The impact of second-order ionospheric delays on the ZWD estimation with GPS and BDS measurements

Abstract

Since millimeter accuracy is required in many GNSS applications such as real-time zenith wet delay (ZWD) estimation, the higher-order ionospheric delays on GNSS signals are no longer negligible. We calculated the second-order ionospheric delays ($$I_{2}$$) and analyzed the impact on the ZWD estimation with GPS-only and combined GPS/BDS observations. The undifferenced PPP model with fixed coordinates was used to estimate the ZWD and horizontal gradients. The method of blockwise sequential least squares was utilized to eliminate the receiver clock biases and compute the $$I_{2}$$ impact on the ZWDs. The $$I_{2}$$ delays on each GNSS satellite observations were calculated with the CODE final TEC map and the 12th generation of the international geomagnetic reference field (IGRF-12) model. The statistical results with the actual observation geometry show that the $$I_{2}$$ delays can reach over 10 mm during the daytime, and the corresponding impact on the estimated ZWD can reach up to several millimeters. At station HKWS, the maximum $$I_{2}$$ impact with GPS only reaches up to 3.1 mm and is still 2.4 mm when both GPS and BDS observations are used. The simulated $$I_{2}$$ impact on the ZWD could reach several millimeters, even though the TEC and geomagnetic values were calculated from relatively moderate background models. Compared with the 5–10 mm precision of real-time ZWD estimation, the $$I_{2}$$ delays must not be ignored, especially during high VTEC periods.