基于极值理论的地基增强系统完好性评估方法

doi:10.12382/bgxb.2022.0636

摘要/Abstract

摘要：

针对地基增强系统(Ground Based Augmentation System, GBAS)完好性风险事件的极端性而导致的无法通过风险事件发生频率评估系统性能的问题,提出一种基于极值理论的GBAS完好性评估方法。根据机载端(位置域)输出的位置误差和保护级计算安全系数,并利用区间极大值模型对安全系数进行建模描述以获得其分布模型;利用极大似然法估计安全系数模型参数,进而利用模型外推法计算GBAS完好性风险值。给出GBAS完好性评估流程,并利用GBAS系统进行了验证实验。研究结果表明:对于C类GBAS进近服务而言,基于全球定位系统(Global Position System, GPS)增强GBAS和基于北斗卫星导航系统(Beidou Navigation Satellite System, BDS)增强GBAS可用性均大于99.9999%;对于F类GBAS进近服务而言,BDS GBAS可用性能要优于GPS GBAS;根据7d观测数据外推得到的GPS GBAS垂直和侧向完好性风险值分别为4.557×10^-8/进近和5.152×10^-8/进近,BDS GBAS垂直和侧向完好性风险值分别为1.612×10^-7/进近和1.823×10^-7/进近,满足航空器终端区I类进近与着陆导航性能需求。

关键词: 地基增强系统, 完好性风险, 极值理论, 安全系数

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

中图分类号:

TN967.1

胡杰, 严勇杰, 丁辉. 基于极值理论的地基增强系统完好性评估方法[J]. 兵工学报, 2024, 45(2): 641-650.

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.

图/表 15

图1 保护级与告警限关系图

Fig.1 Relationship between protection level and alarm limit

图2 GAST-C类GBAS运行24h Stanford图

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

图3 GBAS完好性评估位置域示意图

Fig.3 Position domain of GBAS integrity evaluation

图4 GBAS系统图和卫星信号接收天线

Fig.4 GBAS system and satellite signal receiving antenna

图5 GBAS完好性评估流程结构

Fig.5 GBAS integrity evaluation process structure

图6 24h内GPS可见卫星个数以及DOP值

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

图7 24h内BDS可见卫星个数以及DOP值

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

图8 GPS GBAS机载用户输出VPE、VPL和VAL

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

图9 BDS GBAS机载用户输出VPE、VPL和VAL

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

表1 VPE和VPL数值统计

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

图10 GPS GBAS机载用户7d输出VPE、VPL和VAL

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

图11 GPS GBAS完好性评估Stanford图

Fig.11 Stanford chart of integrity evaluation for GPS GBAS

表2 垂直安全系数BMM模型参数

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]

图12 样本数据实际分布和BMM模型拟合曲线

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

表3 基于极值BMM模型得到的GBAS完好性评估结果

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]

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