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基于SSA方法的共模误差提取及其对GNSS垂向坐标时间序列的影响分析

黄留波

黄留波. 基于SSA方法的共模误差提取及其对GNSS垂向坐标时间序列的影响分析[J]. 全球定位系统, 2024, 49(3): 45-50, 79. doi: 10.12265/j.gnss.2023223
引用本文: 黄留波. 基于SSA方法的共模误差提取及其对GNSS垂向坐标时间序列的影响分析[J]. 全球定位系统, 2024, 49(3): 45-50, 79. doi: 10.12265/j.gnss.2023223
HUANG Liubo. Extraction of common mode error based on SSA method and its impact analysis on GNSS vertical coordinate time series[J]. GNSS World of China, 2024, 49(3): 45-50, 79. doi: 10.12265/j.gnss.2023223
Citation: HUANG Liubo. Extraction of common mode error based on SSA method and its impact analysis on GNSS vertical coordinate time series[J]. GNSS World of China, 2024, 49(3): 45-50, 79. doi: 10.12265/j.gnss.2023223

基于SSA方法的共模误差提取及其对GNSS垂向坐标时间序列的影响分析

doi: 10.12265/j.gnss.2023223
详细信息
    作者简介:

    黄留波:(1983—),男,高级工程师,从事GNSS数据处理、测绘教育等工作. E-mail: Hbh860608@163.com

    通讯作者:

    黄留波 E-mail: Hbh860608@163.com

  • 中图分类号: P228

Extraction of common mode error based on SSA method and its impact analysis on GNSS vertical coordinate time series

  • 摘要: 本研究基于德国北部24个GNSS测站8 a的数据,引入奇异谱分析方法(singular spectrum analysis,SSA),提出一种顾及不同残差子分量互相关性及子分量贡献率的共模误差(common mode error,CME)识别方法. 探讨了CME对GNSS坐标时间序列噪声和参数估计的影响. 通过与主成分分析(principal component analysis,PCA)方法的对比发现,提出的新方法与PCA方法提取的CME结果非常接近,证实了新方法的可行性. GNSS的CME序列主要包含白噪声(white noise,WN)、闪烁噪声(flicker noise,FN)和非整数谱指数幂律噪声(power law noise,PL). 在剔除CME后,各测站的WN和有色噪声量级分别平均下降了30.32%和52.61%,说明CME中有色噪声占主导地位. 同时,CME改正后,坐标的周年周期和半年周期振幅均有所减小,参数拟合的均方根误差(root mean squared error,RMSE)降低了16.7%. 综上所述,新方法在提高GNSS坐标时间序列质量方面具有重要实际意义.

     

  • 图  1  GNSS测站分布

    图  2  残差第1子分量互相关分析

    图  3  TGME测站前10子分量特征值贡献率

    表  1  本文方法提取CME结果

    测站阶次贡献率/%测站阶次贡献率/%
    ESH5813.94TGWV711.77
    ESBC1014.23FLDW812.90
    ESBH812.91TGEM811.82
    RANT812.99KNOC813.44
    TGDA1014.47DZYL913.22
    TGME1112.54DELZ1014.45
    TGCU1014.37TGD2813.37
    TGZU712.67TGDU913.49
    HELG911.19BORJ1014.15
    HEL2812.96TGBF813.96
    TGBU812.35FYHA712.15
    TGBH1013.84HOLT711.84
    下载: 导出CSV

    表  2  PCA方法提取CME贡献率统计

    测站贡献率/%测站贡献率/%
    ESH514.36TGWV10.81
    ESBC14.65FLDW13.08
    ESBH11.36TGEM12.41
    RANT11.69KNOC15.24
    TGDA15.61DZYL13.69
    TGME13.74DELZ14.58
    TGCU12.54TGD215.98
    TGZU11.87TGDU14.01
    HELG10.71BORJ14.39
    HEL212.04TGBF13.14
    TGBU15.69FYHA13.49
    TGBH14.98HOLT12.07
    下载: 导出CSV

