Dissemination of High-Resolution Ionosphere Information from VTEC B-spline Expansions for Single-Frequency Positioning

The ionospheric signal delay is one of the largest error sources in GNSS applications and may cause in case of a single-frequency receiver a positioning error of up to several meters. To avoid such an inaccuracy some of the Ionosphere Associated Analysis Centers (IAAC) of the International GNSS Service (IGS) provide the user the Vertical Total Electron Content (VTEC) as Real-Time Global Ionosphere Maps (RT-GIM) via streaming formats. Currently, the only data format used for the dissemination of these ionospheric corrections is based on the State Space Representation (SSR) message and the RTCM standards.

Mathematically most of the RT-GIMs are based on modeling VTEC as series expansions in spherical harmonics (SH) up to a highest degree of n = 15 which corresponds to a spatial resolution of 12° in latitude and longitude and is therefore, too low for modern GNSS applications such as autonomous driving. However, the SSR VTEC message allows the dissemination of SH coefficients only up to a maximum degree of n = 16.

To avoid the drawbacks of expanding VTEC in SHs other approaches such as a voxel representation or a B-spline series expansion have been proven to be appropriate candidates for global and regional modelling with an enhanced resolution. In order to provide in these cases the significant model parameters to the user, the application of the SSR VTEC message requires a transformation of the model parameters into SH coefficients. In this contribution a methodology will be presented which describes a fast transformation of the B-spline approach into a SH representation with high accuracy by minimizing the information loss.

To test the method, a high-resolution VTEC GIM modeled as a series expansion in B-splines is transformed into SH representations of different highest degree values; the results are validated via dSTEC analysis as well as via an example of single frequency positioning and show a significantly improved accuracy compared to the IGS GIMs.