Tropospheric Second-Order Horizontal Gradient Modeling for GNSS PPP

The asymmetric delay has a considerable impact on Global Navigation Satellite Systems (GNSS) Positioning, Navigation and Timing (PNT) applications. In GNSS analyses, the impacts of the asymmetric delay are commonly compensated by using the classical methods with considering the north-south and east-west horizontal gradients. In this paper, we have initiatively proposed an extended method where the north-south and east-west horizontal gradients as well as the second-order horizontal gradients are included to better fit the asymmetric delay. The modeling accuracy of the extended method was evaluated at globally distributed 905 GNSS stations during 40 days in 2020. Significant performance of the extended method respect to the classical method was found, where the hydrostatic and wet modeling accuracy at 4° elevation angle was improved from 5.3 and 10.6 mm to 1.6 and 4.9 mm by 70% and 54%, respectively. The GNSS Precise Point Positioning (PPP) performance using the extended method was also validated at 107 Multi-GNSS Experiment (MGEX) stations. The superior performance on the coordinate repeatability and significant effectiveness on the coordinate and Zenith Total Delay (ZTD) estimations were also found, and the maximal vertical (U) coordinate and ZTD difference biases reached 8.6 and −4.5 mm. The extended method is therefore recommended to substitute the classical methods in the GNSS analyses, especially under severe atmospheric conditions