    表  3  CME改正前后对坐标时间序列噪声特性的影响

    测站 改正前 改正后 改正前后各分量改善的百分比/%
    最佳噪声模型 各噪声分量值/mm 最佳噪声模型 各噪声分量值/mm
    ESH5 WN+PL 4.82+9.65 WN+PL 3.69+3.65 23.44+62.18
    ESBC WN+PL 4.75+8.95 WN+PL 4.02+3.25 15.37+63.69
    ESBH WN+PL 4.98+10.36 WN+PL 2.36+4.32 52.61+58.30
    RANT WN+FN 5.32+12.03 WN+PL 3.12+5.1 41.35+57.61
    TGDA WN+PL 4.69+11.25 WN+PL 2.02+6.25 56.93+44.44
    TGME WN+PL 8.32+11.054 WN+PL 7.32+5.14 12.02+53.50
    TGCU WN+FN 5.23+14.23 WN+FN 4.15+6.98 20.65+50.95
    TGZU WN+PL 6.21+14.02 WN+PL 3.34+5.21 46.22+62.84
    HELG WN+PL 5.65+11.36 WN+PL 2.36+5.43 58.23+52.20
    HEL2 WN+PL 4.98+9.23 WN+PL 1.36 +3.69 72.69+60.2
    TGBU WN+PL 6.24+10.67 WN+PL 2.36+5.36 62.18+49.77
    TGBH WN+PL 5.54+11.05 WN+PL 4.32+5.87 22.02+46.88
    ESH5 WN+PL 5.95+12.36 WN+PL 3.98+5.13 33.11+58.50
    ESBC WN+FN 6.24+14.25 WN+FN 5.02+6.11 19.55+57.12
    ESBH WN+PL 6.21+9.87 WN+PL 4.28+3.25 31.08+67.07
    RANT WN+PL 5.65+8.26 WN+PL 4.98+3.64 11.86+55.93
    TGDA WN+PL 4.87+13.91 WN+PL 3.65+6.53 25.05+53.06
    TGME WN+PL 5.21+15.36 WN+PL 3.53+8.32 32.25+45.83
    TGCU WN+PL 5.69+11.03 WN+PL 3.25+6.42 42.88+41.80
    TGZU WN+FN 5.14+15.03 WN+PL 3.32+5.12 35.41+65.93
    HELG WN+PL 6.32+12.36 WN+PL 3.36+7.25 46.84+41.34
    HEL2 WN+FN 5.24+13.02 WN+FN 4.36+5.82 16.79+55.30
    TGBU WN+PL 4.25+14.03 WN+PL 3.65+7.54 14.12+46.26
    TGBH WN+PL 6.24+12.36 WN+PL 4.36+5.53 30.13+55.26
    TGWV WN+PL 5.21+13.65 WN+PL 3.21+0.59 38.39+95.68
    FLDW WN+PL 5.12+11.02 WN+PL 2.65+1.36 48.24+87.66
    TGEM WN+PL 4.52+14.36 WN+PL 3.36+1.98 25.66+86.21
    KNOC WN+FN 6.24+13.65 WN+PL 4.63+2.36 25.80+82.71
    DZYL WN+PL 5.74+11.69 WN+PL 3.02+5.66 47.39+51.58
    DELZ WN+PL 4.05+14.03 WN+PL 2.65+6.01 34.57+57.16
    TGD2 WN+FN 5.06+13.25 WN+FN 2.39+5.98 52.77+54.87
    TGDU WN+PL 6.3+14.14 WN+PL 4.36+7.01 30.79+50.42
    BORJ WN+PL 2.87+15.02 WN+PL 2.01+7.65 29.97+49.07
    TGBF WN+PL 5.24+12.36 WN+PL 3.98+8.06 24.05+34.79
    FYHA WN+PL 4.93+5.69 WN+PL 3.68+3.25 25.35+42.88
    HOLT WN+PL 5.07+9.54 WN+PL 3.98+5.36 21.50+43.82
    TGWV WN+PL 7.09+6.68 WN+PL 5.36+2.36 24.40+64.67
    FLDW WN+PL 5.91+9.25 WN+PL 5.36+5.87 9.31+36.54
    TGEM WN+PL 6.45+6.45 WN+PL 4.69+6.35 27.29+1.55
    KNOC WN+FN 6.81+10.36 WN+PL 3.98+6.98 41.56+32.63
    DZYL WN+PL 5.67+13.21 WN+PL 5.02+4.5 11.46+65.93
    DELZ WN+PL 5.48+10.98 WN+PL 5.36+6.97 2.19+36.52
    TGD2 WN+FN 5.21+11.05 WN+FN 4.69+5.23 9.98+52.67
    TGDU WN+PL 6.71+9.21 WN+PL 5.21+8.35 22.35+9.34
    BORJ WN+PL 6.52+8.65 WN+PL 5.36+5.41 17.79+37.46
    TGBF WN+PL 5.32+7.98 WN+PL 4.69+5.69 11.84+28.70
    FYHA WN+PL 4.96+10.95 WN+PL 3.69+4.36 25.60+60.18
    HOLT WN+PL 4.87+12.32 WN+PL 3.69+5.36 24.23+56.49
    下载: 导出CSV

    表  4  CME对坐标时间序列参数拟合的影响

    改正状态 周年振幅/mm 周年相位/(°) 半年振幅/mm 半年相位/(°) 站速度/(mm·a−1) RMSE
    改正前 5.89 26.5 1.36 152.3 0.58 1.02
    改正后 5.61 25.2 1.25 151.6 0.58 0.85
    下载: 导出CSV
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  • 收稿日期:  2023-12-05
  • 录用日期:  2023-12-05
  • 网络出版日期:  2024-04-25

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