Layered Grid Modeling of Local Wet Delay Using Kriging+LSTM for PPP-RTK Performance Analysis

With the improvement of satellite orbit and clock products and the continuous development of precise point positioning with ambiguity resolution (PPP-AR), the positioning performance of PPP-AR has significantly advanced. However, the uncertainty of atmospheric delays—especially tropospheric wet delay, which is strongly affected by weather changes, temperature, and other factors—still results in long convergence times, severely limiting the wider application of PPP-AR. To improve positioning accuracy and convergence performance, this study proposes a local tropospheric wet delay grid modeling approach in a southern province of China, aiming to provide a tropospheric delay-enhanced PPP-RTK service. Due to the varied elevations of reference stations, an exponential function-based height normalization is first applied. Based on the normalized wet delay values, several interpolation methods are used to generate grid products, which are then used to estimate wet delays at user stations. The interpolated values are compared with user station-derived tropospheric delays (treated as ground truth), and the accuracy of each method is assessed using RMSE, bias, and correlation metrics. The results show that the RMSEs of inverse distance weighting (IDW) and ordinary Kriging interpolation are 10.01 mm and 9.19 mm, respectively, while those of BP neural network and LSTM-based methods are 12.26 mm and 13.04 mm. The proposed Kriging + LSTM hybrid method achieves the best performance, with an RMSE of 6.65 mm, and also outperforms other methods in terms of bias and correlation. To further verify the impact of wet delay grid model accuracy on positioning performance, the study evaluates convergence and accuracy in standard PPP-AR and in a simulated kinematic PPP-RTK mode with additional wet delay constraints. Compared to standard PPP-AR, the vertical (U) direction accuracy improves from 12.04 mm to 11.02 mm (7.74% improvement), and convergence time is reduced from 24.2 minutes to 18.4 minutes (23.97% improvement). Additionally, the ambiguity fixing rate increases by an average of approximately 1.09% with the inclusion of wet delay constraints.