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Article(id=1322916807484506334, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322916705915249052, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.11.376, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1762099200000, receivedDateStr=2025-11-03, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793337545510, onlineDateStr=2026-10-30, pubDate=1784044800000, pubDateStr=2026-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793337545510, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793337545510, creator=13701087609, updateTime=1793337545510, updator=13701087609, issue=Issue{id=1322916705915249052, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='7', pageStart='790', pageEnd='912', issueExtLink='null', onlineDate='null', pubDate='1784044800000', pubDateStr='2026-07-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793337521294, creator='13701087609', updateTime=1793337521294, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=834, endPage=841, ext={EN=ArticleExt(id=1322916808893792480, articleId=1322916807484506334, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=A Polar Motion Prediction Model Based on Improved LS and Component Correlation Fusion, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To explore high-accuracy autonomous polar motion (PM) prediction using purely data-driven methods, we propose a hybrid model named PSO-FFRLS+MAR (forgetting factor recursive least squares optimized by particle swarm optimization and multivariate autoregressive). This model dynamically weights historical data to track slow system variations and jointly models the co-oscillations of PMX and PMY residuals. Experiments show that during the 1 to 90 days prediction horizon, the proposed model outperforms mainstream models in both accuracy and stability, with particularly significant improvements for PMY (compared with the classical LS+AR model, a 35.4% reduction in MAE). Day-by-day validation confirms the statistical significance of these improvements. The greater enhancement in PMY accuracy may be physically attributed to the model's enhanced ability to capture the strong seasonal atmospheric excitation that dominates this component. This study provides a high-performance data-driven method for medium- to short-term autonomous prediction of Earth orientation parameters and, through error analysis, links the model's physical mechanisms with geophysical angular momentum excitation functions.

, authors=Yaxin YAO1, 2, Feiyu HAO3, *, Tong CHENG1, 2, Qianxin WANG1, 2, authorsList=Yaxin YAO, Feiyu HAO, Tong CHENG, Qianxin WANG, authorCompany=null, correspAuthors=Feiyu HAO, authorNote=null, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322916810760257773, articleId=1322916807484506334, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=融合改进LS与分量相关性的极移预报模型, columnId=1281909276545356011, journalTitle=大地测量与地球动力学, columnName=大地测量学, runingTitle=null, highlight=null, articleAbstract=

为探索纯数据驱动的极移(PM)高精度自主预报, 提出一种粒子群耦合遗忘因子递归最小二乘和多元自回归(PSO-FFRLS+MAR)模型。该模型对历史数据进行动态加权, 以跟踪系统缓慢变化, 并对PMX与PMY残差协同波动进行联合建模。实验表明, 该模型在1~90 d预报期内, 精度和稳定性均优于主流模型, 对PMY的提升尤为显著(相较于经典LS+AR模型, 其MAE降低35.4%), 且逐天检验证明了该提升的统计显著性。PMY精度提升更多, 从物理机制上可能源于模型更有效地捕捉到了主导该方向的强季节性大气激发。本文研究为地球定向参数的中短期自主预报提供了一种高性能数据驱动方法, 可通过误差分析关联地球角动量激发函数来理解模型物理机制。

, authors=要亚鑫1, 2, 郝飞宇3, *, 程彤1, 2, 王潜心1, 2, authorsList=要亚鑫, 郝飞宇, 程彤, 王潜心, authorCompany=null, correspAuthors=郝飞宇, authorNote=

要亚鑫, 硕士生, 主要研究方向为卫星精密定轨, E-mail:

, correspAuthorsNote=
郝飞宇, 主要研究方向为卫星精密定轨, E-mail:
, copyrightStatement=版权所有，未经授权，不得转载。, copyrightOwner=大地测量与地球动力学编辑部, extLink=null, articleAbsUrl=null, sourceXml=AaiqFG5KNMz6q2BPCpbQ1g==, magXml=ro18eE8ZW4ZzGE3MuMdp4A==, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=AZ3uZuvfc72S9jRdZmKznw==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=/A3DNMQbkOhXdVEtjV/lTg==, mapNumber=null, fund=null)}, authors=[Author(id=1322916811473289464, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=ts23160047a31tm@cumt.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322916811573952763, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, authorId=1322916811473289464, language=EN, stringName=Yaxin YAO, firstName=Yaxin, middleName=null, lastName=YAO, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, 2, address=1 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
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要亚鑫, 硕士生, 主要研究方向为卫星精密定轨, E-mail:

