Abstract
The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.
Highlights
The delay on electromagnetic signals traveling through the atmosphere is mostly caused by free electrons which are available within the ionosphere between approximately
It should be mentioned that the present B-spline model according to Goss et al [15] and Erdogan et al [17] was generated by means of hourly GNSS observations and ultra-rapid
Other models which are not based on spherical harmonic (SH) need to be converted and suffer from degeneration in the accuracy of the global ionosphere maps (GIM)
Summary
The delay on electromagnetic signals traveling through the atmosphere is mostly caused by free electrons which are available within the ionosphere between approximately50 km to 1000 km. The delay on electromagnetic signals traveling through the atmosphere is mostly caused by free electrons which are available within the ionosphere between approximately. The so called ionospheric delay dion , which can be approximated better than 99.9%, affects the propagation of GNSS signals between a satellite S and a receiver R, and is one of the largest error sources in positioning and navigation [1]. Using the ionospheric linear-combination (LC) [5], the user of a dual-frequency receiver can determine the so-called Slant Total Electron Content (STEC). Single-frequency receivers, require external information about the state of the ionosphere to increase the accuracy in positioning
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