Abstract: A method for optimally fitting GIVE ionospheric correction error bounds and/or a method for computing variances of residuals of IGP points of an ionospheric grid for correcting an SBAS system each comprise a step of inverse interpolation implemented on a set of observation pierce points IPPi. In the method for optimally fitting the GIVEs, the step of inverse interpolation scatters for each observation pierce point IPPi concerned a variance increment ?UIVEi2 over the IGP points of the mesh cell of the said IPPi by using a least squares scheme. In the computation of the variances of residuals, the step of inverse interpolation scatters for each observation pierce point IPPi concerned a residual Resi2 over the IGP points of the mesh cell of the said IPPi by using a least squares scheme.

Abstract: A method for determining an error in the estimation of time taken to cross the ionosphere by a signal along a vertical sight axis associated with a receiver, the vertical sight axis cutting the ionosphere at a point of interest, the vertical sight axis being an axis passing through the receiver and a satellite of interest, comprises: determining at least two points of cutting of the ionosphere by two sight axes between a satellite and at least two ground stations; determining at least one angle formed by segments going from the point of interest to two of the cutting points; and determining the spatial dispersion of the cutting points with respect to the point of interest on the basis of the angle, by finding the difference with a predetermined angle and taking the average of the difference or differences.

Abstract: An adaptive method for estimating the electron content of the ionosphere comprises: collecting a set of measurements carried out by a plurality of beacons receiving radio frequency signals transmitted by a plurality of transmitting satellites; computing coordinates of the points of intersection between the transmission axis of the signals and a surface surrounding the Earth, and of a vertical total electron content determined at each of these points; computing a vertical total electron content for each of the nodes of an initial mesh of the surface; a statistical dispersion analysis of the vertical total electron content; a computation step making it possible to define a suitable statistical estimator, or a computation step making it possible to generate a suitable mesh of the surface; a statistical error analysis making it possible to select between a validation of the adaptation of the method and a stopping of the method.