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accuracy of models with different base sequence lengths, figureFileSmall=BQvAcabzLoB3XUVuLISS9Q==, figureFileBig=D3wiLj3dSbWBzGaawSxKBA==, tableContent=null), ArticleFig(id=1322916815252357404, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=图2, caption=不同基础序列时长模型预报精度对比, figureFileSmall=BQvAcabzLoB3XUVuLISS9Q==, figureFileBig=D3wiLj3dSbWBzGaawSxKBA==, tableContent=null), ArticleFig(id=1322916815336243485, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Fig. 3, caption=Performance and improvement magnitude of model accuracy in the PMX direction, figureFileSmall=BeZwmX+lvTFV7JLv0w20iQ==, figureFileBig=EWQaHGQxV3QCIsfHUxp/Mw==, tableContent=null), ArticleFig(id=1322916815415935262, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=图3, caption=PMX方向模型精度表现与提升幅度分析, figureFileSmall=BeZwmX+lvTFV7JLv0w20iQ==, figureFileBig=EWQaHGQxV3QCIsfHUxp/Mw==, tableContent=null), ArticleFig(id=1322916815491432735, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Fig. 4, caption=Performance and improvement magnitude of model accuracy in the PMY direction, figureFileSmall=5uG7RPzFi/tGtIPxLPcn7g==, figureFileBig=9hhnKcGIhrS9xtr0OOp+jg==, tableContent=null), ArticleFig(id=1322916815566930208, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=图4, caption=PMY方向模型精度表现与提升幅度, figureFileSmall=5uG7RPzFi/tGtIPxLPcn7g==, figureFileBig=9hhnKcGIhrS9xtr0OOp+jg==, tableContent=null), ArticleFig(id=1322916815646621985, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 1, caption=

Base sequence lengths

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方案编号 基础序列长度/d 近似年数/a
1 183 0.5
2 365 1
3 730 2
4 1 095 3
5 1 460 4
6 1 825 5
7 2 190 7
8 2 555 7
9 2 920 8
10 3 285 9
11 4 380 12
12 6 570 18
13 7 300 20
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基础序列长度

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方案编号 基础序列长度/d 近似年数/a
1 183 0.5
2 365 1
3 730 2
4 1 095 3
5 1 460 4
6 1 825 5
7 2 190 7
8 2 555 7
9 2 920 8
10 3 285 9
11 4 380 12
12 6 570 18
13 7 300 20
), ArticleFig(id=1322916815826977059, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 2, caption=

PSO parameter settings and optimization outcomes

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参数组合 种族规模N 迭代次数T 惯性权重W 学习因子c1, c2 速度限幅Vmax 单次PSO平均计算时间/s 适应度(平均值) /mas 达到收敛所需平均迭代次数 变异系数
PMX PMY PMX PMY PMX PMY PMX PMY
1 25 40 1.0 (0.05，0.05) 0.02 0.003 3 0.003 4 34.648 131 23.469 798 1.0 1.0 0.00% 0.00%
2 30 50 1.0 (0.1，0.1) 0.1 0.004 2 0.004 9 34.647 858 23.469 735 1.0 1.0 0.00% 0.00%
3 30 50 0.9 (0.2，0.2) 0.04 0.004 2 0.004 9 34.648 130 23.469 932 1.0 1.0 0.00% 0.00%
4 35 60 0.8 (0.3，0.3) 0.05 0.005 5 0.006 1 34.647 939 23.469 841 1.0 1.0 0.00% 0.00%
5 50 80 0.9 (0.15，0.15) 0.03 0.009 9 0.010 4 34.647 943 23.469 878 1.0 1.0 0.00% 0.00%
6 25 40 0.9 (0.1，0.1) 0.08 0.002 8 0.003 0 34.647 858 23.469 735 1.0 1.0 0.00% 0.00%
7 30 50 0.9 (0.25，0.1) 0.04 0.004 1 0.004 2 34.647 949 23.469 827 1.0 1.0 0.00% 0.00%
8 30 50 0.9 (0.1，0.25) 0.04 0.004 8 0.004 0 34.648 382 23.469 870 1.0 1.0 0.00% 0.00%
), ArticleFig(id=1322916815906668836, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=表2, caption=

PSO参数组合与结果

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参数组合 种族规模N 迭代次数T 惯性权重W 学习因子c1, c2 速度限幅Vmax 单次PSO平均计算时间/s 适应度(平均值) /mas 达到收敛所需平均迭代次数 变异系数
PMX PMY PMX PMY PMX PMY PMX PMY
1 25 40 1.0 (0.05，0.05) 0.02 0.003 3 0.003 4 34.648 131 23.469 798 1.0 1.0 0.00% 0.00%
2 30 50 1.0 (0.1，0.1) 0.1 0.004 2 0.004 9 34.647 858 23.469 735 1.0 1.0 0.00% 0.00%
3 30 50 0.9 (0.2，0.2) 0.04 0.004 2 0.004 9 34.648 130 23.469 932 1.0 1.0 0.00% 0.00%
4 35 60 0.8 (0.3，0.3) 0.05 0.005 5 0.006 1 34.647 939 23.469 841 1.0 1.0 0.00% 0.00%
5 50 80 0.9 (0.15，0.15) 0.03 0.009 9 0.010 4 34.647 943 23.469 878 1.0 1.0 0.00% 0.00%
6 25 40 0.9 (0.1，0.1) 0.08 0.002 8 0.003 0 34.647 858 23.469 735 1.0 1.0 0.00% 0.00%
7 30 50 0.9 (0.25，0.1) 0.04 0.004 1 0.004 2 34.647 949 23.469 827 1.0 1.0 0.00% 0.00%
8 30 50 0.9 (0.1，0.25) 0.04 0.004 8 0.004 0 34.648 382 23.469 870 1.0 1.0 0.00% 0.00%
), ArticleFig(id=1322916815986360613, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 3, caption=

