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Abstract

Precise atmospheric delay and proper constraints are critical for achieving rapid convergence and accurate positioning. However, ionospheric delay models over wide-area face challenges due to significant spatial and temporal variations, impacting real-time correction precision. To address this, we propose a novel ionospheric slant delay fitting model that adaptively selects the optimal reference path within coverage areas, describing differences between the refer- ence propagation path and others through trigonometric functions. With ten coefficients, the model surpasses legacy polynomial fitting accuracy. Using a 166-station, 150 km-spaced European networks for atmospheric delays and 113 external stations for validation, our model achieves a 59.6% standard deviation reduction compared to the legacy model. Compared to the legacy ionospheric delay model, new model positioning convergence time (≤10 cm) accelerates by 37.7% and 34.2% for horizontal and vertical components, respectively. Meanwhile, two 2° × 2° uncertainty grids, generated from tropospheric and ionospheric delay fitting residuals at 15-min intervals, accurately describe fitting performance in all coverage areas with a maximum of 475 points. Adaptive constraints from uncertainty grids can reduce convergence time by 42.1% and 28.8% for horizontal and vertical, surpassing three-time modeling sigma solutions. These findings underscore the effectiveness of our novel iono- spheric delay fitting model and the associated uncertainty grids in providing precise informa- tion across extensive regions with minimal coefficients.