A New PatchTST-ZTD Forecasting Model Based on Different Global Climates and Its Performance in PPP

Accurate modeling of zenith tropospheric delay (ZTD) is crucial for real-time high-precision positioning in Global Navigation Satellite Systems (GNSS). Deep learning methods are capable of effectively capturing the complex temporal patterns of ZTD time series, which in turn contributes to improved its prediction accuracy and faster convergence in Precise Point Positioning (PPP). However, existing models generally suffer from insufficient temporal resolution, limited generalization ability, and reliance on latitude-based station division, which fails to comprehensively reflect the global error distribution characteristics. To this end, we develop a novel ZTD Forecasting model based on PatchTST (PBZTD), which more effectively captures local dependencies in time series by segmenting the ZTD data into patches. Meanwhile, the GNSS stations are categorized into five major climate types based on the Köppen-Geiger climate classification: Equatorial, Drought, Temperate, Frigid, and Polar. Three prediction schemes were analyzed to compare the performance of different models PBZTD, Informer-based ZTD, and LSTM-based ZTD), using data from 189 ZTD stations provided by the Nevada Geodetic Laboratory across five global climate types from 2012 to 2023. Additionally, the prediction results serve as external constraints in PPP to further evaluate the reliability of the proposed PBZTD model. The results reveal that ZTD prediction accuracy varies across different climate types, with the highest and lowest accuracy observed in polar and equatorial types, showing average RMSEs of 15.54 mm and 25.05 mm, respectively. The PBZTD outperforms IBZTD and LBZTD, with average accuracy improvements of 2.40% and 34.50%, respectively across five climate types. In addition, PBZTD demonstrates superior generalization ability, achieving improvements of 4.20% and 34.27% on 25 stations that were not involved in the model training. Moreover, the incorporation of PBZTD prediction results into PPP leads to faster convergence, achieving average improvements of 15.4%, 9.42%, and 26.51% in the E, N, and U directions, respectively.