Control group setup

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对照组编号 基础序列长度/a 预报模型
① 4 LS+AR
② 20 LS+AR
③ 20 LS+MAR
④ 20 PSO-FFRLS+AR
⑤ 20 WD-LS+WNN
), ArticleFig(id=1322916816078635302, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=表3, caption=

对照组设置

, figureFileSmall=null, figureFileBig=null, tableContent=
对照组编号 基础序列长度/a 预报模型
① 4 LS+AR
② 20 LS+AR
③ 20 LS+MAR
④ 20 PSO-FFRLS+AR
⑤ 20 WD-LS+WNN
), ArticleFig(id=1322916817743773991, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 4, caption=

Comparison of accuracy in the PMX direction

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预报跨度/d 实验组MAE/mas对照组① 对照组② 对照组③ 对照组④ 对照组⑤
MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/%
1 0.205 0.223 7.881 0.218 5.771 0.244 15.911 0.219 6.149 0.013 -1 503.26
5 1.697 1.856 8.587 1.837 7.620 1.988 14.643 1.785 4.952 0.371 -357.598
10 2.996 3.414 12.256 3.331 10.080 3.390 11.647 3.252 7.881 1.565 -91.361
15 4.099 5.073 19.191 4.691 12.615 4.746 13.633 4.617 11.207 3.100 -32.219
20 5.135 6.679 23.111 6.226 17.525 5.923 13.306 6.099 15.800 4.849 -5.905
30 6.743 9.235 26.985 8.742 22.872 7.880 14.437 8.415 19.869 8.402 19.751
60 9.955 15.388 35.306 14.566 31.656 11.631 14.408 13.873 28.242 18.547 46.326
90 13.432 20.871 35.646 21.761 38.278 13.996 4.035 20.230 33.607 26.734 49.759
), ArticleFig(id=1322916817810882856, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=表4, caption=

PMX方向精度对比

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预报跨度/d 实验组MAE/mas对照组① 对照组② 对照组③ 对照组④ 对照组⑤
MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/% MAE/mas 精度改善/%
1 0.205 0.223 7.881 0.218 5.771 0.244 15.911 0.219 6.149 0.013 -1 503.26
5 1.697 1.856 8.587 1.837 7.620 1.988 14.643 1.785 4.952 0.371 -357.598
10 2.996 3.414 12.256 3.331 10.080 3.390 11.647 3.252 7.881 1.565 -91.361
15 4.099 5.073 19.191 4.691 12.615 4.746 13.633 4.617 11.207 3.100 -32.219
20 5.135 6.679 23.111 6.226 17.525 5.923 13.306 6.099 15.800 4.849 -5.905
30 6.743 9.235 26.985 8.742 22.872 7.880 14.437 8.415 19.869 8.402 19.751
60 9.955 15.388 35.306 14.566 31.656 11.631 14.408 13.873 28.242 18.547 46.326
90 13.432 20.871 35.646 21.761 38.278 13.996 4.035 20.230 33.607 26.734 49.759
), ArticleFig(id=1322916817890574633, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 5, caption=

Comparison of accuracy in the PMY direction

, figureFileSmall=null, figureFileBig=null, tableContent=
预报跨度/d 实验组MAE/mas对照组① 对照组② 对照组③ 对照组④ 对照组⑤
MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/%
1 0.184 0.201 8.362 0.194 4.750 0.206 10.653 0.200 7.919 0.005 -3 813.16
5 1.059 1.209 12.399 1.143 7.313 1.261 16.005 1.143 7.325 0.121 -778.894
10 1.813 2.290 20.830 2.044 11.307 2.021 10.283 2.023 10.359 0.537 -237.818
15 2.181 3.309 34.086 2.797 22.028 2.649 17.674 2.788 21.780 1.182 -84.565
20 2.674 4.467 40.144 3.453 22.569 3.284 18.588 3.473 23.027 1.952 -36.960
30 3.493 6.761 48.333 4.738 28.720 4.435 21.245 4.949 29.423 3.616 3.412
60 5.707 13.906 58.958 9.093 37.233 7.349 22.338 8.983 36.463 9.322 38.774
90 7.705 21.777 64.621 13.041 40.919 9.545 19.285 12.451 38.119 15.860 51.421
), ArticleFig(id=1322916817970266410, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=表5, caption=

