Volume 48 Issue 9
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CHEN Xiang, YANG Zhiqiang, TIAN Zhen, YANG Bing, LIANG Pei. Denoising Method for GNSS Time Series Based on GA‑VMD and Multi‐scale Permutation Entropy[J]. Geomatics and Information Science of Wuhan University, 2023, 48(9): 1425-1434. DOI: 10.13203/j.whugis20210215
Citation: CHEN Xiang, YANG Zhiqiang, TIAN Zhen, YANG Bing, LIANG Pei. Denoising Method for GNSS Time Series Based on GA‑VMD and Multi‐scale Permutation Entropy[J]. Geomatics and Information Science of Wuhan University, 2023, 48(9): 1425-1434. DOI: 10.13203/j.whugis20210215
shu

Denoising Method for GNSS Time Series Based on GA‑VMD and Multi‐scale Permutation Entropy

  • 1.

    School of Geological Engineering and Surveying, Chang'an University, Xi'an 710064, China

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  • Received Date: December 03, 2021
  • Available Online: January 13, 2022
    Graphical Abstract
    • Abstract
  • Objectives 

    Global navigation satellite system (GNSS) coordinate time series provide important data support for the study of crustal movement and deformation, and plate tectonics. Due to the noise caused by various external factors, the GNSS coordinate time series cannot reflect the real motion information of the station well. To effectively reduce the noise in the GNSS time series, we adopted a noise-reduction method combining genetic algorithm (GA) and variational mode decomposition (VMD-GA-VMD).

    Methods 

    First, the genetic algorithm was used to optimize VMD parameters, and the envelope entropy of the input signal was used as the fitness function of the genetic algorithm to find the optimal VMD parameter combination suitable for the signal. According to the optimized parameters, the signal was decomposed by VMD to obtain a series of modal components. Then we calculated the multi-scale permutation entropy (MPE) of each component and then regarded the MPE as the criterion of the noise component. Finally, according to the MPE, the noise components were identified and removed, and the remaining components were reconstructed to obtain the noise-reduced signal. In this paper, the noise reduction effect of GA-VMD was analyzed through the example of noise reduction of analog signal and observation data, and compared with wavelet denoising (WD) and empirical mode decomposition (EMD) methods.

    Results 

    The experiment results show that: (1) The noise reduction results from the analog signals show that WD and EMD have the incomplete and excessive troubles on the noise reduction, respectively. However, GA-VMD can effectively eliminate noise and retain effective signals. From the evaluation index, compared with WD and EMD, the signal-to-noise ratio were increased by 5.18 dB and 2.91 dB, the correlation coefficient by 0.05 and 0.02, respectively, when using GA-VMD. (2) For the complex observation, we used the noise and velocity uncertainty as accuracy indicators to evaluate the noise reduction effects of the three methods. The results show that WD can only extract a part of the white noise, while EMD and GA-VMD can completely remove the white noise. GA-VMD can reduce the flicker noise to the range of 0 to 6 mm/a0.25. For the velocity uncertainty, the average gain rates of GA-VMD relative to the WD and EMD are 69% and 15.33%, respectively. GA-VMD has an average correction rate of 79.89% and 84.46% for the velocity uncertainty and flicker noise of GNSS coordinate time series.

    Conclusions 

    Therefore, GA-VMD is the most effective one among the three noise reduction methods, which can effectively reduce the noise in the GNSS time series and improve its accuracy. However, in this paper, we only discussed the effect of GA on VMD parameter optimization without comparing it with other methods. Hence, it will be the key for studying the advantages and shortcomings of those optimization algorithms in the selection of VMD, and improving the accuracy on the GNSS time series in the future.

