Research on Reliable Long-Baseline NRTK Positioning Method Considering Ionospheric Residual Interpolation Uncertainty

Abstract

In the past few decades, network real-time kinematic (NRTK) positioning technology has developed rapidly. Generally, in the continuously operating reference stations (CORS) network, within a moderate baseline length, e.g., 80–100 km, atmospheric delay can be effectively processed through regional modeling and, thus, can support almost instantaneous centimeter-level NRTK positioning. However, in long-baseline CORS networks, especially during the active period of the ionosphere, ionospheric delays cannot be fully eliminated through modeling, leading to decreased NRTK positioning accuracy. To address this issue, this study proposes a long-baseline NRTK positioning method considering ionospheric residual interpolation uncertainty (IRIU). The method utilizes the ionospheric residual interpolation standard deviation (IRISTD) calculated during atmospheric delay modeling, then fits an IRISTD-related stochastic model through the fitting of the absolute values of the ionospheric delay modeling residuals and IRISTD. Finally, based on the ionosphere-weighted model, the IRISTD processed by the stochastic model is used to constrain the ionospheric pseudo-observations. This method achieves good comprehensive performance in handling ionospheric delay and model strength, and the advantage is validated through experiments using CORS data with baseline lengths ranging from 54 km to 106 km in western China and from 84 km to 180 km in AUSCORS data. Quantitative results demonstrate that, across the three sets of experiments, the proposed ionosphere-weighted model achieves an average increase in the fixed rate of 16.9% compared to the ionosphere-fixed model and 25.6% compared to the ionosphere-float model. In terms of positioning accuracy, the proposed model yields average improvements of 67.4%, 76.4%, and 66.0% in the N/E/U directions, respectively, compared to the ionosphere-fixed model, and average improvements of 21.0%, 32.0%, and 24.4%, respectively, compared to the ionosphere-float model. Overall, the proposed method can achieve better NRTK positioning performance in situations where ionospheric delay modeling is inaccurate, such as long baselines and ionospheric activity.