PMY方向精度对比

, figureFileSmall=null, figureFileBig=null, tableContent=
预报跨度/d 实验组MAE/mas对照组① 对照组② 对照组③ 对照组④ 对照组⑤
MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/% MAE /mas 精度改善/%
1 0.184 0.201 8.362 0.194 4.750 0.206 10.653 0.200 7.919 0.005 -3 813.16
5 1.059 1.209 12.399 1.143 7.313 1.261 16.005 1.143 7.325 0.121 -778.894
10 1.813 2.290 20.830 2.044 11.307 2.021 10.283 2.023 10.359 0.537 -237.818
15 2.181 3.309 34.086 2.797 22.028 2.649 17.674 2.788 21.780 1.182 -84.565
20 2.674 4.467 40.144 3.453 22.569 3.284 18.588 3.473 23.027 1.952 -36.960
30 3.493 6.761 48.333 4.738 28.720 4.435 21.245 4.949 29.423 3.616 3.412
60 5.707 13.906 58.958 9.093 37.233 7.349 22.338 8.983 36.463 9.322 38.774
90 7.705 21.777 64.621 13.041 40.919 9.545 19.285 12.451 38.119 15.860 51.421
), ArticleFig(id=1322916818045763883, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 6, caption=

Statistical results of PM prediction model performance

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项目 指标 PMX方向 PMY方向
误差改善MAE改善率 29.425% 35.351%
RMSE改善率 28.722% 35.171%
统计显著性MAE(t检验) t(181)=8.477；p=1.528×10-7 t(181)=6.056；p=7.862×10-9
MAE(95%CI) [2.193, 4.673] mas [1.667, 3.277] mas
RMSE(t检验) t(181)=9.709；p=1.317×10-7 t(181)=6.140;p=5.099×10-9
RMSE(95%CI) [2.534, 5.374] mas [1.971, 3.839] mas
非参数检验MAE(Wilcoxon) p=3.718×10-7 p=2.668×10-8
RMSE(Wilcoxon) p=3.352×10-7 p=1.962×10-8
效果量MAE(Cohen’s d) 0.405 0.449
RMSE(Cohen’s d) 0.407 0.455
逐天检验未校正显著天数(α=0.05) 0/90 d 90 d/90 d
FDR矫正显著天数(q=0.05) — 90 d/90 d
Bonferroni矫正显著天数 — 0/90 d
分布特性正态性检验(Lilliefors检验) 非 非
方差齐性 不 不
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极移预报模型性能统计检验结果

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 指标 PMX方向 PMY方向
误差改善MAE改善率 29.425% 35.351%
RMSE改善率 28.722% 35.171%
统计显著性MAE(t检验) t(181)=8.477；p=1.528×10-7 t(181)=6.056；p=7.862×10-9
MAE(95%CI) [2.193, 4.673] mas [1.667, 3.277] mas
RMSE(t检验) t(181)=9.709；p=1.317×10-7 t(181)=6.140;p=5.099×10-9
RMSE(95%CI) [2.534, 5.374] mas [1.971, 3.839] mas
非参数检验MAE(Wilcoxon) p=3.718×10-7 p=2.668×10-8
RMSE(Wilcoxon) p=3.352×10-7 p=1.962×10-8
效果量MAE(Cohen’s d) 0.405 0.449
RMSE(Cohen’s d) 0.407 0.455
逐天检验未校正显著天数(α=0.05) 0/90 d 90 d/90 d
FDR矫正显著天数(q=0.05) — 90 d/90 d
Bonferroni矫正显著天数 — 0/90 d
分布特性正态性检验(Lilliefors检验) 非 非
方差齐性 不 不
), ArticleFig(id=1322916818200953133, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=EN, label=Tab. 7, caption=

Correlation analysis results between PM prediction errors and EAM excitation residuals

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项目 PMX方向 PMY方向
与EAM残差的总体相关系数 0.049 0(p=3.6479×10-10) 0.064 3(p=1.798 0×10-16)
与EAM残差的相关系数分段1~30 d预报期 0.073 2 0.143 2
31~60 d预报期 0.050 9 0.055 0
61~90 d预报期 0.046 9 0.047 9
各分量残差的贡献AAM贡献 ~100 ~100
OAM贡献 ~0 ~0
HAM贡献 ~0 ~0
与各分量残差的相关系数与AAM残差 0.049 0 0.064 3
与OAM残差 -0.129 2(p=7.817 7×10-4) -0.011 5(p=70.139 9)
与HAM残差 -0.026 2(p=6.439 0×10-62) -0.137 1(p=1.413 1×10-69)
), ArticleFig(id=1322916818268061998, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322916807484506334, language=CN, label=表7, caption=

