A semi-analytical estimation of the effect of second-order ionospheric correction on the GPS positioning

We developed a semi-analytical method to evaluate the effect of the second-order ionospheric correction on GPS positioning. This method is based on the semi-analytical positioning error simulation method developed by Geiger and Santerre in which, assuming the continuous distribution of the satellites, a normal equation is formed to estimate the positioning error taking all the contributions of the ranging error by the visible satellites into account. Our method successfully reproduced the averaged time-series of three IGS sites which is comparable to the rigorous simulation. We then evaluated the effect of the ionospheric error on the determination of the reference frame. We evaluated the additional Helmert parameters that are required for the ionospheric effect. We found that the ionospheric effect can lead to annual scale changes of 0.1 ppb, with an offset of 1.8 mm and a semi-annual oscillation of 1 mm in the z-direction. However, these values are too small to explain the current deviations between the GPS-derived reference frame and the ITRF reference frame. Next, we estimated the apparent scale changes due to the ionospheric error in the GEONET coordinate time-series in Japan. We could qualitatively reproduce the observed semi-annual scale changes peaking at the equinoxes and having asymmetrical amplitudes between the vernal and autumnal equinoxes.