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  • [1]
    王敏, 沈正康, 董大南. 非构造形变对GPS连续站位置时间序列的影响和修正[J]. 地球物理学报, 2005, 48(5): 1045-1052. doi: 10.3321/j.issn:0001-5733.2005.05.010

    Wang Min, Shen Zhengkang, Dong Da􀆳nan. Effects of No-Tectonic Crustal Deformation on Continuous GPS Position Times Series and Correction to Them[J]. Chinese Journal of Geophysics, 2005, 48(5): 1045-1052 doi: 10.3321/j.issn:0001-5733.2005.05.010
    [2]
    姜卫平, 李昭, 刘万科, 等. 顾及非线性变化的地球参考框架建立与维持的思考[J]. 武汉大学学报(信息科学版), 2010, 35(6): 665-669. http://ch.whu.edu.cn/article/id/962

    Jiang Weiping, Li Zhao, Liu Wanke, et al. Some Thoughts on Establishment and Maintenance of Terrestrial Reference Frame Considering Non-linear Variation[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 665-669 http://ch.whu.edu.cn/article/id/962
    [3]
    姜卫平, 王锴华, 李昭, 等. GNSS坐标时间序列分析理论与方法及展望[J]. 武汉大学学报(信息科学版), 2018, 43(12): 2112-2123. doi: 10.13203/j.whugis20180333

    Jiang Weiping, Wang Kaihua, Li Zhao, et al. Prospect and Theory of GNSS Coordinate Time Series Analysis[J]. Geomatics and Information Science of Wuhan University, 2018, 43(12): 2112-2123 doi: 10.13203/j.whugis20180333
    [4]
    李昭, 姜卫平, 刘鸿飞, 等. 中国区域IGS基准站坐标时间序列噪声模型建立与分析[J]. 测绘学报, 2012, 41(4): 496-503. https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201204006.htm

    Li Zhao, Jiang Weiping, Liu Hongfei, et al. Noise Model Establishment and Analysis of IGS Reference Station Coordinate Time Series Inside China[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(4): 496-503 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201204006.htm
    [5]
    鲁铁定, 谢建雄. EEMD-多尺度排列熵的GPS高程时间序列降噪方法[J]. 大地测量与地球动力学, 2021, 41(2): 111-115. doi: 10.14075/j.jgg.2021.02.001

    Lu Tieding, Xie Jianxiong. EEMD-Multiscale Permutation Entropy Noise Reduction Method for GPS Elevation Time Series[J]. Journal of Geodesy and Geodynamics, 2021, 41(2): 111-115 doi: 10.14075/j.jgg.2021.02.001
    [6]
    Wu H, Li K, Shi W Z, et al. A Wavelet-Based Hybrid Approach to Remove the Flicker Noise and the White Noise from GPS Coordinate Time Series[J]. GPS Solutions, 2015, 19(4): 511-523. doi: 10.1007/s10291-014-0412-6
    [7]
    尹晖, 朱锋. 时序数据去噪中的小波策略及评价指标[J]. 武汉大学学报(信息科学版), 2012, 37(11): 1374-1377. http://ch.whu.edu.cn/article/id/377

    Yin Hui, Zhu Feng. Wavelet Strategies and Evaluation Indicator in Time Series Data Denoising[J]. Geomatics and Information Science of Wuhan University, 2012, 37(11): 1374-1377 http://ch.whu.edu.cn/article/id/377
    [8]
    张双成, 何月帆, 李振宇, 等. EMD用于GPS时间序列降噪分析[J]. 大地测量与地球动力学, 2017, 37(12): 1248-1252. doi: 10.14075/j.jgg.2017.12.009

    Zhang Shuangcheng, He Yuefan, Li Zhenyu, et al. EMD for Noise Reduction of GPS Time Series[J]. Journal of Geodesy and Geodynamics, 2017, 37(12): 1248-1252 doi: 10.14075/j.jgg.2017.12.009
    [9]
    贾瑞生, 赵同彬, 孙红梅, 等. 基于经验模态分解及独立成分分析的微震信号降噪方法[J]. 地球物理学报, 2015, 58(3): 1013-1023. https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX201503026.htm

    Jia Ruisheng, Zhao Tongbin, Sun Hongmei, et al. Micro-seismic Signal Denoising Method Based on Empirical Mode Decomposition and Independent Component Analysis[J]. Chinese Journal of Geophysics, 2015, 58(3): 1013-1023 https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX201503026.htm
    [10]
    霍炬, 王石静, 杨明, 等. 基于小波变换阈值法处理光纤陀螺信号噪声[J]. 中国惯性技术学报, 2008, 16(3): 343-347. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGXJ200803021.htm