PM预报误差与EAM激发残差的关联分析结果

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 PMX方向 PMY方向
与EAM残差的总体相关系数 0.049 0(p=3.6479×10-10) 0.064 3(p=1.798 0×10-16)
与EAM残差的相关系数分段1~30 d预报期 0.073 2 0.143 2
31~60 d预报期 0.050 9 0.055 0
61~90 d预报期 0.046 9 0.047 9
各分量残差的贡献AAM贡献 ~100 ~100
OAM贡献 ~0 ~0
HAM贡献 ~0 ~0
与各分量残差的相关系数与AAM残差 0.049 0 0.064 3
与OAM残差 -0.129 2(p=7.817 7×10-4) -0.011 5(p=70.139 9)
与HAM残差 -0.026 2(p=6.439 0×10-62) -0.137 1(p=1.413 1×10-69)
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融合改进LS与分量相关性的极移预报模型
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要亚鑫 1, 2 , 郝飞宇 3, * , 程彤 1, 2 , 王潜心 1, 2
大地测量与地球动力学 | 大地测量学 2026,46(7): 834-841
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大地测量与地球动力学 |大地测量学 2026 , 46 (7) : 834 -841
融合改进LS与分量相关性的极移预报模型
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要亚鑫1, 2 , 郝飞宇3, * , 程彤1, 2, 王潜心1, 2
作者信息
  • 1 中国矿业大学环境与测绘学院, 徐州, 221116
  • 2 广西精密导航技术与应用重点实验室, 桂林, 541004
  • 3 徐州市国有资产投资经营集团有限公司, 徐州, 221000
通讯作者:
郝飞宇, 主要研究方向为卫星精密定轨, E-mail:
作者简介:

要亚鑫, 硕士生, 主要研究方向为卫星精密定轨, E-mail:

A Polar Motion Prediction Model Based on Improved LS and Component Correlation Fusion
Yaxin YAO1, 2 , Feiyu HAO3, * , Tong CHENG1, 2, Qianxin WANG1, 2
Affiliations
  • 1 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
  • 2 Guangxi Key Laboratory of Precision Navigation Technology and Application, Guilin 541004, China
  • 3 State-owned Assets Investment & Management Group Co Ltd of Xuzhou, Xuzhou 221000, China
出版时间: 2026-07-15 doi: 10.14075/j.jgg.2025.11.376
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摘要
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为探索纯数据驱动的极移(PM)高精度自主预报, 提出一种粒子群耦合遗忘因子递归最小二乘和多元自回归(PSO-FFRLS+MAR)模型。该模型对历史数据进行动态加权, 以跟踪系统缓慢变化, 并对PMX与PMY残差协同波动进行联合建模。实验表明, 该模型在1~90 d预报期内, 精度和稳定性均优于主流模型, 对PMY的提升尤为显著(相较于经典LS+AR模型, 其MAE降低35.4%), 且逐天检验证明了该提升的统计显著性。PMY精度提升更多, 从物理机制上可能源于模型更有效地捕捉到了主导该方向的强季节性大气激发。本文研究为地球定向参数的中短期自主预报提供了一种高性能数据驱动方法, 可通过误差分析关联地球角动量激发函数来理解模型物理机制。

极移  /  遗忘因子递归最小二乘法  /  多元自回归  /  PMX-PMY相关性  /  中短期预报

To explore high-accuracy autonomous polar motion (PM) prediction using purely data-driven methods, we propose a hybrid model named PSO-FFRLS+MAR (forgetting factor recursive least squares optimized by particle swarm optimization and multivariate autoregressive). This model dynamically weights historical data to track slow system variations and jointly models the co-oscillations of PMX and PMY residuals. Experiments show that during the 1 to 90 days prediction horizon, the proposed model outperforms mainstream models in both accuracy and stability, with particularly significant improvements for PMY (compared with the classical LS+AR model, a 35.4% reduction in MAE). Day-by-day validation confirms the statistical significance of these improvements. The greater enhancement in PMY accuracy may be physically attributed to the model's enhanced ability to capture the strong seasonal atmospheric excitation that dominates this component. This study provides a high-performance data-driven method for medium- to short-term autonomous prediction of Earth orientation parameters and, through error analysis, links the model's physical mechanisms with geophysical angular momentum excitation functions.

