核模糊C均值聚类算法优选BDS-3三频组合观测值

doi:10.3969/j.issn.1001-506X.2020.03.025

摘要/Abstract

摘要：

目前对全球导航卫星系统(global navigation satellite system, GNSS)三频组合观测值优选的研究,主要集中在全球定位系统(global positioning system, GPS)和北斗二号(beidou navigation satellite system, BDS-2)上,对BDS-3的研究相对较少。为克服以往聚类优选算法中存在的仅适用于类球形簇、聚类数目和初始聚类中心的确定主观性强、对离群点敏感、易陷于局部最优等不足,提出一种改进的核模糊C均值聚类算法,引入核函数与抑制离群点的新距离度量,基于多类广义核极化准则优化核参数,用改进爬山法确定聚类数目与初始聚类中心。然后,以模糊C均值聚类算法为对照进行了对比实验,在短、长两种基线下分别解算组合模糊度。通过对优选所得代表性组合的模糊度固定成功率进行对比分析,验证了该算法的可行性与算法改进的有效性。

关键词: 三频组合观测值, 改进的核模糊C均值聚类算法, 矩阵变换法, 模糊度固定

Abstract:

At present, researches on the optimization of global navigation satellite system (GNSS) triple-frequency combination observations mainly focus on global positioning system (GPS) and Beidou navigation satellite system (BDS)-2, while researches on BDS-3 are relatively few. In order to overcome the shortcomings of previous clustering optimization algorithms, which are only applicable to spherical clusters, highly subjective in the determination of clustering number and initial clustering centers, sensitive to outliers, and easily trapped in local optimal, a modified kernel-based fuzzy C-means (KFCM) clustering algorithm is introduced. This algorithm improves the above deficiencies by using the kernel function and a new kind of distance measure which can suppress the effect of outliers, optimize Gaussian kernel parameters based on generalized kernel polarization, initiale the number of clusters and the selection of initial clustering centers based on a new kind of modified mountain method. Then the fuzzy C-means clustering algorithm is used as a comparison experiment. Under short and long baseline conditions, the combination ambiguity is calculated respectively. By comparing and analyzing the ambiguity fixed success rate of the selected representative combinations, the feasibility of the algorithm and the effectiveness of the improved algorithm are proved.

Key words: triple-frequency combination, kernel-based fuzzy C-means clustering algorithm based on parameters optimization, matrix transformation algorithm, ambiguities fixing

中图分类号:

P288.4

田睿, 范祥祥, 戴影, 孙宪兵, 董绪荣. 核模糊C均值聚类算法优选BDS-3三频组合观测值[J]. 系统工程与电子技术, 2020, 42(3): 686-697.

Rui TIAN, Xiangxiang FAN, Ying DAI, Xianbing SUN, Xurong DONG. Optimal triple-frequency combination observations for BDS-3 derived from a modified kernel-based fuzzy C-means clustering algorithm[J]. Systems Engineering and Electronics, 2020, 42(3): 686-697.