    Huo Ju, Wang Shijing, Yang Ming, et al. Noise Processing of FOG Signal Based on Wavelet Threshold-Value[J]. Journal of Chinese Inertial Technology, 2008, 16(3): 343-347 https://www.cnki.com.cn/Article/CJFDTOTAL-ZGXJ200803021.htm
    [11]
    杨国华, 张风霜, 武艳强, 等. GPS基准站坐标分量噪声的时间序列与分类特征[J]. 国际地震动态, 2007, 37(7): 80-86. doi: 10.3969/j.issn.0253-4975.2007.07.012

    Yang Guohua, Zhang Fengshuang, Wu Yanqiang, et al. Time Sequences of Noise of the Coordinate Component of GPS Reference Stations and Its Classified Characteristics[J]. Recent Developments in World Seismology, 2007, 37(7): 80-86 doi: 10.3969/j.issn.0253-4975.2007.07.012
    [12]
    马俊, 曹成度, 姜卫平, 等. 利用小波包系数信息熵去除GNSS站坐标时间序列有色噪声[J]. 武汉大学学报(信息科学版), 2021, 46(9): 1309-1317. doi: 10.13203/j.whugis20190353

    Ma Jun, Cao Chengdu, Jiang Weiping, et al. Elimination of Colored Noise in GNSS Station Coordinate Time Series by Using Wavelet Packet Coefficient Information Entropy[J]. Geomatics and Information Science of Wuhan University, 2021, 46(9): 1309-1317 doi: 10.13203/j.whugis20190353
    [13]
    李宗春, 邓勇, 张冠宇, 等. 变形测量异常数据处理中小波变换最佳级数的确定[J]. 武汉大学学报(信息科学版), 2011, 36(3): 285-288. http://ch.whu.edu.cn/article/id/496

    Li Zongchun, Deng Yong, Zhang Guanyu, et al. Determination of Best Grading of Wavelet Transform in Deformation Measurement Data Filtering[J]. Geomatics and Information Science of Wuhan University, 2011, 36(3): 285-288 http://ch.whu.edu.cn/article/id/496
    [14]
    Huang N, Shen Z, Long S, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis[J]. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995. doi: 10.1098/rspa.1998.0193
    [15]
    钱文龙, 鲁铁定, 贺小星, 等. GPS高程时间序列降噪分析的改进EMD方法[J]. 大地测量与地球动力学, 2020, 40(3): 242-246. https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB202003005.htm

    Qian Wenlong, Lu Tieding, He Xiaoxing, et al. A New Method for Noise Reduction Analysis of GPS Elevation Time Series Based on EMD[J]. Journal of Geodesy and Geodynamics, 2020, 40(3): 242-246 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB202003005.htm
    [16]
    Wu Z, Huang N. Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method[J]. Advances in Adaptive Data Analysis, 2009, 1(1), DOI: 10. 1142/S1793536909000047.
    [17]
    Dragomiretskiy K, Zosso D. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62(3): 531-544. doi: 10.1109/TSP.2013.2288675
    [18]
    鲁铁定, 谢建雄. 变分模态分解结合样本熵的变形监测数据降噪[J]. 大地测量与地球动力学, 2021, 41(1): 1-6. https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB202101001.htm

    Lu Tieding, Xie Jianxiong. Deformation Monitoring Data De-noising Method Based on Variational Mode Decomposition Combined with Sample Entropy[J]. Journal of Geodesy and Geodynamics, 2021, 41(1): 1-6 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB202101001.htm
    [19]
    罗亦泳, 黄城, 张静影. 基于变分模态分解的变形监测数据去噪方法[J]. 武汉大学学报(信息科学版), 2020, 45(5): 784-790. doi: 10.13203/j.whugis20180437

    Luo Yiyong, Huang Cheng, Zhang Jingying. Denoising Method of Deformation Monitoring Data Based on Variational Mode Decomposition[J]. Geomatics and Information Science of Wuhan University, 2020, 45(5): 784-790 doi: 10.13203/j.whugis20180437
    [20]
    黄维新, 刘敦文. 基于变分模态分解和独立成分分析的矿山微震信号降噪[J]. 振动与冲击, 2019, 38(4): 56-63. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201904010.htm

