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 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 Res2 over the IGP points of the mesh cell of the IPPi by using a least squares scheme.

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: A space-based augmentation system improving the accuracy and reliability of satellite navigation system data includes, each at least: a ground station transmitting data to satellites, a ground station receiving signals transmitted by a satellite and by a satellite equipped with transmitting/receiving means for transmitting data received from the ground transmitting station for a given geographical area; two ground computing centers, redundantly and respectively calculating navigation message streams and transmitting to the ground transmitting station navigation message streams and information representative of Quality of Service provided by the system, from signals transmitted by the ground receiving stations. The computing centers, ground receiving station and ground transmitting station are connected by a communication network.

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.

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.