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Evaluation of different approaches to modeling the second‐order ionospheric delay on GPS measurements

This work evaluates various approaches to compute the second order ionospheric correction (SOIC) to Global Positioning System (GPS) measurements. When estimating the reference frame using GPS, applying this correction is known to primarily affect the realization of the origin of the Earth's reference frame along the spin axis (Z coordinate). Therefore, the Z translation relative to the International Terrestrial Reference Frame 2008 is used as the metric to evaluate various published approaches to determining the slant total electron content (TEC) for the SOIC: getting the slant TEC from GPS measurements, and using the vertical total electron content (TEC) given by a Global Ionospheric Model (GIM) to transform it to slant TEC via a mapping function. All of these approaches agree to 1 mm if the ionospheric shell height needed in GIM‐based approaches is set to 600 km. The commonly used shell height of 450 km introduces an offset of 1 to 2 mm. When the SOIC is not applied, the Z axis translation can be reasonably modeled with a ratio of +0.23 mm/TEC units of the daily median GIM vertical TEC. Also, precise point positioning (PPP) solutions (positions and clocks) determined with and without SOIC differ by less than 1 mm only if they are based upon GPS orbit and clock solutions that have consistently applied or not applied the correction, respectively. Otherwise, deviations of few millimeters in the north component of the PPP solutions can arise due to inconsistencies with the satellite orbit and clock products, and those deviations exhibit a dependency on solar cycle conditions.