    Huang Weixin, Liu Dunwen. Mine Microseismic Signal Denosing Based on Variational Mode Decomposition and Independent Component Analysis[J]. Journal of Vibration and Shock, 2019, 38(4): 56-63 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201904010.htm
    [21]
    张杏莉, 卢新明, 贾瑞生, 等. 基于变分模态分解及能量熵的微震信号降噪方法[J]. 煤炭学报, 2018, 43(2): 356-363. https://www.cnki.com.cn/Article/CJFDTOTAL-MTXB201802008.htm

    Zhang Xingli, Lu Xinming, Jia Ruisheng, et al. Micro-seismic Signal Denoising Method Based on Variational Mode Decomposition and Energy Entropy[J]. Journal of China Coal Society, 2018, 43(2): 356-363 https://www.cnki.com.cn/Article/CJFDTOTAL-MTXB201802008.htm
    [22]
    Ram R, Mohanty M N. Comparative Analysis of EMD and VMD Algorithm in Speech Enhancement[J]. International Journal of Natural Computing Research, 2017, 6(1): 17-35.
    [23]
    郑义, 岳建海, 焦静, 等. 基于参数优化变分模态分解的滚动轴承故障特征提取方法[J]. 振动与冲击, 2021, 40(1): 86-94. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202101013.htm

    Zheng Yi, Yue Jianhai, Jiao Jing, et al. Fault Feature Extraction Method of Rolling Bearing Based on Parameter Optimized VMD[J]. Journal of Vibration and Shock, 2021, 40(1): 86-94 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202101013.htm
    [24]
    Habob A A, Dobre O A, Armada A G, et al. Task Scheduling for Mobile Edge Computing Using Genetic Algorithm and Conflict Graphs[J]. IEEE Transactions on Vehicular Technology, 2020, 69(8): 8805-8819.
    [25]
    吉根林. 遗传算法研究综述[J]. 计算机应用与软件, 2004, 21(2): 69-73. https://www.cnki.com.cn/Article/CJFDTOTAL-JYRJ201811001.htm

    Ji Genlin. Survey on Genetic Algorithm[J]. Computer Applications and Software, 2004, 21(2): 69-73 https://www.cnki.com.cn/Article/CJFDTOTAL-JYRJ201811001.htm
    [26]
    谢建峰, 杨啟明, 戴树岭, 等. 基于强化遗传算法的无人机空战机动决策研究[J]. 西北工业大学学报, 2020, 38(6): 1330-1338. https://www.cnki.com.cn/Article/CJFDTOTAL-XBGD202006024.htm

    Xie Jianfeng, Yang Qiming, Dai Shuling, et al. Air Combat Maneuver Decision Based on Reinforcement Genetic Algorithm[J]. Journal of Northwestern Polytechnical University, 2020, 38(6): 1330-1338 https://www.cnki.com.cn/Article/CJFDTOTAL-XBGD202006024.htm
    [27]
    洪晓翠, 段礼祥, 杨晓光, 等. 智能优化算法在机械故障诊断领域的应用综述[J]. 测控技术, 2021, 40(7): 1-8. https://www.cnki.com.cn/Article/CJFDTOTAL-IKJS202107001.htm

    Hong Xiaocui, Duan Lixiang, Yang Xiaoguang, et al. Review on the Application of Intelligent Optimization Algorithms in Mechanical Fault Diagnosis[J]. Measurement & Control Technology, 2021, 40(7): 1-8 https://www.cnki.com.cn/Article/CJFDTOTAL-IKJS202107001.htm
    [28]
    蔡宇, 欧阳缮, 廖可非. 基于遗传算法优化参数的VMD-WVD的无人机微动特征时频分析方法[J]. 桂林电子科技大学学报, 2020, 40(2): 102-107. https://www.cnki.com.cn/Article/CJFDTOTAL-GLDZ202002003.htm

    Cai Yu, Ouyang Shan, Liao Kefei. Time-Frequency Analysis of Micro-doppler Signature of UAV Based on VMD-WVD Optimized by Genetic Algorithms[J]. Journal of Guilin University of Electronic Technology, 2020, 40(2): 102-107 https://www.cnki.com.cn/Article/CJFDTOTAL-GLDZ202002003.htm
    [29]
    纪洁, 胡汉, 高远, 等. 基于遗传算法优化参数的支持向量机风电功率预测[J]. 电子测试, 2020(21): 32-35. https://www.cnki.com.cn/Article/CJFDTOTAL-WDZC202021011.htm

