BDS-3 Clock Error Prediction Algorithm Based on Semi-parametric-SVM Combined Model

PAN Xiong; HUANG Weikai; WANG Cong; ZHAO Wanzhuo; JIN Lihong

doi:10.13203/j.whugis20220787

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BDS-3 Clock Error Prediction Algorithm Based on Semi-parametric-SVM Combined Model

Geodesy and Survey Engineering | 更新时间：2026-11-05

- BDS-3 Clock Error Prediction Algorithm Based on Semi-parametric-SVM Combined Model
- Geomatics and Information Science of Wuhan University Vol. 50, Issue 4, Pages: 617-627(2025)
- 作者机构：
  
  1.武汉纺织大学计算机与人工智能学院，湖北武汉，430200
  2.武汉纺织大学数理学院，湖北武汉，430200
  3.中国地质大学（武汉）地理与信息工程学院，湖北武汉，430078
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(42174010;41874009)
- DOI：10.13203/j.whugis20220787
  CLC： P228
- Received：19 January 2023，
  
  Published：05 April 2025
- 稿件说明：
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潘雄,黄伟凯,王聪，等.半参数与支持向量机组合模型的BDS-3钟差预报[J].武汉大学学报（信息科学版）,2025,50(4):617-627.

PAN Xiong,HUANG Weikai,WANG Cong,et al.BDS-3 Clock Error Prediction Algorithm Based on Semi-parametric-SVM Combined Model[J].Geomatics and Information Science of Wuhan University,2025,50(4):617-627.
潘雄,黄伟凯,王聪，等.半参数与支持向量机组合模型的BDS-3钟差预报[J].武汉大学学报（信息科学版）,2025,50(4):617-627. DOI：,10.13203/j.whugis20220787

PAN Xiong,HUANG Weikai,WANG Cong,et al.BDS-3 Clock Error Prediction Algorithm Based on Semi-parametric-SVM Combined Model[J].Geomatics and Information Science of Wuhan University,2025,50(4):617-627. DOI：,10.13203/j.whugis20220787

摘要

针对卫星钟差序列中非线性特性较为复杂的问题，为了有效地分离周期项改正误差和顾及不能函数化的因素，提高钟差预报的精度，将钟差周期项模型扩充到半参数模型。利用核估计方法将窗宽参数与模型参数解算综合考虑，建立了半参数变系数模型，综合支持向量机进行卫星钟差数据的参数解算、周期项改正分离、异常值识别和残差拟合。首先，利用泰勒展开式对非参数分量进行修正，引入核估计方法，建立了半参数变系数模型；然后，构造分值检验统计量进行异常值识别，提出了一种综合分值检验统计量的钟差异常值识别方法；最后，为了避免对观测值过拟合或拟合不足，对经过预处理的残差利用支持向量机进行拟合，提高模型的预报精度。采用北斗三号全球卫星导航系统（BeiDou-3 global navigation satellite system，BDS-3）的钟差数据与常用方法进行了对比实验，验证了新模型的可靠性。实验结果表明，建立的模型能够精确高效地对BDS-3钟差异常值进行定位，识别并分离周期项改正，有效地提高BDS-3钟差数据预处理的质量和效率。建立的组合模型预报精度优于传统的二次多项式模型、周期项模型和半参数模型，对于1 h、6 h和12 h预报，新模型的钟差数据的预报平均精度优于0.164 ns。

Abstract

Objectives

The nonlinear characteristics of satellite clock offset sequences are complex. To effectively separate the correction error of the periodic term while accounting for non-functionalized factors and improving the accuracy of clock bias prediction

this study extends the clock error periodic term model to a semi-parametric clock error model.

Methods

By employing the kernel estimation method

both the window width parameter and parameter solution of the kernel function are comprehensively considered

resulting in the establishment of a semi-parametric varying coefficient model. First

the kernel estimation method is introduced

and the parameter components are modified by Taylor expansion. By synthesizing the kernel function and window width parameters

the parameters and periodic term correction estimates of the semi-parametric varying coefficient model are obtained via a three-step estimation method. Then

score test statistics are constructed to detect outliers

and an outlier identification method is proposed for the semi-parametric varying coefficient clock difference prediction model with periodic correction. Finally

to avoid over-fitting or under-fitting of the observed values

a support vector machine is used to further fit the pre-processed clock residual data

thereby improving the model's fitting and prediction accuracy. The reliability of the proposed model is verified by comparing BDS-3 satellite clock difference data with conventional methods.

Results

Experimental results show that the proposed model can accurately and efficiently determine the constant value of the BeiDou-3 global navigation satellite system (BDS-3) clock difference

identify and separate periodic term corrections

and significantly improve the quality and efficiency of BeiDou navigation satellite system clock difference data preprocessing. The prediction accuracy of the proposed combined forecast model surpasses that of the traditional quadratic polynomial model

periodic term model

and semi-parametric model. For 1 h

6 h

and 12 h forecasts

the average prediction accuracy for BDS-3 satellite clock difference data is better than 0.164 ns.

Conclusions

The proposed model provides a high level of precision and efficiency in preprocessing and predicting BDS-3 satellite clock difference data. It demonstrates superior performance compared to traditional models and offers significant potential for broader applications in satellite clock offset prediction tasks.

关键词

Keywords

references

杨宇飞，杨元喜，陈金平，等 . 北斗三号星座拟稳钟差测定及其预报［J］. 测绘学报， 2021 ， 50 （ 12 ）： 1728 - 1737 .

