Abstract
The continuity of satellite clock corrections in the international GNSS service (IGS) real-time service (RTS) stream is crucial for maintaining high-precision precise point positioning (PPP). When real-time (RT) satellite clock corrections remain unavailable for prolonged periods due to communication outages, the positioning accuracy of the RT-PPP solution will be severely impaired. In this contribution, we propose a hybrid satellite clock offset (SCO) prediction model that integrates singular spectrum analysis (SSA) with a temporal convolutional network (TCN). The SSA is used to decompose the single difference SCO sequence into several signal components with distinct time-frequency characteristics. The TCN is employed to predict each signal component of the single difference SCO sequence independently. The predicted components are reconstructed to sufficiently maintain high-precision SCO prediction for a long interval. The proposed model is compared with the traditional physical, statistical, and neural network models to comprehensively evaluate the performance of SCO prediction. The experimental results show that the SSA-TCN model significantly reduces root mean square error (RMSE) by 67.6%, 45.1%, 42.4%, 71.1%, 56.2%, 23.9%, 22.3%, 13.8%, and 60.5%, respectively, when compared with linear polynomial (LP), quadratic polynomial (QP), spectral analysis (SA), grey (GM), autoregressive integrated moving average (ARIMA), wavelet neural network (WNN), long short-term memory (LSTM), TCN models, and IGS ultra-rapid predicted (IGU-P) product control group in a 24 h long-term prediction task. In addition to achieving substantial improvements in RMSE, the SSA-TCN model demonstrates comparable superiority in mean absolute error (MAE). Furthermore, the variance absolute error (VAE) of the SSA-TCN model exhibits superior performance in the SCO prediction tasks at 3 h, 6 h, 12 h, and 24 h, outperforming the benchmark models and product. The SSA-TCN model achieves the state-of-the-art (SOTA) performance in terms of both prediction accuracy and stability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The experimental data in the manuscript are all public and can be downloaded from the website of the CNES (http://www.ppp-wizard.net/products/REAL_TIME/).
Abbreviations
- ARIMA:
-
Autoregressive integrated moving average
- CNES:
-
Centre National d'Études Spatiales
- GM:
-
Grey model
- GNSS:
-
Global navigation satellite system
- IGS:
-
International GNSS service
- IGU-P:
-
IGS ultra-rapid predicted
- LP:
-
Linear polynomial
- LSTM:
-
Long short-term memory
- MAE:
-
Mean absolute error
- NN:
-
Neural network
- PPP:
-
Precise point positioning
- QP:
-
Quadratic polynomial
- RMSE:
-
Root mean square error
- RNN:
-
Recurrent neural network
- RTS:
-
Real-time service
- RT-PPP:
-
Real-time PPP
- SA:
-
Spectral analysis
- SCO:
-
Satellite clock offset
- SOTA:
-
State-of-the-art
- SSA:
-
Singular spectrum analysis
- SVD:
-
Singular value decomposition
- TCN:
-
Temporal convolutional network
- TSF:
-
Time series forecasting
- VAE:
-
Variance absolute error
- WNN:
-
Wavelet neural network
References
Bai S, Kolter JZ, Koltun V (2018) An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803.01271. https://doi.org/10.48550/arXiv.1803.01271
Bi J, Xu K, Yuan H, Zhang J, Zhou M (2024) Network attack prediction with hybrid temporal convolutional network and bidirectional GRU. IEEE Internet Things J 11(7):12619–12630. https://doi.org/10.1109/JIOT.2023.3334912
Cai C, Liu M, Li P, Li Z, Lv K (2024) Enhancing satellite clock bias prediction in BDS with LSTM-attention model. GPS Solut 28(2):92. https://doi.org/10.1007/s10291-024-01640-8
Cheng R, Yang D, Liu D, Zhang G (2024) A reconstruction-based secondary decomposition-ensemble framework for wind power forecasting. Energy 308:132895. https://doi.org/10.1016/j.energy.2024.132895
