal is received from the satellite in Line of Sight (LOS), the pseudorange error distribution is considered Gaussian. Otherwise, when the signal arrives to the antenna only after one or more reflections, the pseudorange error distribution can be represented by a Gaussian Mixture. In real urban environment, such assumptions are in some way restrictive. In fact, a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments. In order to ensure high accuracy positioning a good estimation of the observation error in such cases is required. 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. This novel approach will be compared to a Jump Markov System (JMS) based on a finite gaussian mixture modeling. Hence, the paper will contain three main parts. The first part presents a JMS based on a finite gaussian mixture modeling. The second part focuses on the modeling of the pseudorange noises using DPMs and its suitability in the estimation problem handled by an efficient particle filter. The last part contains interesting validation schemes.