Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

Asma Rabaoui, Nicolas Viandier, Emmanuel Duflos, Juliette Marais, Philippe Vanheeghe
2012 IEEE Transactions on Signal Processing  
In Global Positioning System (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning a
more » ... ood estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and non-linearity and besides it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient particle filter called Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a GNSS based localization context where the GPS information may be inaccurate because of multipath/masking effects. Index Terms Global Positioning System (GPS), navigation, urban canyon, pseudorange errors, density estimation, nonparametric Bayesian Methods, sequential Monte Carlo methods, Rao-Blackwellized particle filter.
doi:10.1109/tsp.2011.2180901 fatcat:nbypnqtspvayjbowscyqzuq5di