A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM

Tropospheric delay products play a critical role in achieving high-precision positioning in Precise Point Positioning Real-Time Kinematic (PPP-RTK) applications. The short-term prediction of these products remains a significant challenge that warrants further exploration. This study proposes a novel short-term prediction method for tropospheric delay products in PPP-RTK applications, leveraging a multi-scale sliding window and Long Short-Term Memory (LSTM) network. The multi-scale sliding window approach effectively captures data features across different temporal scales, while LSTM, a well-established and robust time series forecasting technique, ensures the accurate modeling of temporal dependencies. The integration of these two methods significantly enhances the precision of short-term tropospheric delay predictions. Experimental analysis utilizing one week of data from the Hong Kong Continuously Operating Reference Stations (CORS) network demonstrates that the proposed method achieves a maximum prediction error of less than 1.5 cm. Furthermore, compared to the standard LSTM approach, the Root Mean Square Error (RMSE) values are improved by 18.9% and 36.6% for different reference values, respectively. PPP-RTK positioning experiments reveal that the predicted products generated by this method exhibit notable improvements in Root Mean Square (RMS) values for the east, north, and up directions, with enhancements of 10.7%, 19.1%, and 4.1%, respectively, over those obtained using the conventional LSTM method. These results comprehensively validate the effectiveness and superiority of the proposed approach.