El-Mowafy A, Deo M, Kubo N (2017) Maintaining real-time precise point positioning during outages of orbit and clock corrections. GPS Solut 21(3):937–947. https://doi.org/10.1007/s10291-016-0583-4
Elsobeiey M, Al-Harbi S (2016) Performance of real-time precise point positioning using IGS real-time service. GPS Solut 20(3):565–571. https://doi.org/10.1007/s10291-015-0467-z
Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010. https://doi.org/10.1109/TSP.2013.2265222
Golyandina N, Zhigljavsky A (2020) Singular spectrum analysis for time series, 2nd edn. Springer, Berlin, Heidelberg
Gu X, Qiu Z, Wang Y, Jiang W (2024) LSTM-based clock synchronization for satellite systems using inter-satellite ranging measurements. GPS Solut 28(3):147. https://doi.org/10.1007/s10291-024-01684-w
Hadas T, Bosy J (2015) IGS RTS precise orbits and clocks verification and quality degradation over time. GPS Solut 19(1):93–105. https://doi.org/10.1007/s10291-014-0369-5
He S, Liu J, Zhu X, Dai Z, Li D (2023) Research on modeling and predicting of BDS-3 satellite clock bias using the LSTM neural network model. GPS Solut 27(3):108. https://doi.org/10.1007/s10291-023-01451-3
He K, Zhang X, Ren S, Sun J (2015) Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385. https://doi.org/10.48550/arXiv.1512.03385
Heo YJ, Cho J, Heo MB (2010) Improving prediction accuracy of GPS satellite clocks with periodic variation behaviour. Meas Sci Technol 21(7):073001. https://doi.org/10.1088/0957-0233/21/7/073001
Huang G, Cui B, Zhang Q, Fu W, Li P (2018) An improved predicted model for BDS ultra-rapid satellite clock offsets. Remote Sens 10(1):60. https://doi.org/10.3390/rs10010060
Huang W, Li M, Li L, Wang R, Wang L, Wang N (2023) Characterizing the fault performance of real-time precise satellite orbit and clock correction products. Meas Sci Technol 35(2):025033. https://doi.org/10.1088/1361-6501/ad0e3c
Li B, Ge H, Bu Y, Zheng Y, Yuan L (2022a) Comprehensive assessment of real-time precise products from IGS analysis centers. Satell Navig 3(1):12. https://doi.org/10.1186/s43020-022-00074-2
Li D, Jiang F, Chen M, Qian T (2022b) Multi-step-ahead wind speed forecasting based on a hybrid decomposition method and temporal convolutional networks. Energy 238:121981. https://doi.org/10.1016/j.energy.2021.121981
Li N, Zhao L, Li H (2024) BDS multiple satellite clock offset parallel prediction based on multivariate CNN-LSTM model. GPS Solut 28(3):189. https://doi.org/10.1007/s10291-024-01733-4
Liang Y, Xu J, Wu M, Li F (2022) Analysis of the long-term characteristics of BDS on-orbit satellite atomic clock: since BDS-3 was officially commissioned. Remote Sens 14(18):4535. https://doi.org/10.3390/rs14184535
Liu Y, Gong C, Yang L, Chen Y (2020) DSTP-RNN: A dual-stage two-phase attention-based recurrent neural network for long-term and multivariate time series prediction. Expert Syst Appl 143:113082. https://doi.org/10.1016/j.eswa.2019.113082
Liu P, Ling KV, Qin H, Liu T (2023) Performance analysis of real-time precise point positioning with GPS and BDS state space representation. Measurement 215:112880. https://doi.org/10.1016/j.measurement.2023.112880
Lu J, Zhang C, Zheng Y, Wang R (2018) Fusion-based satellite clock bias prediction considering characteristics and fitted residue. J Navig 71(4):955–970. https://doi.org/10.1017/S0373463317001035
Mao Y, Chen J, Dai W, Jia X (2012) Analysis of error sources on orbital atomic clocks’ stability. Geo-Spat Inf Sci 15(3):207–211. https://doi.org/10.1080/10095020.2012.720458
Moradi M (2022) Wavelet transform approach for denoising and decomposition of satellite-derived ocean color time-series: Selection of optimal mother wavelet. Adv Space Res 69(7):2724–2744. https://doi.org/10.1016/j.asr.2022.01.023
