Comparison of Implementation Strategies of the 2nd-order Ionosphere Correction in GPS Data Processing

The 2nd-order ionospheric delay of the GPS signal has been shown to be a contributing factor to both static and seasonal errors of GPS station positions. Caused by Faraday rotation of the GPS electromagnetic waves traveling through the ionosphere in the presence of the Earth's magnetic field, the effect was demonstrated to contribute a latitude-dependent southward bias of the order of several millimeters to the station position, and a similar size error to the vertical component. Since this 2nd-order error is proportional to the Total Electron Content (TEC) along the signal propagation path, it also displays a semi-annual cycle, which corresponds to seasonal fluctuations of the ionosphere. These seasonal variations mimic similar variations in the uncorrected GPS station position time series. Two approaches to implement the corrections have been proposed in the literature. The first approach is equivalent to applying a time varying epoch-by-epoch linear combination of the L1 and L2 signals, which eliminates higher-order terms. The second approach is based on a calculation of the TEC and a correction to the LC range measurement. We implemented the two methods in the GIPSY-OASIS software package, and compared their accuracy and practicality of their implementation in routine GPS data processing. We have found that although harder to implement, the TEC approach is more precise. The time-dependent method "leaks" about 10% of the correction into a phase bias error, which may also affect the quality of bias fixing. Both methods give rise to latitude dependent seasonal and long term corrections, which may be misinterpreted as geocenter fluctuations if not accounted for.