polar motion(PM)  /  forgetting factor recursive least squares(FFRLS)  /  multivariate autoregressive(MAR)  /  PMX-PMY correlation  /  medium- to short-term prediction
要亚鑫, 郝飞宇, 程彤, 王潜心. 融合改进LS与分量相关性的极移预报模型. 大地测量与地球动力学, 2026 , 46 (7) : 834 -841 . DOI: 10.14075/j.jgg.2025.11.376
Yaxin YAO, Feiyu HAO, Tong CHENG, Qianxin WANG. A Polar Motion Prediction Model Based on Improved LS and Component Correlation Fusion[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (7) : 834 -841 . DOI: 10.14075/j.jgg.2025.11.376
正文
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极移(PM)是地球自转轴相对于地表的运动，和日长变化(ΔLOD)并称为地球自转参数(ERP)，常用于描述地球运动状态[1]。ERP不仅决定地球参考系的空间姿态，也支撑着地基观测站在宇宙空间中的精准定位，为大地控制网建立、卫星定轨、自主导航和深空探测等提供关键基准[2-3]。但固有的滞后性使得自主导航卫星运行等的实际应用必须依赖预报值，如何达到足够精度仍是当前的核心挑战。传统方法如线性的最小二乘和自回归(LS+AR)模型及纯数据驱动的人工神经网络(ANN)各有优势[4-6]。
对于1~90 d内的极移预报，其精度主要受其自身趋势项、周期项时变特征及其分量间的动态耦合关系的限制。面对这个复杂的物理过程，当前研究主要形成两类预报方法：一类是基于奇异谱分析(SSA)等分解技术的经典模型改进方法[7-9]；另一类是LSTM、Transformer及其变体(如Informer)等深度学习架构[10-11]。但两类方法都因为无法准确捕捉上述时变规律导致预报性能受限。虽然引入有效角动量(EAM)这类外部物理数据能提高精度[12-13]，但这类方法依赖实时产品，在自主、实时或数据受限的场景下难以施展。本文选择回归模型本身，通过改进经典LS来精确表征极移的时变规律及相关性，从而系统性地提升1~90 d的预报性能。
极移预报的精度受制于参数变化与分量间的协同扰动，针对这一问题，本文提出粒子群耦合遗忘因子递归最小二乘和多元自回归(PSO-FFRLS+MAR)模型[14-15]。该模型利用FFRLS追踪系统参数的缓慢变化，并引入PSO对加权机制进行自适应优化, 同时对PMX与PMY的残差序列进行联合建模来分析二者之间的协同波动关系。在1~90 d预报窗口内，设计对比实验来检验新模型的性能。模型结果与地球角动量激发函数之间存在一定的对应关系，暗示其在反映极移激发物理过程方面具有一定潜力。本文研究为ERP中短期预报的自主性与精度提升提供了新的思路。
1 研究理论与方法
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1.1 实验数据与框架
本文使用的极移观测数据来自国际地球自转与参考系统服务(IERS)提供的基于国际参考框架ITRF2014的EOP 14C04序列，时间跨度为2000-01-01—2025-05-05。预报实验采用滚动预报，时段为2020-01-01—2025-03-25，每个滚动周期为10 d，每次预报1~90 d(共182期)。
激发数据来源于德国地学研究中心地球系统建模小组(ESMGFZ)提供的包括AAM、HAM、OAM和SLAM的EAM χ3数据集，通过EAM= AAM+OAM+HAM+SLAM得到相应EAM数据。为去除季节性信号，利用半年截止频率的Butterworth低通滤波器对各分量及EAM序列进行滤波，得到激发残差序列。
1.2 PSO-FFRLS+MAR预报模型原理及处理流程
PSO-FFRLS+MAR预报模型主要分为2个阶段：1)使用PSO-FFRLS分别分解PMX和PMY序列，获得其确定性项和随机项；2)将PMX和PMY的随机项视为一个协同系统，基于MAR模型利用其间的物理关联进行联合外推预测。该方案利用分量间的物理关联提升预测精度和稳定性。
使用PSO-FFRLS+MAR预报模型进行极移预报包括以下步骤：
1) 数据预处理。在处理包含周年项等周期信号的拟合问题时，建立一个连续且均匀的时间基准至关重要。所以本文将UTC时间转换为相对于J2000.0历元(TT 2000-01-01 12:00)的时间差，进而构建了一个以1 a=365.24 d为单位长度的连续时间序列，并将其起点归一化为0。统一时间基准，一方面简化了模型，另一方面也保证了LS等算法在求解时的稳定与精度。
2) 建模与分解。使用PSO-FFRLS将极移数据分解为确定性项和随机项，以拟合PMX/PMY模型。针对传统LS方法无法体现动态系统中近期数据更重要的局限，本文引入全局遗忘因子λ(0＜λ ≤1) 控制的衰减权重机制加以改进。λ越小，对旧数据“遗忘”越快，对近期变化越敏捷；λ=1时，退化为传统LS。每轮更新前，采用PSO算法以近期预报误差最小化为目标优化遗忘因子确定λ值，据此构建权重，用于加权最小二乘的参数自适应更新。该机制可根据系统最新动态，调整历史数据的影响权重。将经过预处理后长度为n的数据序列分为A初始化数据和B更新数据2个部分，其中A包括第1~n-1个数据序列，B只包括第n个数据序列。对A部分的数据序列进行最小二乘处理，获得初始逆相关矩阵 P0和初始参数矩阵 X0。为了平衡收敛速度与优化精度，通过预实验优化确定PSO算法参数，以获取最优遗忘因子λ。参数设置为：种群规模N=25、迭代次数T=40、惯性权重w=0.9、学习因子c1=c2= 0.1、速度限幅Vmax=0.08。将B部分数据、 P0、 X0和λ代入RLS公式：
