﻿ 基于GPS的地基增强系统机载端完好性算法研究
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 大地测量与地球动力学  2020, Vol. 40 Issue (10): 1007-1011  DOI: 10.14075/j.jgg.2020.10.003

### 引用本文

HU Jie, ZHOU Ling. Research on Airborne Integrity Algorithm for Ground Based Augmentation System Based on GPS[J]. Journal of Geodesy and Geodynamics, 2020, 40(10): 1007-1011.

### Foundation support

Technical Innovation Program for Universities in Shanxi Province, No. 2019L0856;National Key Research and Development Program of China, No. 2017YFB0503401.

### 第一作者简介

HU Jie, PhD, engineer, majors in satellite navigation and signal processing research, E-mail: hj_cetc28@163.com.

### 文章历史

1. 运城学院物理与电子工程系，山西省运城市复旦西街1155号，044000

1 机载端完好性算法

 ${\rm Prob\left( {NSE > PL} \right)} < p$ (1)

 $\Delta \mathit{\boldsymbol{\vec y}} = \mathit{\boldsymbol{G}}\Delta \mathit{\boldsymbol{\vec x}} + \mathit{\boldsymbol{\vec \varepsilon }}$ (2)

 $\begin{array}{l} {\mathit{\boldsymbol{G}}_i} = \left[ { - \cos \left( {{\theta _i}} \right)\cos \left( {{\alpha _i}} \right)\;\cos \left( {{\theta _i}} \right)\sin \left( {{\alpha _i}} \right)\;\;} \right.\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. { - \sin \left( {{\theta _i}} \right),\;1} \right] \end{array}$ (3)

 $\Delta \mathit{\boldsymbol{\vec x}} = \left( {{\mathit{\boldsymbol{G}}^{\rm T}}\mathit{\boldsymbol{WG}}} \right){}^{ - 1}{\mathit{\boldsymbol{G}}^{\rm T}}\mathit{\boldsymbol{W}}\Delta \mathit{\boldsymbol{\vec y}} = \mathit{\boldsymbol{S}}\Delta \mathit{\boldsymbol{\vec y}}$ (4)

 ${\mathit{\boldsymbol{W}}^{ - 1}} = \left[ {\begin{array}{*{20}{c}} {\sigma _1^2}&0& \cdots &0\\ {0}&{\sigma _2^2}& \cdots &0\\ \vdots & \vdots & \ddots &0\\ 0&0&0&{\sigma _N^2} \end{array}} \right]$ (5)

 ${\rm{LPL}} = \max \left\{ {{\rm{LP}}{{\rm{L}}_{{H_0}}},\;{\rm{LP}}{{\rm{L}}_{{H_1}}}} \right\}$ (6)
 ${\rm{VPL}} = \max \left\{ {{\rm{VP}}{{\rm{L}}_{{H_0}}},\;{\rm{VP}}{{\rm{L}}_{{H_1}}}} \right\}$ (7)

H0假设下的LPL和VPL计算方法为：

 ${\rm{LP}}{{\rm{L}}_{{H_0}}} = {K_{{\rm{ffmd}}}}\sqrt {\sum\limits_{i = 1}^N {s_{{\rm{lat}},i}^2} \times \sigma _i^2}$ (8)
 ${\rm{VP}}{{\rm{L}}_{{H_0}}} = {K_{{\rm{ffmd}}}}\sqrt {\sum\limits_{i = 1}^N {s_{{\rm{vert}},i}^2} \times \sigma _i^2}$ (9)

H1假设下的LPL和VPL计算方法为：

 ${\rm{LP}}{{\rm{L}}_{{H_1}}} = \max \left\{ {{\rm{LP}}{{\rm{L}}_{{H_1},j}}} \right\}$ (10)
 ${\rm{VP}}{{\rm{L}}_{{H_1}}} = \max \left\{ {{\rm{VP}}{{\rm{L}}_{{H_1},j}}} \right\}$ (11)

