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Academic Journal of Computing & Information Science, 2026, 9(3); doi: 10.25236/AJCIS.2026.090310.

Satellite Clock Bias Prediction Based on Metabolizing GM(1,1) and BP Neural Network

Author(s)

Jianlong Cheng, Ye Yu, Guodong Jin, Jianwei Zhao, Xiaoyu Gao, Minli Yao

Corresponding Author:
Ye Yu
Affiliation(s)

Rocket Force University of Engineering, Xi'an, 710025, Shaanxi, China

Abstract

This study proposes a hybrid satellite clock bias prediction method combining the metabolizing GM (1,1) model and a BP neural network: GM (1,1) provides initial short-term forecasts; residuals between predictions and true values are modelled by the BP network; final predictions are obtained by adding BP-predicted residuals to GM (1,1) outputs. Validated on eight GPS satellite clocks using high-precision products from Wuhan University’s GNSS Analysis Centre, the method achieves superior accuracy and stability over standalone models. The hybrid model attains average error of 1.14 ns and stability of 2.04 ns—improving accuracy by 19.72% relative to the linear polynomial model and by 15.56% relative to the grey model, and improving stability by 21.54% relative to the linear polynomial model and by 17.07% relative to the grey model.

Keywords

Linear polynomial model; Grey model; Metabolism; BP neural network; Satellite clock bias; Forecast

Cite This Paper

Jianlong Cheng, Ye Yu, Guodong Jin, Jianwei Zhao, Xiaoyu Gao, Minli Yao. Satellite Clock Bias Prediction Based on Metabolizing GM(1,1) and BP Neural Network. Academic Journal of Computing & Information Science (2026), Vol. 9, Issue 3: 82-90. https://doi.org/10.25236/AJCIS.2026.090310.

References

[1] Lu C L, Lei Y, Zhao D N. Design and Implementation of GNSS Satellite Clock Performance Analysis and Prediction Software[J]. GNSS World of China, 2025, 50(05): 51-59.

[2] Yu Y, Yang C P, Ding Y, et al. A hybrid short-term prediction model for BDS-3 satellite clock bias supporting real-time applications in data-denied environments[J]. Remote Sensing, 2025, 17(16):2888-2913.

[3] Ma Z X, Yang L, Jia X L, et al. Improved Satellite Clock Difference Prediction Method Based on Polynomial Model[J]. GNSS World of China, 2016, 41(02): 27-31+37.

[4] Yu Y, Huang M, Duan T, et al. Satellite clock offset forecasting using a combination of particle swarm optimization and weighted grey regression [J]. Journal of Harbin Institute of Technology, 2020, 52(10): 144-151.

[5] Yu Y, Huang M, Wang C Y, et al. A new BDS-2 satellite clock bias prediction algorithm with an improved exponential smoothing method [J], Applied Sciences,2020,10(21):7456-7479.

[6] Wang Y H, Song X L, Gong J J. Application of Error-Corrected Grey Model in Navigation Satellite Clock Difference Prediction[J]. Journal of Time and Frequency, 2025, 48(01): 68-78.

[7] Zhang J R, Tang L N. Rubidium Atomic Clock Difference Prediction Based on Improved Kalman Filter[J]. Journal of Xi'an University of Posts and Telecommunications, 2019, 24(05): 1-5.

[8] Yu Y, Zhang H J, Li X H, et al. Medium and Short-term Prediction of GPS Satellite Clock Difference Based on GM (1,1) and MECM Combined Model[J]. Acta Astronomica Sinica, 2018, 59(03): 19-30.

[9] Li T, Wang J M, Zhang W C. Establishment of BDS Clock Difference Combined Prediction Model Based on Entropy Weight Method[J]. Journal of Navigation and Positioning, 2022, 10(04): 65-72.

[10] Guo R X, Yi M, Gao Y P. Research on Real-time GPS Satellite Clock Difference Prediction Based on Metabolizing Grey Model[J]. Beijing Surveying and Mapping, 2016, (06): 22-26.

[11] Sun G Q. Prediction of Slope Foundation Bearing Capacity Based on Metabolizing Grey GM (1,1) Model[J]. Guangdong Building Materials, 2025, 41(11): 103-106.

[12] Li Y F, Shi S H. Satellite Clock Difference Prediction Based on GM (1,1) and BP Neural Network[J]. Electronic Design Engineering, 2020, 28(09): 7-11.

[13] Liu W C, Zhou Z G. Research on GPS Satellite Clock Difference Combined Prediction Model[J]. Geomatics & Spatial Information Technology, 2023, 46(10): 118-120+124+127.

[14] Fang C Z. Research on Wind Power Combined Prediction Based on BP Neural Network and Support Vector Machine[D]. Inner Mongolia University of Science and Technology, 2021.