式中，下标B表示该变量对应的B部分数据，各变量的定义与参考文献[14]一致。
3) 随机项建模。使用MAR对获得的PMX和PMY随机项进行联合建模，MAR模型阶数通过施瓦茨贝叶斯准则(SBC)确定。SBC准则倾向于选择更简洁的模型，可避免过拟合。SBC准则确定MAR模型阶数的计算公式为：
$\operatorname{SBC}(p)=\frac{l_p}{2}-\left(1-\frac{2 p+1}{n-p}\right) \lg (n-p)$
式中，各变量的定义与参考文献[15]一致。
4) 极移预报。基于步骤2)模型外推预测PMX与PMY的确定性项，同时基于步骤3)的随机项模型预测其随机项。PMX与PMY的最终预报值分别由其对应的确定性项预测值和随机项预测值相加得到，完整技术路线见图 1。为评估模型性能，将本文方法与LS+AR、LS+MAR、PSO-FFRLS+AR和WD-LS+WNN等4种模型进行对比，重点分析其在中短期预报中的精度与稳健性。
1.3 精度评定与统计检验方法
选择平均绝对误差(MAE)作为预报精度的主要评价指标，并参考均方根误差(RMSE)作为重要补充，同时使用双层次统计检验来验证模型的可靠性。
$\operatorname{MAE}_i=\frac{1}{M} \sum\limits_{j=1}^M\left|\varepsilon_{i, j}\right|$
$\operatorname{RMSE}_i=\sqrt{\frac{1}{M} \sum\limits_{j=1}^M \varepsilon_{i, j}^2}$
式中，i为预报天数；M为预报期数；εi，j为预报值与观测值之差。
在相同的实验设置下，采用双层次统计检验策略，通过配对样本t检验、非参数检验与多重比较分析来系统对比传统LS+AR模型与PSO-FFRLS+MAR模型的预报性能。
1) 整体检验。以MAE为主、RMSE为辅进行检验，分别计算1~90 d内2个模型的MAE和RMSE序列(各182期)，得到2组误差序列，通过配对t检验与非参数检验评估2个模型预报精度的整体差异。
2) 逐日检验。对2个模型在182个样本上的预报误差进行逐日配对t检验，以评估两者在特定预报时效上的精度差异。进行90次独立检验，应用Bonferroni和FDR校正控制假阳性。
2 PSO-FFRLS+MAR模型极移预报实验与结果分析
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2.1 实验参数与对比方案设置
研究表明，LS+AR模型在10~90 d预报跨度下，最优基础序列长度为3~5 a[16]，本文预报跨度为0~90 d，且需进行精度对比，故选取约4 a基础序列长度的LS+AR模型预报结果作为对照组①。
为准确提取周期信号，数据时长必须大于各周期数倍。为确定最优序列长度，设计13种长度(表 1)，并对比不同长度下的模型预报精度。图 2(a)和2(b)分别对比了PMX和PMY方向在13种序列长度下的预报精度，并与对照组①进行比较。结果表明，在PMX方向上，方案12/13(约18 a/20 a)预报精度相当，且多数优于对照组①。在PMY方向上，方案13(约20 a)的预报精度最好，亦高于对照组①。由于MAR同步处理PMX与PMY方向的数据，最终选取方案13(约20 a)为最优方案。
为评估PSO参数的敏感性及模型的鲁棒性，从182期数据中选取第1、91和182期作为代表进行2个方向的测试。本文实验设计8种参数组合(表 2第1~6列)，每种组合重复运行10次，记录平均适应度、单次PSO平均计算时间、达到收敛所需平均迭代次数和变异系数。由于3期结果的规律高度一致，表 2第7~14列以第1期结果为例进行展示。分析发现，PSO-FFRLS算法具有全方位的强鲁棒性，这主要得益于算法设计与本文提出的遗忘因子特性。组合2与组合6的适应度最优，但组合6的计算效率更高，所以本文选择组合6为最终配置。
选取LS+AR、LS+MAR、PSO-FFRLS+AR模型进行1~90 d的预报，并与非线性预报模型——小波去噪后最小二乘与小波神经网络(WD-LS+WNN)进行对比实验[4]，表 3展示了对照组的预报模型和输入数据长度。
2.2 结果分析
实验组与5组对照组的预报结果见表 4、表 5、图 3、图 4。
在1~90 d的极移预报中，PSO-FFRLS+MAR模型优于所有其他模型(对照组⑤除外)，在PMX与PMY分量上都获得了显著更低的MAE。对照组⑤在短期预报精度最高(PMX：1~21 d；PMY：1~28 d)，可归因于其采用了小波去噪处理，该处理可抑制高频噪声，有效延缓初期误差累积。超过该时段后出现的误差迅速增大且稳定性下降，充分表明了仅优化初始场而缺乏强动态建模机制的局限。PSO-FFRLS+MAR模型在中短期至中期预报中表现出更稳定的精度，得益于其融合了PSO-FFRLS的初始参数优化能力与MAR对时间序列残差相关性的敏感性，能有效跟踪极移中的复杂物理过程(如周年与钱德勒摆动)的缓慢变化，还能解析这些分量之间的非线性耦合特征，使其在预报时长和稳健性之间取得更好的平衡。