图/表 19

表1

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

图15

图16

图17

图18

参考文献 53

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 Y X . Progress, contribution and challenges of compass/Beidou satellite navigation system[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39 (1): 1- 6.
2	BEIDOU I C D. Beidou navigation satellite system signal in space interface control document open service signal B1I(Version 3.0)[EB/OL].[2019-12-02].http://www.beidou.gov.cn/xt/gfxz/index.html.
3	BEIDOU I C D. Beidou navigation satellite system signal in space interface control document open service signal B1C (Version 1.0)[EB/OL].[2019-12-02].http://www.beidou.gov.cn/xt/gfxz/index_1.html.
4	BEIDOU I C D. Beidou navigation satellite system signal in space interface control document open service signal B3I (Version 1.0)[EB/OL].[2019-12-02].http://www.beidou.gov.cn/xt/gfxz/index.html.
5	BEIDOU I C D. Beidou navigation satellite system signal in space interface control document open service signal B2a (Version 1.0)[EB/OL].[2019-12-02].http://www.beidou.gov.cn/xt/gfxz/index.html.
6	付伟, 董绪荣, 王敏, 等. 北斗三号三频组合观测值特性分析研究[J]. 全球定位系统, 2018, 43 (5): 1- 8.
	FU W , DONG X R , WANG M , et al. Analysis and research on the characteristics of BDS-3 three-frequency combination observation[J]. GNSS World of China, 2018, 43 (5): 1- 8.
7	FENG Y . GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals[J]. Journal of Geodesy, 2008, 82 (12): 847- 862. doi: 10.1007/s00190-008-0209-x
8	肖凯, 孙付平, 王浩源, 等. 北斗/INS紧组合的惯性辅助三频周跳探测和修复[J]. 中国惯性技术学报, 2018, 26 (2): 215- 222.
	XIAO K , SUN F P , WANG H Y , et al. Auxiliary triple frequency cycle slip detection and repair of BDS/INS tight combination[J]. Journal of Chinese Inertial Technology, 2018, 26 (2): 215- 222.
9	肖凯, 孙付平, 王浩源. 三频差分GNSS/INS紧组合模型[J]. 中国惯性技术学报, 2018, 26 (2): 180- 186.
	XIAO K , SUN F P , WANG H Y . Three-frequency differential GNSS/ INS tight combination model[J]. Journal of Chinese Inertial Technology, 2018, 26 (2): 180- 186.
10	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. doi: 10.3969/j.issn.1009-3516.2014.04.017
	WANG Y , ZHAO X B , PANG C L , et al. A selective method and analysis of BDS/GPS four-frequency combination observation coefficients[J]. Journal of Air Force Engineering University (Natural Science Edition), 2014, 4, 70- 74. doi: 10.3969/j.issn.1009-3516.2014.04.017
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): 30- 35.
	MENG F J , LI S J , PAN Z P , et al. Optimization selection of BDS three-frequency carrier phase combination observation based on FCM algorithm[J]. Journal of Geodesy and Geodynamics, 2019, 39 (3): 30- 35.
12	COCARD M , STÉPHANIE B , 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. doi: 10.1007/s00190-007-0201-x
13	李金龙, 杨元喜, 何海波, 等. 函数极值法求解三频GNSS最优载波相位组合观测量[J]. 测绘学报, 2012, 41 (6): 797- 803.
	LI J L , YANG Y X , HE H B , et al. Optimal carrier-phase combinations for triple-frequency GNSS derived from an analytical method[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41 (6): 797- 803.
14	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 Z , WANG Z M , WU Y . Choice of carrier phase combined observation of GPS using fuzzy cluster[J]. Geomatics And Information Science Of Wuhan University, 2006, 31 (1): 23- 26.
15	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 L Y , SONG L J , LIU X D . Optimization of GPS trifrequency carrier phase combination observation based on adaptive clustering algorithm[J]. Journal of Geodesy and Geodynamics, 2011, 31 (4): 99- 102.
16	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 W , TAO T Y , WANG Z P . Selection of Beidou tri-band combined observation value based on improved FCM[J]. Chinese Space Science and Technology, 2014, 34 (4): 24- 30.
17	孟凡军, 李树军, 潘宗鹏, 等. 加权模糊C均值聚类算法实现BDS三频组合观测值优选[J]. 国防科技大学学报, 2019, 41 (3): 92- 98.