Nie Z, Gao Y, Wang Z, Ji S, Yang H (2017) An approach to GPS clock prediction for real-time PPP during outages of RTS stream. GPS Solut 22(1):14. https://doi.org/10.1007/s10291-017-0681-y
Ren Y, Zhao D, Luo D, Ma H, Duan P (2022) Global-local temporal convolutional network for traffic flow prediction. IEEE Trans Intell Transp Syst 23(2):1578–1584. https://doi.org/10.1109/TITS.2020.3025076
Tan X, Xu J, Li F, Wu M, Liang Y, Chen D, Zhu B (2024) Grey modelling and real-time forecasting for the approximate non-homogeneous white exponential law BDS clock bias sequences. Sci Rep 14(1):17897. https://doi.org/10.1038/s41598-024-69005-2
Wang Y, Lv Z, Chen Z, Huang L, Li L, Gong X (2016) A new data preprocessing method for satellite clock bias and its application in WNN to predict medium-term and long-term clock bias. Geomat Inf Sci Wuhan Univ 41(3):373–379. https://doi.org/10.13203/j.whugis20140216
Wang Y, Lu Z, Qu Y, Li L, Wang N (2017) Improving prediction performance of GPS satellite clock bias based on wavelet neural network. GPS Solut 21(2):523–534. https://doi.org/10.1007/s10291-016-0543-z
Wang D, Guo R, Xiao S, Xin J, Tang T, Yuan Y (2019) Atomic clock performance and combined clock error prediction for the new generation of BeiDou navigation satellites. Adv Space Res 63(9):2889–2898. https://doi.org/10.1016/j.asr.2018.01.020
Wang X, Chai H, Wang C (2020) A high-precision short-term prediction method with stable performance for satellite clock bias. GPS Solut 24(4):105. https://doi.org/10.1007/s10291-020-01019-5
Xue H, Xu T, Nie W, Yang Y, Ai Q (2021) An enhanced prediction model for BDS ultra-rapid clock offset that combines singular spectrum analysis, robust estimation and gray model. Meas Sci Technol 32(10):105002. https://doi.org/10.1088/1361-6501/abfcec
Ye Z, Li H, Wang S (2021) Characteristic analysis of the GNSS satellite clock. Adv Space Res 68(8):3314–3326. https://doi.org/10.1016/j.asr.2021.06.030
Zhang X, Chen X, Guo F (2015) High-performance atomic clock modeling and its application in precise point positioning. Acta Geod Cartogr Sin 44(4):392. https://doi.org/10.11947/j.AGCS.2015.20140287
Zhang L, Yang H, Gao Y, Yao Y, Xu C (2018) Evaluation and analysis of real-time precise orbits and clocks products from different IGS analysis centers. Adv Space Res 61(12):2942–2954. https://doi.org/10.1016/j.asr.2018.03.029
Zhang X, Hu J, Ren X (2020) New progress of PPP/PPP-RTK and positioning performance comparison of BDS/GNSS PPP. Acta Geod Cartogr Sin 49(9):1084. https://doi.org/10.11947/j.AGCS.2020.20200328
Zhang G, Han S, Ye J, Hao R, Zhang J, Li X, Jia K (2021) A method for precisely predicting satellite clock bias based on robust fitting of ARMA models. GPS Solut 26(1):3. https://doi.org/10.1007/s10291-021-01182-3
Zhao L, Li N, Li H, Wang R, Li M (2021) BDS satellite clock prediction considering periodic variations. Remote Sens 13(20):4058. https://doi.org/10.3390/rs13204058
Acknowledgements
This research was jointly funded by the National Key Research and Development Program (No. 2021YFB3901300), the National Natural Science Foundation of China (Nos. 62373117, 62403158).
Funding
This research was jointly funded by the National Key Research and Development Program (No. 2021YFB3901300), the National Natural Science Foundation of China (Nos. 62373117, 62403158).
Author information
Authors and Affiliations
Contributions
LZ provided the initial idea; ZN and LL jointly designed the research and wrote the paper; PC and ZN collected experimental data and prepared figures and tables; LL and LZ advised, revised and improved the manuscript. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhao, L., Na, Z., Li, L. et al. SSA-TCN: satellite clock offset prediction during outages of RTS stream. GPS Solut 29, 105 (2025). https://doi.org/10.1007/s10291-025-01857-1
Received:
Accepted:
Published:
Version of record:
DOI: https://doi.org/10.1007/s10291-025-01857-1