 ${\rm{LP}}{{\rm{L}}_{{H_1},j}} = \left| {{B_{j,{\rm{lat}}}}} \right| + {K_{{\rm{md}}}}{\sigma _{{\rm{lat}},{H_1}}}$ (12)
 ${\rm{VP}}{{\rm{L}}_{{H_1},j}} = \left| {{B_{j,{\rm{vert}}}}} \right| + {K_{{\rm{md}}}}{\sigma _{{\rm{vert}},{H_1}}}$ (13)

 ${B_{j,{\rm{lat}}}} = \sum\limits_{i = 1}^N {{s_{{\rm{lat}},i}}{B_{i,j}}}$ (14)
 ${B_{j,{\rm{vert}}}} = \sum\limits_{i = 1}^N {{s_{{\rm{vert}},i}}{B_{i,j}}}$ (15)
 $\sigma _{{\rm{lat}},{H_1}}^2 = \sum\limits_{i = 1}^N {s_{{\rm{lat}},i}^2 \times \sigma _{i,{H_1}}^2}$ (16)
 $\sigma _{{\rm{vert}},{H_1}}^2 = \sum\limits_{i = 1}^N {s_{{\rm{vert}},i}^2 \times \sigma _{i,{H_1}}^2}$ (17)
 $\sigma _{i,{H_1}}^2 = \frac{{M\sigma _{{\rm{pr}}\_{\rm{gnd}},i}^2}}{{M - 1}} + \sigma _{{\rm{air}},i}^2 + \sigma _{{\rm{iono}},i}^2 + \sigma _{{\rm{tropo}},i}^2$ (18)

 ${B_{i,j}} = \frac{1}{M}\sum\limits_{k = 1}^M {{\rm{PR}}{{\rm{c}}_{i,k}}} - \frac{1}{{M - 1}}\mathop {\sum\limits_{k = 1}^M {} }\limits_{k \ne j} {\rm{PR}}{{\rm{c}}_{i,k}}$ (19)

2 非完好性事件分析

“虚警”和“漏警”是GBAS中两类典型非完好性事件，会引起导航系统性能的降低，因此需要对这两类非完好性事件进行分析，为CAT Ⅲ GBAS的研制提供理论依据。

“虚警”即为机载端计算得到的保护级超出规定的告警门限，而实际的导航系统误差却在告警门限以内，会导致系统的连续性和可用性降低。以H0假设下的垂直保护级计算为例，由式(9)可知，影响保护级计算结果的主要因素有卫星几何分布结构及伪距差分校正后残余误差标准差等。由于空间卫星几何分布随时间变化，可见卫星个数在不同时间段内存在差异，因此当卫星个数较少且分布较差时，计算得到的保护级也会变大，易引起非完好性事件中的“虚警”现象。

“漏警”即为实际的导航系统误差超出规定的告警门限，但机载端计算得到的保护级却在告警门限以内，没能及时向机载端发出告警指示，即出现危险的虚假信息(HMI)，引起较大的完好性风险。根据分析可知，电离层风暴是引起非完好性事件中“漏警”现象发生的主要误差源，下面以斯坦福大学提出的电离层风暴模型为例，对“漏警”现象进行分析。

 图 1 斯坦福大学电离层风暴模型 Fig. 1 Ionospheric storm model of Stanford University
3 验证实验 3.1 GBAS位置域实验结果与分析