	MENG F J , LI S J , PAN Z P , et al. Optimization and selection of BDS triple-frequency combination obvervations based on a weighted fuzzy C-menas algorithm[J]. Journal of National University of Defense Technology, 2019, 41 (3): 92- 98.
18	孔攀.模糊聚类分析及其有效性研究[D].重庆:西南大学, 2009.
	KONG P.Fuzzy clustering analysis and its validity[D]. Chongqing: Southwest University, 2009.
19	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 Z B.Research and improvement of fuzzy C-means clustering algorithm[D]. Zhengzhou: Zhengzhou University, 2014.
20	伍忠东, 高新波, 谢维信. 基于核方法的模糊聚类算法[J]. 西安电子科技大学学报(自然科学版), 2004, 31 (4): 533- 537. doi: 10.3969/j.issn.1001-2400.2004.04.011
	WU Z D , GAO X B , XIE W X . Fuzzy clustering algorithm based on kernel method[J]. Journal Of Xidian University (Natural Science), 2004, 31 (4): 533- 537. doi: 10.3969/j.issn.1001-2400.2004.04.011
21	张敏, 于剑. 基于划分的模糊聚类算法[J]. 软件学报, 2004, 15 (6): 858- 868.
	ZHANG M , YU J . Fuzzy clustering algorithm based on partition[J]. Journal of Software, 2004, 15 (6): 858- 868.
22	程可嘉.基于核函数的模糊聚类算法研究[D].成都:电子科技大学, 2009.
	CHENG K J. Research on fuzzy clustering algorithm based on kernel function[D]. Chengdu: University of Electronic Science and Technology of China, 2009.
23	WU F, ZHENG W, LI Z, et al.Improving the positioning accuracy of satellite-borne GNSS-R specular reflection point on sea surface based on the ocean tidal correction positioning method[J]. Remote Sensing, 2019, 11(13): Article ID: 1626.
24	WU F, ZHENG W, LI Z, et al. Improving the GNSS-R specular reflection point positioning accuracy using the gravity field normal projection reflection reference surface combination correction method[J]. Remote Sensing, 2019, 11(1): Article ID: 33.
25	陆德彪, 唐德璋, 蔡伯根, 等. 基于最大偏差准则的列车卫星定位完好性监测方法[J]. 铁道学报, 2019, 41 (6): 81- 90. doi: 10.3969/j.issn.1001-8360.2019.06.012
	LU D B , TANG D J , CAI B G , et al. A method for monitoring the integrity of train satellite positioning based on maximum deviation criterion[J]. Journal of the China Railway Society, 2019, 41 (6): 81- 90. doi: 10.3969/j.issn.1001-8360.2019.06.012
26	吴波前, 蔡伯根, 陆德彪, 等. 基于卫星导航的列车轨道占用加权识别方法研究[J]. 交通运输系统工程与信息, 2019, 19 (3): 62- 67, 80.
	WU B Q , CAI B G , LU D J , et al. Study on weighted recognition method of train track occupation based on satellite navigation[J]. Transportation Systems Engineering and Information, 2019, 19 (3): 62- 67, 80.
27	伍岳.第二代导航卫星系统多频数据处理理论及应用[D].武汉:武汉大学, 2005.
	WU Y.The theory and application of multi-frequency data processing in the second generation navigation satellite system[D].Wuhan: Wuhan University, 2005.
28	MOHAMED B, AHMED T, LASSAD H, et al. A new extension of fuzzy C-means algorithm using non euclidean distance and Kernel methods[C]//Proc.of the International Conference on Control, Decision and Information Technologie, 2013: 242-249.
29	CHUI S L . Fuzzy model identification based on cluster estimation[J]. Journal of Intelligent and Fuzzy Systems, 1994, 2 (3): 267- 278. doi: 10.3233/IFS-1994-2306
30	牛莉博, 李玉兰, 傅楗强, 等. 基于改进爬山法的带电粒子圆径迹重建[J]. 原子能科学技术, 2014, 48 (S1): 673- 678.
	NIU L B , LI Y L , FU Y Q , et al. Revolution of charged particle circular track based on improved hill climbing method[J]. Atomic Energy Science and Technology, 2014, 48 (S1): 673- 678.
31	孔祥玉, 胡启安, 董旭柱, 等. 引入改进模糊C均值聚类的负荷数据辨识及修复方法[J]. 电力系统自动化, 2017, 41 (9): 96- 101.
	KONG X Y , HU Q A , DONG X Z , et al. Load data identification and repair method based on improved fuzzy C-means clustering[J]. Automation of Electric Power Systems, 2017, 41 (9): 96- 101.
32	SCHÖLKOPF B , SMOLA A J . Learning with kernels[M]. 1st ed. Massachusetts: MIT Press, 2001.
33	GIROLAMI M . Mercer kernel-based clustering in feature space[J]. IEEE Trans.on Neural Networks, 2002, 13 (3): 780- 784. doi: 10.1109/TNN.2002.1000150
34	LIU S Y, DONG L, LIAO X Z, et al. Photovoltaic array fault diagnosis based on gaussian kernel fuzzy C-means clustering algorithm[J]. Sensors, 2019, 19(7): Article ID: 1520.
