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...

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Main Authors: Linyu He, Xingyu Zhou, Hua Chen, Jie He, Runhua Chen, Jie Ding
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Atmosphere
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Online Access:https://www.mdpi.com/2073-4433/16/5/503
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author Linyu He
Xingyu Zhou
Hua Chen
Jie He
Runhua Chen
Jie Ding
author_facet Linyu He
Xingyu Zhou
Hua Chen
Jie He
Runhua Chen
Jie Ding
author_sort Linyu He
collection DOAJ
description 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.
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spelling doaj-art-83702c8a359c4ee8b184076ae33470fa2025-08-20T03:14:39ZengMDPI AGAtmosphere2073-44332025-04-0116550310.3390/atmos16050503A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTMLinyu He0Xingyu Zhou1Hua Chen2Jie He3Runhua Chen4Jie Ding5School of Geodesy and Geomatics, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaGNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaSchool of Geodesy and Geomatics, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaGNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaSchool of Geodesy and Geomatics, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaGNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, ChinaTropospheric 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.https://www.mdpi.com/2073-4433/16/5/503PPP-RTKtropospheric delayshort-term predictionmulti-scale sliding windowLSTM
spellingShingle Linyu He
Xingyu Zhou
Hua Chen
Jie He
Runhua Chen
Jie Ding
A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
Atmosphere
PPP-RTK
tropospheric delay
short-term prediction
multi-scale sliding window
LSTM
title A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
title_full A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
title_fullStr A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
title_full_unstemmed A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
title_short A Short-Term Prediction Method for Tropospheric Delay Products in PPP-RTK Based on Multi-Scale Sliding Window LSTM
title_sort short term prediction method for tropospheric delay products in ppp rtk based on multi scale sliding window lstm
topic PPP-RTK
tropospheric delay
short-term prediction
multi-scale sliding window
LSTM
url https://www.mdpi.com/2073-4433/16/5/503
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