加权模糊C均值聚类算法实现BDS三频组合观测值优选
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摘要
在对BDS三频载波相位组合观测值进行误差分析的基础上,确定了优选载波相位线性组合系数的筛选标准。针对传统聚类算法在高维多频混合数据集分类中存在的不足,采用一种基于加权的模糊C均值聚类算法,通过对同一维度在不同簇上赋予不同的权重值,对传统遍历搜索法所获得的部分BDS三频载波相位组合观测值进行了优化分类选取,有效解决了传统全球导航卫星系统载波相位观测值选取方法效率低的问题,同时为多系统多频数据组合观测值系数的优化选取提供了一种新的思路。对分类结果进行分析,确定了各类组合观测量的适用范围,并结合实测数据,利用无几何层叠模糊度解算方法对优选组合进行了整周模糊度的解算,结果验证了该方法的可行性。
Based on the error analysis of the BDS( BeiDou navigation satellite system) triple-frequency carrier phase observations,the screening criteria for the optimal carrier phase linear combination coefficients was determined. For high-dimensional multi-frequency mixed data sets,a weighted fuzzy C-means clustering algorithm was used to assign partial BDS triple-frequency carrier phase observations obtained by traditional ergodic search methods through assigning different weight values to different clusters on the same dimension. The combined observations were optimized for classification and selection,which effectively solved the problem of low efficiency of the traditional GNSS( global navigation satellite system) carrier phase observations selection method,and provided an idea for the optimal selection of the combined observation value coefficients of multi-system multi-frequency data. Finally,the classification results were analyzed,and the applicable range of all kinds of combined observations was determined. The integer ambiguity of the optimal combination is calculated by using the geometric-freed CIR( cascading integer resolution) algorithm and the measured data,and the feasibility and reliability of the method are proved.
Based on the error analysis of the BDS( BeiDou navigation satellite system) triple-frequency carrier phase observations,the screening criteria for the optimal carrier phase linear combination coefficients was determined. For high-dimensional multi-frequency mixed data sets,a weighted fuzzy C-means clustering algorithm was used to assign partial BDS triple-frequency carrier phase observations obtained by traditional ergodic search methods through assigning different weight values to different clusters on the same dimension. The combined observations were optimized for classification and selection,which effectively solved the problem of low efficiency of the traditional GNSS( global navigation satellite system) carrier phase observations selection method,and provided an idea for the optimal selection of the combined observation value coefficients of multi-system multi-frequency data. Finally,the classification results were analyzed,and the applicable range of all kinds of combined observations was determined. The integer ambiguity of the optimal combination is calculated by using the geometric-freed CIR( cascading integer resolution) algorithm and the measured data,and the feasibility and reliability of the method are proved.
引文
[1]杨元喜.北斗卫星导航系统的进展、贡献与挑战[J].测绘学报,2010,39(1):1-6.YANG Yuanxi. Progress,contribution and challenges of Compass/BeiDou satellite navigation system[J]. Acta Geodaetica et Cartographica Sinica,2010,39(1):1-6.(in Chinese)
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[3]宁津生,姚宜斌,张小红.全球导航卫星系统发展综述[J].导航定位学报,2013,1(1):3-8.NING Jinsheng,YAO Yibin,ZHANG Xiaohong. Review of the development of global satellite navigation system[J].Journal of Navigation and Positioning,2013,1(1):3-8.(in Chinese)
[4]邢喆,王泽民,伍岳.利用模糊聚类方法筛选GPS载波相位组合观测值[J].武汉大学学报(信息科学版),2006,31(1):23-26.XING Zhe,WANG Zemin,WU Yue. Choice of carrier phase combined observation of GPS using fuzzy cluster[J].Geomatics and Information Science of Wuhan University,2006,31(1):23-26.(in Chinese)
[5]黄令勇,宋力杰,刘先冬.基于自适应聚类算法的GPS三频载波相位组合观测值优化选取[J].大地测量与地球动力学,2011,31(4):99-102.HUANG Lingyong,SONG Lijie,LIU Xiandong. Optimization and selection of GPS triple-carries phase combination observations based self-adaptive clustering algorithm[J].Journal of Geodesy and Geodynamics,2011,31(4):99-102.(in Chinese)
[6]何伟,陶庭叶,王志平.基于改进FCM的北斗三频组合观测值选取[J].中国空间科学技术,2014,34(4):24-30.HE Wei, TAO Tingye, WANG Zhiping. Selection on improved fuzzy C-means algorithm of BeiDou triple-frequency combination observations[J]. Chinese Space Science and Technology,2014,34(4):24-30.(in Chinese)
[7]王勇,赵修斌,庞春雷,等. BDS/GPS四频组合观测值系数选择方法与分析[J].空军工程大学学报(自然科学版),2014(4):70-74.WANG Yong, ZHAO Xiubin, PANG Chunlei, et al. A selective method and analysis of BDS/GPS four-frequency combination observational coefficients[J]. Journal of Air Force Engineering University(Natural Science Edition),2014(4):70-74.(in Chinese)
[8]Cocard M, Bourgon S, Kamali O, et al. A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS[J]. Journal of Geodesy,2008,82(9):555-564.