    Ji Jie, Hu Han, Gao Yuan, et al. The Wind Power Prediction Based on the Genetic Algorithm to Optimize Parameters of Support Vector Machine[J]. Electronic Test, 2020(21): 32-35 https://www.cnki.com.cn/Article/CJFDTOTAL-WDZC202021011.htm
    [30]
    刘嘉敏, 彭玲, 刘军委, 等. 遗传算法VMD参数优化与小波阈值轴承振动信号去噪分析[J]. 机械科学与技术, 2017, 36(11): 1695-1700. https://www.cnki.com.cn/Article/CJFDTOTAL-JXKX201711010.htm

    Liu Jiamin, Peng Ling, Liu Junwei, et al. Denoising Analysis of Bearing Vibration Signal Based on Genetic Algorithm and Wavelet Threshold VMD[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(11): 1695-1700 https://www.cnki.com.cn/Article/CJFDTOTAL-JXKX201711010.htm
    [31]
    边杰. 基于遗传算法参数优化的变分模态分解结合1.5维谱的轴承故障诊断[J]. 推进技术, 2017, 38(7): 1618-1624. https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201707024.htm

    Bian Jie. Fault Diagnosis of Bearing Combining Parameter Optimized Variational Mode Decomposition Based on Genetic Algorithm with 1.5-Dimensional Spectrum[J]. Journal of Propulsion Technology, 2017, 38(7): 1618-1624 https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201707024.htm
    [32]
    何勇, 王红, 谷穗. 一种基于遗传算法的VMD参数优化轴承故障诊断新方法[J]. 振动与冲击, 2021, 40(6): 184-189. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202106025.htm

    He Yong, Wang Hong, Gu Sui. New Fault Diagnosis Approach for Bearings Based on Parameter Optimized VMD and Genetic Algorithm[J]. Journal of Vibration and Shock, 2021, 40(6): 184-189 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202106025.htm
    [33]
    唐贵基, 王晓龙. 参数优化变分模态分解方法在滚动轴承早期故障诊断中的应用[J]. 西安交通大学学报, 2015, 49(5): 73-81. https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201505012.htm

    Tang Guiji, Wang Xiaolong. Parameter Optimized Variational Mode Decomposition Method with Application to Incipient Fault Diagnosis of Rolling Bearing[J]. Journal of Xi􀆳an Jiaotong University, 2015, 49(5): 73-81 https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201505012.htm
    [34]
    Aziz W, Arif M. Multiscale Permutation Entropy of Physiological Time Series[C]// Pakistan Section Multitopic Conference, Karachi, Pakistan, 2007.
    [35]
    Bandt C, Pompe B. Permutation Entropy: A Natural Complexity Measure for Time Series[J]. Physical Review Letters, 2002, 88(17): 174102.
    [36]
    嵇昆浦, 沈云中. 含缺值GNSS基准站坐标序列的非插值小波分析与信号提取[J]. 测绘学报, 2020, 49(5): 537-546. https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB202005001.htm

    Ji Kunpu, Shen Yunzhong. Dyadic Wavelet Transform and Signal Extraction of GNSS Coordinate Time Series with Missing Data[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(5): 537-546 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB202005001.htm
    [37]
    黄智刚, 吕虎波, 林一庚, 等. 基于CEEMDAN-MPE算法的隧道爆破地震波信号降噪方法及应用[J]. 爆破, 2020, 37(4): 138-144. https://www.cnki.com.cn/Article/CJFDTOTAL-BOPO202004023.htm

    Huang Zhigang, Lü Hubo, Lin Yigeng, et al. Denoising Method of Tunnel Blasting Seismic Wave Signal Based on CEEMDAN-MPE Algorithm and Its Application[J]. Blasting, 2020, 37(4): 138-144 https://www.cnki.com.cn/Article/CJFDTOTAL-BOPO202004023.htm
    [38]
    彭宇. GNSS高精度垂向分量探寻区域地表形变机制及地球深部构造运动信号[D]. 上海: 华东师范大学, 2019.