 图 2 24 h内可见卫星个数 Fig. 2 Number of visible satellite in 24 hours

 图 3 可见卫星几何精度因子 Fig. 3 GDOP of visible satellite

 图 4 垂直误差和保护级 Fig. 4 Vertical position error and protection level

 图 5 CAT Ⅰ标准Stanford图 Fig. 5 Stanford chart for category Ⅰ standard

3.2 非完好性事件仿真 3.2.1 虚警模拟仿真

 图 6 可见卫星几何精度因子 Fig. 6 GDOP of visible satellite

 图 7 垂直误差和保护级 Fig. 7 Vertical position error and protection level

3.2.2 漏警模拟仿真

 图 8 垂直误差和保护级 Fig. 8 Vertical position error and protection level

4 结语

 [1] Felux M, Dautermann T, Becker H. GBAS Landing System-Precision Approach Guidance after ILS[J]. Aircraft Engineering and Aerospace Technology, 2012, 85(5): 382-388 (0) [2] Lee J, Pullen S, Dattabarua S, et al. Real-Time Ionospheric Threat Adaptation Using a Space Weather Prediction for GNSS-Based Aircraft Landing Systems[J]. IEEE Transactions on Intelligent Transportation Systems, 2017, 18(7): 1 752-1 761 DOI:10.1109/TITS.2016.2627600 (0) [3] Pullen S, Pervan B, Enge P, et al. A Comprehensive Integrity Verification Architecture for on-Airport LAAS Category Ⅲ Precision Landing[C]. ION GPS, Salt Lake City, 1996 (0) [4] 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 (0) [5] 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 (0) [6] Sung Y T, Lin Y W, Yeh S J, et al. A Dual-Frequency Ground Based Augmentation System Prototype for GPS and BDS[C]. ION GNSS+, Miami, 2019 (0) [7] Song J, Milner C, Selmi L, et al. Assessment of Dual-Frequency Signal Quality Monitor to Support CAT Ⅱ/Ⅲ GBAS[C]. ION GNSS+, Miami, 2019 (0) [8] Xing Z D, Zhao J B, Wang Z H, et al. Analysis and Improvement to Ionosphere Grads Integrity Monitoring Algorithm in Ground Based Augmentation System[C]. CSNC, Xi'an, 2015 (0) [9] Hu J, Sun Q W, Shi X Z. Differential Positioning Algorithm for GBAS Based on Extended Kalman Filtering[C]. WCICA, Changsha, 2018 (0) [10] Wang Z P, Wang S J, Zhu Y B, et al. Assessment of Ionospheric Gradient Impacts on Ground-Based Augmentation System(GBAS) Data in Guangdong Province, China[J]. Sensors, 2017, 17: 1-23 DOI:10.1109/JSEN.2017.2761499 (0) [11] Zhu Y B, Liu Y, Wang Z P, et al. Evaluation of GBAS Flight Trials Based on BDS and GPS[J]. IET Radar, Sonar and Navigation, 2020, 14(2): 233-241 DOI:10.1049/iet-rsn.2019.0284 (0) [12] Xue R, Zhang J, Zhu Y B. Cascade Dual Frequency Smoothing for Local Area Augmentation System[J]. Chinese Journal of Aeronautics, 2009, 22(1): 49-55 DOI:10.1016/S1000-9361(08)60068-0 (0)
Research on Airborne Integrity Algorithm for Ground Based Augmentation System Based on GPS
HU Jie1     ZHOU Ling1
1. Department of Physics and Electronic Engineering, Yuncheng University, 1155 West-Fudan Street, Yuncheng 044000, China
Abstract: In view of the extremes of the non-integrity events of the ground based augmentation system(GBAS), we study the integrity algorithm of GBAS. We give the calculation method of airborne protection level under H0 and H1 assumptions, and analyze the influences of the main error sources of two kinds of non-integrity events, false alarm and missed alarm. We carry out verification experiments, and the experimental results show that the accuracy of the position solution of the airborne terminal after differential correction is better than 1 meter, and its availability is greater than 99.999 9%, which meets the requirements of class Ⅰ precision approach and landing navigation. At the same time, we carry out simulations of non-integrity events, and the results show that the geometric distribution of satellite and ionospheric storm are the main error sources of false and missed alarms. In the future, class Ⅲ GBAS needs to expand the single constellation to multiple constellations including Beidou, and upgrade the single frequency to dual frequency. Among them, multiple constellations can optimize the geometric layout of satellites and dual frequency can eliminate the ionospheric storm impact.
Key words: ground based augmentation system; protection level; non-integrity event; multiple constellations; dual frequency