Ionospheric gradient modeling for fast ambiguity resolution in multi-GNSS RTK and NRTK

Abstract

Abstract

Abstract Conventional Real-Time Kinematic (RTK) and Network RTK (NRTK) functional models for medium-to-long baselines typically parameterize Double-Differenced (DD) slant ionospheric delays for individual satellite pairs to mitigate ionospheric effects. When multi-constellation observations are integrated, this strategy introduces severe over-parameterization, which weakens the model strength and degrades ambiguity resolution performance. To address this problem, we propose an ionospheric gradient modeling method that replaces the conventional DD slant-ionosphere parameterization in RTK and NRTK functional models while maintaining effective ionospheric mitigation. Specifically, all DD slant ionospheric parameters in the RTK/NRTK functional models are replaced by an ionospheric gradient model constructed from ionospheric pierce points. The gradient model coefficients are estimated simultaneously with ambiguities, tropospheric delays, and position parameters. Experimental results show that the ionospheric gradient model can effectively represent DD ionospheric delays for all tracked satellites. The modeling residuals exhibit a clear elevation-dependent behavior, with larger residuals at low satellite elevations and an average standard deviation of less than 4 cm. For NRTK positioning, the float ambiguity precision and ambiguity-fixing success rate are increased by 12.1% and 2.6%, respectively, when the ionospheric gradient model is applied. Compared with the conventional Ionosphere-Weighted (IW) model, the proposed functional model reduces the average RTK convergence time from 10.4 to 7.4 s. Meanwhile, the positioning accuracy is improved from 2.8, 3.2, and 4.3 cm to 2.4, 2.8, and 3.9 cm in the north, east, and up components, respectively, and the ambiguity-fixing success rate increases from 96.2 to 98.6%.