    Peng Yu. Explorating Mechanism of the Regional Surface Deformation and the Deep Tectonic Signals Using High-Precision GNSS Vertical Solutions[D]. Shanghai: East China Normal University, 2019
    [39]
    明锋, 杨元喜, 曾安敏, 等. 中国区域IGS站高程时间序列季节性信号及长期趋势分析[J]. 中国科学: 地球科学, 2016, 46(6): 834-844. https://www.cnki.com.cn/Article/CJFDTOTAL-JDXK201606008.htm

    Ming Feng, Yang Yuanxi, Zeng Anmin, et al. Seasonal Signal and Long-Term Trend Analysis of Elevation Time Series of IGS Station in China Area[J]. Scientia Sinica (Terrae), 2016, 46(6): 834-844 https://www.cnki.com.cn/Article/CJFDTOTAL-JDXK201606008.htm
    [40]
    胡顺强, 王坦, 管雅慧, 等. 利用GPS和水文负载模型研究云南地区垂向季节性波动变化和构造变形[J]. 地球物理学报, 2021, 64(8): 2613-2630. https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX202108004.htm

    Hu Shunqiang, Wang Tan, Guan Yahui, et al. Analyzing the Seasonal Fluctuation and Vertical Deformation in Yunnan Province Based on GPS Measurement and Hydrological Loading Model[J]. Chinese Journal of Geophysics, 2021, 64(8): 2613-2630 https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX202108004.htm
    [41]
    黄立人. GPS基准站坐标分量时间序列的噪声特性分析[J]. 大地测量与地球动力学, 2006, 26(2): 31-33. https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB200602005.htm

    Huang Liren. Noise Properties in Time Series of Coordinate Component at GPS Fiducial Stations[J]. Journal of Geodesy and Geodynamics, 2006, 26(2): 31-33 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB200602005.htm
    [42]
    占伟, 黄立人, 刘志广, 等. 数据缺失对GNSS时间序列分析的影响[J]. 大地测量与地球动力学, 2013, 33(2): 49-53. https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201302012.htm

    Zhan Wei, Huang Liren, Liu Zhiguang, et al. Effect of Data Defect on Analyzing GNSS Time Series[J]. Journal of Geodesy and Geodynamics, 2013, 33(2): 49-53 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201302012.htm
    [43]
    张卫柱, 严薇, 孙亮, 等. 北斗全球导航卫星的运动学解算方法研究[J]. 测绘与空间地理信息, 2014, 37(8): 50-52. https://www.cnki.com.cn/Article/CJFDTOTAL-DBCH201408015.htm

    Zhang Weizhu, Yan Wei, Sun Liang, et al. Research on Kinematics Parameters Calculation Algorithms of Compass Global Navigation Satellite[J]. Geomatics & Spatial Information Technology, 2014, 37(8): 50-52 https://www.cnki.com.cn/Article/CJFDTOTAL-DBCH201408015.htm
    [44]
    安云飞. 一种用于BDS-3接收机的分段Hermite插值方法[J]. 全球定位系统, 2020, 45(4): 95-100. https://www.cnki.com.cn/Article/CJFDTOTAL-QUDW202004016.htm

    An Yunfei. A Piecewise Hermite Interpolation Method for BDS-3 Receiver[J]. GNSS World of China, 2020, 45(4): 95-100 https://www.cnki.com.cn/Article/CJFDTOTAL-QUDW202004016.htm
    [45]
    Bos M S, Fernandes R S, Williams S P, et al. Fast Error Analysis of Continuous GNSS Observations with Missing Data[J]. Journal of Geodesy, 2013, 87(4): 351-360.
    [46]
    Williams S D P, Bock Y, Fang P, et al. Error Analysis of Continuous GPS Position Time Series[J]. Journal of Geophysical Research: Solid Earth, 2004, 109(B3), DOI: 10.1029/2003JB002741.
    [47]
    乔学军, 王琪, 吴云, 等. 中国大陆GPS基准站的时间序列特征[J]. 武汉大学学报(信息科学版), 2003, 28(4): 413-416. http://ch.whu.edu.cn/article/id/4838

    Qiao Xuejun, Wang Qi, Wu Yun, et al. Time Series Characteristic of GPS Fiducial Stations in China[J]. Geomatics and Information Science of Wuhan University, 2003, 28(4): 413-416 http://ch.whu.edu.cn/article/id/4838
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