Method and device for improving positioning accuracy in the across track axis for a road navigation application

The invention relates to a method for improving positioning accuracy in the across track axis for a road navigation application using a Global Navigation Satellite System - GNSS, comprising - receiving signals from n satellite of the GNSS in view (S10), - processing a n-dimensional vector y (S12), which represents the difference between the ranges observed from the n satellite of the GNSS in view, and the theoretical range from an arbitrary chosen linearization space/time point and the n satellite in view, - estimating a vector x (S14) representing the user space/time position respective to the linearization space/time point by using the processed vector y, a satellite geometric matrix G, and a weighting matrix W equal to the invert of the variance of user ranging errors, - measuring the accuracy of positioning (S16) along a direction D perpendicular to a vehicle motion by the variance of the expression (D T x), and - finding for the direction D the weighting matrix W(D) (S18) that minimizes the variance of the expression (D T x).