Integrity Evaluation Method for Ground Based Augmentation System Based on Extreme Value Theory

doi:10.12382/bgxb.2022.0636

Abstract

Abstract:

In order to solve the problem that the performance of the ground based augmentation system (GBAS) cannot be evaluated by the frequency of risk event occurrence due to the extreme of the integrity risk events, an integrity evaluation method based on extreme value theory is proposed here. Firstly, the safety factor is calculated according to the position error and protection level of the airborne terminal (position domain) outputs, and it is modeled and described by the block maximum method to obtain its distribution model. And then the maximum likelihood method is used to estimate the parameters of the safety factor model, and the model extrapolation method is used to calculate the integrity risk value of GBAS. GBAS integrity evaluation process based on extreme block maximum method(BMM) model is given, and the verification experiments are carried out by using the self-developed GBAS system. The results show that, for GBAS approach service type C, the availabilities of global position system (GPS) GBAS and Beidou navigation satellite system (BDS) GBAS are greater than 99.9999%, while for GBAS approach service type F, the availability of BDS GBAS is better than that of GPS GBAS. Meanwhile, the vertical and lateral integrity risk values of GPS GBAS extrapolated from 7-day observation data are 4.557×10^-8 per approach and 5.152×10^-8 per approach, respectively, and the vertical and lateral integrity risk values of BDS GBAS are 1.612×10^-7 per approach and 1.823×10^-7 per approach, respectively, which can meet the requirements of Category I navigation performance in the airport terminal area for aircrafts.

Key words: ground based augmentation system, integrity risk, extreme value theory, safety factor

CLC Number:

TN967.1

HU Jie, YAN Yongjie, DING Hui. Integrity Evaluation Method for Ground Based Augmentation System Based on Extreme Value Theory[J]. Acta Armamentarii, 2024, 45(2): 641-650.

Figures/Tables 15

Fig.1 Relationship between protection level and alarm limit

Fig.2 Stanford chart of GAST-C GBAS performing for 24hours

Fig.3 Position domain of GBAS integrity evaluation

Fig.4 GBAS system and satellite signal receiving antenna

Fig.5 GBAS integrity evaluation process structure

Fig.6 The number of visible satellites and its DOP in 24hours for GPS

Fig.7 The number of visible satellites and its DOP in 24hours for BDS

Fig.8 VPE, VPL and VAL of airborne user for GPS GBAS

Fig.9 VPE, VPL and VAL of airborne user for BDS GBAS

Table 1 Statistics of VPE and VPL

增强模式	统计项	VPL/m	VPE/m
	均值	1.954	0.008
GPS	标准差	0.821	0.153
	最大值	7.898	0.731
	最小值	1.221	-0.715
	均值	1.141	0.032
BDS	标准差	0.423	0.142
	最大值	3.711	0.556
	最小值	0.747	-0.453

Fig.10 VPE, VPL and VAL of airborne user in 7days for GPS GBAS

Fig.11 Stanford chart of integrity evaluation for GPS GBAS

Table 2 BMM model parameters of vertical safety factor

参数	ξ	σ	μ
极大似然估计	0.102	0.0309	0.0517
极大似然估计95% 置信区间	[0.063, 0.141]	[0.0297, 0.0321]	[0.0502, 0.0533]

Fig.12 Actual distribution of sample data and fitting curve of BMM model

Table 3 GBAS integrity evaluation results based on extreme BMM model

增强模式	风险值/进近		95%置信区间风险值/进近
增强模式	垂直	侧向	垂直	侧向
GPS	4.557×10^-8	5.152×10^-8	[1.202×10^-9,4.48×10^-7]	[2.876×10^-9, 3.379×10^-7]
BDS	1.612×10^-7	1.823×10^-7	[8.024×10^-9,5.378×10^-7]	[7.212×10^-9, 2.160×10^-7]

