Real-time wide-area precise tropospheric corrections (WAPTCs) jointly using GNSS and NWP forecasts for China

Real-time precise tropospheric corrections are essential for global navigation satellite system (GNSS) positioning with centimetre-level precision. This study presents a new method for generating real-time wide-area precise tropospheric corrections (WAPTCs) for China. Compared with previous models, the new WAPTC has features such as high accuracy, a small number of coefficients and good continuity of service. The new WAPTC utilizes the complementary advantages of numerical weather prediction (NWP) forecasts and GNSS-derived zenith tropospheric delays (ZTDs) with the aid of machine learning and a new polynomial approximation method. The results indicate that (1) the spatially varying biases of NWP-ZTDs can be effectively calibrated using machine learning trained on sparse real-time GNSS-ZTDs, thereby generating a tropospheric data set that is improved in both accuracy and spatial coverage over China, and (2) by incorporating the improved tropospheric data set and the modern empirical IGGtrop model, we succeed in expressing the tropospheric corrections across China using a new polynomial approximation method, thereby reducing the high-volume gridded corrections to only a small number of coefficients to permit easy transmission via satellite. Cross-validation results show that the real-time WAPTCs offer accuracies of 10.0 mm in winter and 16.0 mm in summer in terms of the root mean square (RMS) error across China. The superiority of the proposed WAPTCs to the conventional models is illustrated in both delay and BeiDou-3 positioning domains. These findings can facilitate the provision of tropospheric corrections in BeiDou/GNSS satellite-based PPP services.