[9]张小红,何锡扬.北斗三频相位观测值线性组合模型及特性研究[J].中国科学:地球科学,2015(5):601-610.ZHANG Xiaohong, HE Xiyang. BeiDou triple-frequency phase observation linear combination model and its characteristics[J]. Chinese Science:Earth Science,2015(5):601-610.(in Chinese)
[10]颜怀成,韩保民,张家新.北斗三频相位观测值线性组合研究[J].中国空间科学技术,2017,37(1):104-110.YAN Huaicheng,HAN Baomin,ZHANG Jiaxin. Research on triple-frequency carrier-phase observation linear combination of BeiDou satellite navigation system[J]. Chinese Space Science and Technology,2017,37(1):104-110.(in Chinese)
[11]孟凡军,李树军,潘宗鹏,等.基于FCM算法的BDS三频载波相位组合观测值优化选取[J].大地测量与地球动力学,2019,39(3):246-251.MENG Fanjun, LI Shujun, PAN Zongpeng, et al.Optimization and selection of BDS triple-frequency carrier phase combination observations based on fuzzy C-means algorithm[J]. Journal of Geodesy and Geodynamics,2019,39(3):246-251.(in Chinese)
[12]Ahmad A,Dey L. A k-means type clustering algorithm for subspace clustering of mixed numeric and categorical datasets[J]. Pattern Recognition Letters,2011,32(7):1062-1069.
[13]王振博.模糊C均值聚类算法的研究与改进[D].郑州:郑州大学,2014.WANG Zhenbo. The study and improvement of fuzzy C-means clustering algorithm[D]. Zhengzhou:Zhengzhou University,2014.(in Chinese)
[14]Kwon S H. Cluster validity index for fuzzy clustering[J].Electronic Letters,1998,34(22):2176-2177.
[15]王生朝.北斗三频模糊度解算方法研究[D].徐州:中国矿业大学,2015.WANG Shengzhao. Study on the ambiguity resolution methods based on compass triple-frequency data[D]. Xuzhou:China University of Mining and Technology,2015.(in Chinese)
[16]Tang W M,Deng C L,Shi C,et al. Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system[J]. GPS Solutions,2014,18(3):335-344.
[17]Wang X,Liu W X,Sun G F. An improved geometry-free three carrier ambiguity resolution method for the BeiDou navigation satellite system[J]. Journal of Navigation,2016,69(6):1393-1408.