References 25

[1]	WANG Z P, YIN Y, SONG D, et al. Dual smoothing ionospheric gradient monitoring algorithm for dual-frequency BDS GBAS[J]. Chinese Journal of Aeronautics, 2020, 33(12): 3395-3404. doi: 10.1016/j.cja.2020.04.030 URL
[2]	FELUX M, CIRCIU M S, LEE J Y, et al. Ionospheric gradient threat mitigation in future dual frequency GBAS[J]. International Journal of Aerospace Engineering, 2017, 2017: 4326018.
[3]	谢钢. GPS原理与接收机设计[M]. 北京: 电子工业出版社, 2017.
	XIE G. Principles of GPS and receiver design[M]. Beijing: Publishing House of Electronics Industry, 2017. (in Chinese)
[4]	PATEL J, KHANAFSEH S, PERVAN B. Detecting hazardous spatial gradients at satellite acquisition in GBAS[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(4): 3214-3230. doi: 10.1109/TAES.7 URL
[5]	薛瑞. 多频卫星导航系统完好性研究[D]. 北京: 北京航空航天大学, 2010: 17-18.
	XUE R. Research on integrity of multi-frequency GNSS[D]. Beijing: Beihang University, 2010: 17-18. (in Chinese)
[6]	ICAO. Annex 10, aeronautical telecommunications,Volume 1: radio navigation aids[S]. Montreal, Canada:ICAO, 2009.
[7]	袁运斌, 霍星亮, 张宝成. 近年来我国GNSS电离层延迟精确建模及修正研究进展[J]. 测绘学报, 2017, 46(10): 1364-1378. doi: 10.11947/j.AGCS.2017.20170349
	YUAN Y B, HUO X L, ZHANG B C. Research progress of precise models and correction for GNSS ionospheric delay in China over recent years[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1364-1378. (in Chinese) doi: 10.11947/j.AGCS.2017.20170349
[8]	石先武, 方伟华, 林伟, 等. 基于极值理论的中国台风降水分布不确定性分析[J]. 北京师范大学学报(自然科学版), 2011, 47(5): 493-501.
	SHI X W, FANG W H, LIN W, et al. Uncertainty of China typhoon rainfall probability estimation with different extreme-value models[J]. Journal of Beijing Normal University (Natural Science), 2011, 47(5): 493-501. (in Chinese)
[9]	李红权, 何敏园, 黄莹莹. 我国金融机构的系统重要性评估:基于多元极值理论[J]. 中国管理科学, 2020, 28(5): 14-24.
	LI H Q, HE M Y, HUANG Y Y. The evaluation of systemically important financial institute of China: based on multivariate extreme value theory[J]. Chinese Journal of Management Science, 2020, 28(5): 14-24. (in Chinese)
[10]	伍强, 徐浩军, 裴彬彬, 等. 基于吸引域与二元极值理论的结冰飞机飞行风险量化评估[J]. 航空学报, 2022, 43(5): 186-200.
	WU Q, XU H J, PEI B B, et al. Quantitative evaluation of flight risk of icing aircraft based on theory of region of attraction and binary extreme value[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(5): 186-200. (in Chinese)
[11]	巫诚诚. 基于极值理论的城市交叉口非机动车交通冲突模型研究[D]. 南京: 东南大学, 2021: 45-49.
	WU C C. Research of traffic conflict models between non-motor and motor in the intersection based on extreme theory[D]. Nanjing: Southeast University, 2021: 45-49. (in Chinese)
[12]	OBER P B, IMPARATO D, VERHAGEN S, et al. Empirical integrity verification of GNSS and SBAS based on the extreme value theory[J]. Journal of the Institute of Navigation, 2014, 61(1): 23-38.
[13]	KANNEMANS H. The generalized extreme value statistical method to determine the GNSS integrity performance[C]//Proceedings of the 2010 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing. Noordwijk, Netherlands: IEEE, 2010.
[14]	ZHU Y B, LIU Y, WANG Z P, et al. Evaluation of GBAS flight trials based on BDS and GPS[J]. IET Radar, Sonar & Navigation, 2020, 14(2): 233-241. doi: 10.1049/rsn2.v14.2 URL
[15]	胡杰, 章林, 朱倚娴, 等. 基于码载偏离度的改进自适应Hatch滤波算法[J]. 兵工学报, 2021, 42(3): 555-562. doi: 10.3969/j.issn.1000-1093.2021.03.011
	HU J, ZHANG L, ZHU Y X, et al. Improved adaptive Hatch filter algorithm based on code-carrier divergence[J]. Acta Armamentarii, 2021, 42(3): 555-562. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.03.011
[16]	石潇竹, 梁宸宇, 胡杰, 等. 基于北斗接收机多参考一致性B值阈值计算方法[J]. 探测与控制学报, 2020, 42(3): 31-34, 43.
	SHI X Z, LIANG C Y, HU J, et al. Beidou receivers’ B-value threshold multiple reference consistency computing method[J]. Journal of Detection & Control, 2020, 42(3): 31-34, 43. (in Chinese)
[17]	胡杰, 周玲, 朱倚娴. 双频双星座地基增强系统精度和完好性算法[J]. 导航定位与授时, 2020, 7(5): 82-90.
	HU J, ZHOU L, ZHU Y X. Performance evaluation and integrity algorithm of dual-frequency dual-constellation ground based augmentation system[J]. Navigation Position & Timing, 2020, 7(5): 82-90. (in Chinese)
[18]	CIRCIU M, MEURER M, FELUX M, et al. Evaluation of GPS L5 and Galileo E1 and E5a performance for future multifrequency and multiconstellation GBAS[J]. Journal of the Institute of Navigation, 2017, 64(1): 149-163.
[19]	DAUTERMANN T, MAYER C, ANTREICH F, et al. Non-Gaussian error modeling for GBAS integrity assessment[J]. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(1): 693-706. doi: 10.1109/TAES.2012.6129664 URL
[20]	胡杰, 周玲. 基于GPS的地基增强系统机载端完好性算法研究[J]. 大地测量与地球动力学, 2020, 40(10): 1007-1011.
	HU J, ZHOU L. Research on airborne integrity algorithm for ground based augmentation system based on GPS[J]. Journal of Geodesy and Geodynamics, 2020, 40(10): 1007-1011. (in Chinese)
[21]	孙颢, 石潇竹, 刘海颖, 等. 基于多参数稳定分布的GBAS垂直保护级计算[J]. 系统工程与电子技术, 2021, 43(4): 1030-1035. doi: 10.12305/j.issn.1001-506X.2021.04.20
	SUN H, SHI X Z, LIU H Y, et al. Calculation of GBAS vertical protection level based on multi-parameter stable distribution[J]. Systems Engineering and Electronics, 2021, 43(4): 1030-1035. (in Chinese)
[22]	WANG Z P, MACABIAU C, ZHANG J, et al. Prediction and analysis of GBAS integrity monitoring availability at LinZhi airport[J]. GPS Solutions, 2014, 18: 27-40. doi: 10.1007/s10291-012-0306-4 URL
[23]	DIMITRI P, ARNAB M, WASHINGTON Y O. Extreme value theory-based integrity monitoring of global navigation satellite systems[J]. GPS Solutions, 2014, 18: 133-145. doi: 10.1007/s10291-013-0317-9 URL
[24]	FAA. Siting criteria for ground based augmentation system (GBAS): 6884.1[S]. Washington, DC, US: FAA, 2010.
[25]	Minimum operational performance standards for GPS local area augmentation system airborne equipment:RTCA DO-253[S]. Washington, DC, US:RTCA, 2017.