High-Resolution Ionosphere Corrections for Single-Frequency Positioning

• Main Authors: Andreas Goss, Manuel Hernández-Pajares, Michael Schmidt, David Roma-Dollase, Eren Erdogan, Florian Seitz
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Remote Sensing
• Subjects: ionosphere; GIM-products; vertical total electron content; global navigation satellite systems; B-splines; spherical harmonics
• Online Access: https://www.mdpi.com/2072-4292/13/1/12

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 <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>15</mn></mrow></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>16</mn></mrow></semantics></math></inline-formula>. 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 <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>16</mn></mrow></semantics></math></inline-formula>? Furthermore, we discuss (3) what is the maximum necessary SH degree <i>n</i> 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 <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>30</mn></mrow></semantics></math></inline-formula> coincide with the original B-spline model and improve the positioning accuracy significantly.