[2]冉承其.北斗卫星导航系统的发展[J].卫星应用,2013(4):4-7.RAN Chengqi. Development of BeiDou satellite navigation system[J]. Satellite Application,2013(4):4-7.(in Chinese)
[3]宁津生,姚宜斌,张小红.全球导航卫星系统发展综述[J].导航定位学报,2013,1(1):3-8.NING Jinsheng,YAO Yibin,ZHANG Xiaohong. Review of the development of global satellite navigation system[J].Journal of Navigation and Positioning,2013,1(1):3-8.(in Chinese)
[4]邢喆,王泽民,伍岳.利用模糊聚类方法筛选GPS载波相位组合观测值[J].武汉大学学报(信息科学版),2006,31(1):23-26.XING Zhe,WANG Zemin,WU Yue. Choice of carrier phase combined observation of GPS using fuzzy cluster[J].Geomatics and Information Science of Wuhan University,2006,31(1):23-26.(in Chinese)
[5]黄令勇,宋力杰,刘先冬.基于自适应聚类算法的GPS三频载波相位组合观测值优化选取[J].大地测量与地球动力学,2011,31(4):99-102.HUANG Lingyong,SONG Lijie,LIU Xiandong. Optimization and selection of GPS triple-carries phase combination observations based self-adaptive clustering algorithm[J].Journal of Geodesy and Geodynamics,2011,31(4):99-102.(in Chinese)
[6]何伟,陶庭叶,王志平.基于改进FCM的北斗三频组合观测值选取[J].中国空间科学技术,2014,34(4):24-30.HE Wei, TAO Tingye, WANG Zhiping. Selection on improved fuzzy C-means algorithm of BeiDou triple-frequency combination observations[J]. Chinese Space Science and Technology,2014,34(4):24-30.(in Chinese)
[7]王勇,赵修斌,庞春雷,等. BDS/GPS四频组合观测值系数选择方法与分析[J].空军工程大学学报(自然科学版),2014(4):70-74.WANG Yong, ZHAO Xiubin, PANG Chunlei, et al. A selective method and analysis of BDS/GPS four-frequency combination observational coefficients[J]. Journal of Air Force Engineering University(Natural Science Edition),2014(4):70-74.(in Chinese)
[8]Cocard M, Bourgon S, Kamali O, et al. A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS[J]. Journal of Geodesy,2008,82(9):555-564.
[9]张小红,何锡扬.北斗三频相位观测值线性组合模型及特性研究[J].中国科学:地球科学,2015(5):601-610.ZHANG Xiaohong, HE Xiyang. BeiDou triple-frequency phase observation linear combination model and its characteristics[J]. Chinese Science:Earth Science,2015(5):601-610.(in Chinese)
[10]颜怀成,韩保民,张家新.北斗三频相位观测值线性组合研究[J].中国空间科学技术,2017,37(1):104-110.YAN Huaicheng,HAN Baomin,ZHANG Jiaxin. Research on triple-frequency carrier-phase observation linear combination of BeiDou satellite navigation system[J]. Chinese Space Science and Technology,2017,37(1):104-110.(in Chinese)
[11]孟凡军,李树军,潘宗鹏,等.基于FCM算法的BDS三频载波相位组合观测值优化选取[J].大地测量与地球动力学,2019,39(3):246-251.MENG Fanjun, LI Shujun, PAN Zongpeng, et al.Optimization and selection of BDS triple-frequency carrier phase combination observations based on fuzzy C-means algorithm[J]. Journal of Geodesy and Geodynamics,2019,39(3):246-251.(in Chinese)
[12]Ahmad A,Dey L. A k-means type clustering algorithm for subspace clustering of mixed numeric and categorical datasets[J]. Pattern Recognition Letters,2011,32(7):1062-1069.
[13]王振博.模糊C均值聚类算法的研究与改进[D].郑州:郑州大学,2014.WANG Zhenbo. The study and improvement of fuzzy C-means clustering algorithm[D]. Zhengzhou:Zhengzhou University,2014.(in Chinese)
[14]Kwon S H. Cluster validity index for fuzzy clustering[J].Electronic Letters,1998,34(22):2176-2177.
[15]王生朝.北斗三频模糊度解算方法研究[D].徐州:中国矿业大学,2015.WANG Shengzhao. Study on the ambiguity resolution methods based on compass triple-frequency data[D]. Xuzhou:China University of Mining and Technology,2015.(in Chinese)
[16]Tang W M,Deng C L,Shi C,et al. Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system[J]. GPS Solutions,2014,18(3):335-344.
[17]Wang X,Liu W X,Sun G F. An improved geometry-free three carrier ambiguity resolution method for the BeiDou navigation satellite system[J]. Journal of Navigation,2016,69(6):1393-1408.
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