传统LS+AR对比实验表明，历史数据长度对PMX和PMY方向预报的影响不同。对于PMX方向，4 a与20 a数据训练的模型精度无显著差异；对于PMY方向，20 a数据训练的模型精度显著优于短序列。结果表明，PMY方向可能因影响因素更多或更不稳定，需要约20 a的历史数据才能被模型有效捕捉。
相比于传统AR模型，PSO-FFRLS+MAR模型的预报精度优势随预报时长显著放大。初期(第10 d)提升幅度较小，PMX和PMY方向精度仅分别提高7.881%和10.359%；至第90 d，这一差距明显扩大，精度提升分别达到33.607%和38.119%。产生这一差异的关键在于，MAR模型通过捕捉不同变量残差间的协同波动，有效规避了AR模型中误差指数级放大的问题，从而在提升短期精度的同时增强了中期预报的稳定性。
表 6清晰揭示了PSOGFFRLS+ MAR模型相对于对照组②(LS+AR) 的卓越性能(90 d, 共182期), 本文使用参数检验(t检验) 与非参数检验(Wilcoxon秩和检验) 进行交叉验证, 并从PMX和PMY两个方向对预测精度展开全面比较. 结果表明, 在90 d的误差序列分析中, 该模型在2个方向上均取得了极显著的统计水平(p＜0.001). 进一步分析发现, PMX方向的逐日对比不显著, 但整体MAE降低29.425%, 显示提升来自预报过程中微小改进的累积. 而PMY方向的表现更稳健, 整体MAE降低了35.351 %, 且逐日精度持续优于对照组② (FDR校正, p＜0.05), 表明模型在PMY方向的预测可靠性高, 可为实际应用提供支撑.
为深入探究PMY方向预报精度提升更显著的原因, 检验预报误差与EAM残差的相关性(表 7). 结果显示, 预报误差几乎完全源于模型对非季节性大气波动(尤其是AAM) 的刻画不足, AAM贡献接近100% (p＜0.001). PMY方向与AAM残差的相关性(0.064 3) 明显高于PMX方向(0.049 0), 表明PMY方向对大气波动更敏感, 这一差异在短期预报中尤为突出. 该发现印证了PSOGFFRLS+ MAR模型在捕捉驱动PMY方向季节性变化的关键大气过程上的潜力, 或将成为降低其误差的突破口. 相比之下, PMX方向的精度提升空间有限, 推测与其响应较弱或受其他因素干扰有关.
3 结语
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针对高精度预报需求，本文提出了一种粒子群耦合遗忘因子递归最小二乘和多元自回归模型。该模型在1~90 d内的预报精度较高，能够为定轨、GNSS服务及地球物理信号分离等提供有力支持。主要结论如下：
1) 相对于传统预报模型，本文提出的模型在1~90 d极移预报中综合表现最佳，特别是在中期预报(21~28 d)中稳定性优势突出，显著提升了预报精度。
2) PMY方向在物理机制上更明确，提升效果也超过PMX方向。误差与激发函数对比表明，PMY方向精度提升的关键在于模型抓住了影响该方向的季节性大气演变规律。
3) 模型预测的表现会受到输入数据量的影响，PMY方向至少需20 a的数据才能准确刻画长期趋势，而PMX方向仅需4 a的数据。两者源于相同的激发机制，但PMY方向可能受长期趋势主导，而PMX方向则可能对短期波动敏感。这种响应特征的不同，导致了模型对输入的数据长度表现出非对称敏感性。
综上所述，本文研究为极移中短期预报提供了不依赖外部数据的新方案，并通过建立误差与大气激发信号之间的联系，清晰呈现模型的物理意义，同时提升其可解释性。
基金
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  • 中国矿业大学基本科研业务费项目-重大项目培育专项基金(2023ZDPYRH03)
  • 广西科技基地和人才专项: 精密导航关键技术的研究与应用(桂科 AD25069103)
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2026年第46卷第7期
32
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doi: 10.14075/j.jgg.2025.11.376
  • 接收时间：2025-11-03
  • 首发时间：2026-10-30
  • 出版时间：2026-07-15
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  • 收稿日期：2025-11-03
基金
中国矿业大学基本科研业务费项目-重大项目培育专项基金(2023ZDPYRH03)
广西科技基地和人才专项: 精密导航关键技术的研究与应用(桂科 AD25069103)
作者信息
    1 中国矿业大学环境与测绘学院, 徐州, 221116
    2 广西精密导航技术与应用重点实验室, 桂林, 541004
    3 徐州市国有资产投资经营集团有限公司, 徐州, 221000

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郝飞宇, 主要研究方向为卫星精密定轨, E-mail:
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species		 占总种数比例
Percentage of
total species (%)		 属
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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