YANG Yufei ， YANG Yuanxi ， CHEN Jinping ， et al . Pseudo-Stable Constellation Bias Error of BDS-3 and Its High-Precision Prediction ［J］. Acta Geodaetica et Cartographica Sinica ， 2021 ， 50 （ 12 ）： 1728 - 1737 .

YANG Y X ， MAO Y ， SUN B J . Basic Performance and Future Developments of BeiDou Global Navigation Satellite System ［J］. Satellite Navigation ， 2020 ， 1 （ 1 ）： 1 - 11 .

潘雄，杨玉锋，卿晨昕，等 . Galileo在轨卫星钟性能评估与分析［J］. 中国惯性技术学报， 2020 ， 28 （ 1 ）： 53 - 59 .

PAN Xiong ， YANG Yufeng ， QING Chenxin ， et al . Performance Evaluation and Analysis of Galileo Satellite Clock in Orbit ［J］. Journal of Chinese Inertial Technology ， 2020 ， 28 （ 1 ）： 53 - 59 .

蒋可，潘雄，罗小敏，等 . 利用半参数核估计的电离层建模新方法［J］. 武汉大学学报（信息科学版）， 2023 ， 48 （ 9 ）： 1416 - 1424 .

JIANG Ke ， PAN Xiong ， LUO Xiaomin ， et al . A New Method of Ionospheric Modeling Based on Semi‑Parametric Kernel Estimation ［J］. Geomatics and Information Science of Wuhan University ， 2023 ， 48 （ 9 ）： 1416 - 1424 .

YAN X ， LI W T ， YANG Y F ， et al . BDS Satellite Clock Offset Prediction Based on a Semiparametric Adjustment Model Considering Model Errors ［J］. Satellite Navigation ， 2020 ， 1 （ 1 ）： 11 .

田婕 . GPS/BDS原子钟性能分析及钟差预报模型研究［D］. 西安：长安大学， 2015 .

TIAN Jie . GPS/BDS Atomic Clock Performance Analysis and Clock Offset Prediction Model ［D］. Xi'an ： Chang'an University ， 2015 .

梅长松，黄海军，蒋可，等 . 级比离散灰色模型在卫星钟差预报中的应用［J］. 武汉大学学报（信息科学版）， 2021 ， 46 （ 8 ）： 1154 - 1160 .

MEI Changsong ， HUANG Haijun ， JIANG Ke ， et al . Application of Discrete Grey Model Based on Stepwise Ratio Sequence in the Satellite Clock Offset Prediction ［J］. Geomatics and Information Science of Wuhan University ， 2021 ， 46 （ 8 ）： 1154 - 1160 .

HUANG G W ， CUI B B ， ZHANG Q ， et al . An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets ［J］. Remote Sensing ， 2018 ， 10 （ 1 ）： 60 .

黄观文，崔博斌，张勤，等 . 附加周期和神经网络补偿的实时钟差预报模型［J］. 宇航学报， 2018 ， 39 （ 1 ）： 83 - 88 .

HUANG Guanwen ， CUI Bobin ， ZHANG Qin ， et al . Real-Time Clock Offset Prediction Model with Periodic and Neural Network Corrections ［J］. Journal of Astronautics ， 2018 ， 39 （ 1 ）： 83 - 88 .

李文涛，边少峰，任青阳，等 . 基于粒子群优化核极限学习机的北斗超快速钟差预报［J］. 宇航学报， 2019 ， 40 （ 9 ）： 1080 - 1088 .

LI Wentao ， BIAN Shaofeng ， REN Qingyang ， et al . Kernel Extreme Learning Machine Based on Particle Swarm Optimization for Prediction of BeiDou Ultra-Rapid Clock Offset ［J］. Journal of Astronautics ， 2019 ， 40 （ 9 ）： 1080 - 1088 .

WANG X ， CHAI H Z ， WANG C . A High-Precision Short-Term Prediction Method with Stable Performance for Satellite Clock Bias ［J］. GPS Solutions ， 2020 ， 24 （ 4 ）： 105 .

HE S F ， LIU J L ， ZHU X W ， et al . Research on Modeling and Predicting of BDS-3 Satellite Clock Bias Using the LSTM Neural Network Model ［J］. GPS Solutions ， 2023 ， 27 （ 3 ）： 108 .

GAO W Z ， LI Z ， CHEN Q S ， et al . Modelling and Prediction of GNSS Time Series Using GBDT， LSTM and SVM Machine Learning Approaches ［J］. Journal of Geodesy ， 2022 ， 96 （ 10 ）： 71 .

邱封钦，潘雄，罗小敏，等 . 综合半参数核估计和自回归补偿的全球电离层总电子含量预报模型［J］. 地球物理学报， 2021 ， 64 （ 9 ）： 3021 - 3029 .

QIU Fengqin ， PAN Xiong ， LUO Xiaomin ， et al . Global Ionospheric TEC Prediction Model Integrated with Semi‑parametric Kernel Estimation and Autoregressive Compensation ［J］. Chinese Journal of Geophysics ， 2021 ， 64 （ 9 ）： 3021 - 3029 .

曾林蕊 . 半参数广义线性模型若干问题的研究［D］. 上海：华东师范大学， 2004 .

ZENG Linrui . Some Studies on the Semiparametric Generalized Linear Model ［D］. Shanghai ： East China Normal University ， 2004 .

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