35	刘云, 刘富, 侯涛, 等. 优化核参数的模糊C均值聚类算法[J]. 吉林大学学报(工学版), 2016, 46 (1): 246- 251.
	LIU Y , LIU F , HOU T , et al. Fuzzy C-means clustering algorithm for optimizing kernel parameters[J]. Journal of Jilin University (Engineering Science), 2016, 46 (1): 246- 251.
36	CRISTIANINI N, SHAWETAYLOR J, ELISSEEFF A, et al. On kernel-target alignment[C]//Proc.of the International Conference on Neural Information Processing Systems, Natural & Synthetic, 2002: 367-373.
37	CORTES C, MOHRI M, ROSTAMIZADEH A, et al. Two-stage learning kernel algorithms[C]//Proc.of the 27th International Conference on Machine Learning, 2010: 239-246.
38	NGUYEN C H, TU B H. Kernel matrix evaluation[C]//Proc.of the International Joint Conference on Artifical Intelligence, 2007: 987-992.
39	LIU Y , LIAO S Z . Kernel selection with spectral perturbation stability of kernel matrix[J]. Science China Information Sciences, 2014, 57 (11): 1- 10.
40	田萌, 王文剑. 高斯核函数选择的广义核极化准则[J]. 计算机研究与发展, 2015, 52 (8): 1722- 1734.
	TIAN M , WANG W J . Generalized kernel polarization criterion for Gaussian kernel function selection[J]. Journal of Computer Research and Development, 2015, 52 (8): 1722- 1734.
41	WANG W , XU Z , LU W , et al. Determination of the spread parameter in the Gaussian kernel for classification and regression[J]. Neurocomputing, 2003, 55 (3): 643- 663.
42	WANG T , ZHAO D , FENG Y . Two-stage multiple kernel learning with multiclass kernel polarization[J]. Knowledge-Based Systems, 2013, 48 (2): 10- 16.
43	WANG T , TIAN S , HUANG H , et al. Learning by local kernel polarization[J]. Neurocomputing, 2009, 72 (13/15): 3077- 3084.
44	CORTES C , MOHRI M , ROSTAMIZADEH A . Algorithms for learning kernels based on centered alignment[J]. Journal of Machine Learning Research, 2012, 13 (2): 795- 828.
45	HAN S, RIZOS C. The impact of two additional civilian GPS frequencies on ambiguity resolution strategies[C]//Proc.of the ION Annual Technical Meeting, 1999: 315-321.
46	ZHANG X H , HE X Y . BDS triple-frequency carrier-phase linear combination models and their characteristics[J]. Science China Earth Sciences, 2015, 58 (6): 896- 905. doi: 10.1007/s11430-014-5027-9
47	LI J , YANG Y , HE H , et al. An analytical study on the carrier-phase linear combinations for triple-frequency GNSS[J]. Journal of Geodesy, 2017, 91 (2): 151- 166. doi: 10.1007/s00190-016-0945-2
48	TODD R , NASER E S . Optimal linear combinations of triple frequency carrier phase data from future global navigation satellite systems[J]. GPS Solutions, 2007, 11 (1): 11- 19.
49	王生朝.北斗三频模糊度解算方法研究[D].北京,中国矿业大学, 2015.
	WANG S C. Research on the solution method of Beidou tri-frequency ambiguity[D]. Beijing: China University of Mining and Technology, 2015.
50	黄令勇, 宋力杰, 王琰, 等. 基于矩阵变换算法的长基线多频模糊度快速解算[J]. 大地测量与地球动力学, 2012, 32 (5): 133- 136.
	HUANG L Y , SONG L J , WANG D , et al. A fast solution to long-baseline multi-frequency ambiguity based on matrix transformation algorithm[J]. Geodesy and Geodynamics, 2012, 32 (5): 133- 136.
51	秦大同, 詹森, 漆正刚, 等. 基于K-均值聚类算法的行驶工况构建方法[J]. 吉林大学学报(工学版), 2016, 46 (2): 383- 389.
	QIN D T , ZHAN S , QI Z G , et al. Construction method of driving conditions based on K-means clustering algorithm[J]. Journal of Jilin University (Engineering Science), 2016, 46 (2): 383- 389.
52	高建平, 任德轩, 郗建国. 基于全局K-means聚类算法的汽车行驶工况构建[J]. 河南理工大学学报(自然科学版), 2019, 38 (1): 117- 123.
	GAO J P , REN D X , XI J G . Building of vehicle driving conditions based on global K-means clustering algorithm[J]. Journal of Henan Polytechnic University (Natural Science Edition), 2019, 38 (1): 117- 123.
53	TEUNISSEN P J G . Success probability of integer GPS ambiguity rounding and bootstrapping[J]. Journal of Geodesy, 1998, 72 (10): 606- 612. doi: 10.1007/s001900050199

信号	信号分量	载波频率/MHz	调制方式
B1C	数据分量B1C_data	1 575.420	BOC(1, 1)
B1C	导频分量B1C_pilot	1 575.420	QMBOC(6, 1, 4/33)
B1I	—	1 561.098	BPSk
B2a	数据分量B2a_data	1 176.450	BPSK(10)
B2a	导频分量B2a_pilot	1 176.450	BPSK(10)
B3I	—	1 268.520	BPSK