利用贝叶斯决策的GBAS保护级完好性风险分配

doi:10.3969/j.issn.1001-506X.2020.10.18

摘要/Abstract

摘要：

完好性风险是描述导航系统完好性重要指标之一。美国航空无线电技术委员会(Radio Technical Commission for Aeronautics, RTCA)在其标准DO-245A中提到,可依据Ⅰ类陆基增强系统(groud-based augmentation system, GBAS)地面基准站中的基准台数将保护级完好性风险分配于H₀和H₁假设,用于计算漏检乘积因子和GBAS保护级。此方法未能依据基准台故障情况分配完好性风险概率,导致保护级无法较准确地反映GBAS位置误差。本文利用Bayesian决策,基于最小总错误率准则重新分配H₀和H₁假设下的完好性风险概率。仿真分析了不同基准台数以及不同误差分布下完好性风险概率的分配,并计算了漏检乘积因子和垂直保护级,结果表明在基准台数大于2以及存在零均值或非零均值高斯分布的垂直位置误差时,基于Bayesian决策的完好性分配算法降低了保护级数值。理论分析和仿真实验表明,基于最小总错误率准则重新分配H₀和H₁假设下的完好性风险概率,减小了完好性风险分配的错误率,使保护级紧致地包络实际定位误差。

关键词: 完好性风险, 陆基增强系统, H₀假设, H₁假设, 贝叶斯决策

Abstract:

The integrity risk is one of the important indexes to describe the integrity of navigation systems. The missed multiplication factor and the protection levels of groud-based augmentation system (GBAS) can be calculated according to the protection level integrity risk assigned to the H₀ and H₁ hypotheses based on the number of the reference sites of categroty Ⅰ GBAS, mentioned in the standard DO-245A of the American Radio Technical Commission for Aeronautics (RTCA). This method fails to allocate the integrity risk probability based on the fault conditions of the reference sites, resulting in the protection levels not accurately reflecting the positioning errors of the GBAS. In this paper, the probability of the integrity risk is reallocated for the H₀ and H₁ hypotheses based on the minimum total error rate criterion utilizing the Bayesian decision. The integrity risk probability allocation is simulated and analysed for the conditions of different number of the reference sites and different error distributions, and the missed multiplication factor and vertical protection level are calculated, the results show that the values of the protection levels are reduced based on the integrity allocation algorithm of the Bayesian decision when the number of reference sites is greater than 2 and the vertical position errors obey the zero-mean or non-zero mean Gaussian distribution. Theoretical analysis and simulation experiments show that the error rate of integrity risk allocation is reduced by reallocating the probability of integrity risk under the H₀ and H₁ hypotheses based on the minimum total error rate criterion, and the actual positioning errors are more tightly enveloped by the protection levels.

Key words: integrity risk, groud-based augmentation system(GBAS), H₀ hypothesis, H₁ hypothesis, Bayesian decision

中图分类号:

TN967.1

倪育德, 刘希之, 陈楚佳. 利用贝叶斯决策的GBAS保护级完好性风险分配[J]. 系统工程与电子技术, 2020, 42(10): 2294-2302.

Yude NI, Xizhi LIU, Chujia CHEN. Integrity risk allocation of GBAS protection level using Bayesian decision[J]. Systems Engineering and Electronics, 2020, 42(10): 2294-2302.

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基准台数(M)	完好性风险分配算法	H₀假设			H₁假设			VPL/m
基准台数(M)	完好性风险分配算法	完好性风险	P_ffmd	K_ffmd	完好性风险	P_md	K_md	最大值
2	传统分配	8.333×10^-9	8.333×10^-9	5.762	1.667×10^-8	1.667×10^-3	2.935	7.314
2	优化分配	2.382×10^-8	2.382×10^-8	5.581	1.178×10^-10	1.178×10^-5	3.678	8.920
3	传统分配	6.250×10^-9	6.250×10^-9	5.810	1.875×10^-8	1.875×10^-3	2.898	7.306
3	优化分配	2.295×10^-8	2.295×10^-8	5.587	2.008×10^-9	2.008×10^-4	3.539	7.026
4	传统分配	5.000×10^-9	5.000×10^-9	5.847	2.000×10^-8	2.000×10^-3	2.878	7.350
4	优化分配	2.154×10^-8	2.154×10^-8	5.599	3.463×10^-9	3.463×10^-4	3.394	7.042

误差分布	完好性风险分配算法	H₀假设			H₁假设			VPL/m
误差分布	完好性风险分配算法	完好性风险	P_ffmd	K_ffmd	完好性风险	P_md	K_md	最大值
零均值高斯分布	传统分配	5.000×10^-9	5.000×10^-9	5.847	2.000×10^-8	2.000×10^-3	2.878	7.350
零均值高斯分布	优化分配	2.154×10^-8	2.154×10^-8	5.599	3.463×10^-9	3.463×10^-4	3.394	7.042
非零均值高斯分布	传统分配	5.000×10^-9	5.000×10^-9	5.847	2.000×10^-8	2.000×10^-3	2.878	8.823
非零均值高斯分布	优化分配	1.939×10^-8	1.939×10^-8	5.617	0.561×10^-8	0.561×10^-3	3.258	7.952

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