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.

中文翻译：

---

利用GPS和BDS测量，二阶电离层延迟对ZWD估算的影响

由于在许多GNSS应用中需要毫米精度，例如实时天顶湿延迟（ZWD）估计，因此GNSS信号的高阶电离层延迟不再可忽略不计。我们计算了二阶电离层延迟（\（I_ {2} \）），并通过仅GPS和结合GPS / BDS观测分析了对ZWD估计的影响。使用固定坐标的无差异PPP模型估算ZWD和水平梯度。利用逐块顺序最小二乘法的方法消除了接收器时钟偏差并计算了对ZWD的\（I_ {2} \）影响。的\（I_ {2} \）使用CODE最终TEC图和第12代国际地磁参考场（IGRF-12）模型计算了每个GNSS卫星观测的延迟。具有实际观测几何的统计结果表明，\（I_ {2} \）延迟在白天可以达到10毫米以上，并且对估计的ZWD的相应影响可以达到几毫米。在HKWS站，GPS的最大\（I_ {2} \）撞击仅达到3.1毫米，而同时使用GPS和BDS观测时仍达到2.4毫米。模拟的\（I_ {2} \）即使TEC和地磁值是根据相对中等的背景模型计算得出的，对ZWD的影响也可能达到几毫米。与实时ZWD估计的5–10 mm精度相比，\（I_ {2} \）延迟一定不能忽略，尤其是在高VTEC期间。