Model the Ionospheric Gradients Between Satellites in Network RTK

As the 25th solar cycle commences, users of network RTK (Real-Time Kinematic) encounter significant positioning errors originating from the ionosphere, particularly in low-latitude regions. A significant factor contributing to these errors is the inaccurate broadcast of ionospheric delays from the system to the user. Our analysis has shown that, despite the utilization of double-differencing, ionospheric delays of baselines less than 10km can still reach several decimeters, which posing a considerable challenge for ambiguity resolution and positioning accuracy at the user's end. To tackle this challenge, accurately estimating user ionospheric delays with appropriate methodology becomes crucial. After a thorough analysis, it has been identified that existing linear interpolation algorithms have limitations in capturing ionospheric errors induced by satellite movements. Consequently, a novel approach is proposed, which considers inter-satellite ionospheric variations. First, the underlying mechanism of this proposed approach is theoretically analyzed and explained. Then, the process and data used for interpolation within this new method are described. To validate its effectiveness, tests were conducted using data from two active days, March 14th and 24th, 2024. The results indicate that this new interpolation method could significantly reduce the double-differenced ionospheric delay estimation between the master station and the user. It is acknowledged that this method has its limitations. While it provides more accurate estimates of ionospheric delays, the increased observation noise and the difficulty in resolving ambiguities due to cycle slips during ionospheric scintillation periods remain challenging issues for future research. Addressing these challenges will require advancements in both system-end and user-end algorithms.