Modified ionosphere delay fitting model with atmosphere uncertainty grids for wide-area real-time positioning

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 reference 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 ionospheric delay fitting model and the associated uncertainty grids in providing precise information across extensive regions with minimal coefficients.