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

Abstract

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

CLC Number:

TN967.1

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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References 28

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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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Integrity risk allocation of GBAS protection level using Bayesian decision

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