Optimal allocation of risk probability based on ARAIM algorithm

doi:10.11947/j.AGCS.2021.20200260

Abstract

Abstract: The advanced receiver autonomous integrity monitoring (ARAIM) algorithm distributes the probability of continuity risk and integrity risk equally to all visible satellites, resulting in the relatively conservative vertical protection level (VPL). Therefore, a maximum minimization method was adopted, and fminimax function of Matlab was used to reasonably allocate the intact risk and the continuity risk, improving the availability of single constellation ARAIM. The results of the calculation examples of the measured data show that: whether it is static or dynamic data, the maximum minimization method can reasonably allocate the risk. The average improvement rate of VPL for GPS and BDS single systems is 12.14% and 10.63%, respectively, and the average improvement rate of STD (standard deviation) is 78.69% and 72.33%, respectively. Compared with other two optimization algorithms, the optimization algorithm has a better effect of improving the availability of ARAIM under LPV-200. Global simulation results show that after using the maximum minimization method, GPS ARAIM availability is greater than 90% and 99.5% coverage has increased from 26.60% and 0% to 38.69% and 17.35%, respectively. BDS ARAIM availability is greater than 90%. The coverage of 99.5% has increased from 30.73% and 19.91% to 34.28% and 22.33%, respectively.

Key words: ARAIM, LPV-200, continuity risk, integrity risk, risk probability allocation

CLC Number:

P228

HAN Qingqing, WANG Li, LUO Silong, SHU Bao, YUE Cong. Optimal allocation of risk probability based on ARAIM algorithm[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(12): 1751-1761.

References

[1] 陈金平. GPS完善性增强研究[D].郑州:信息工程大学, 2001. CHEN Jinping. Research of GPS integrity augmentation[D]. Zhengzhou:Information Engineering University, 2001.
[2] FAA GEAS Panel.GNSS evolutionary architecture study phase II report (GEAS)[EB/OL].[2020-05-11]. https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/library/documents/media/GEASPhaseII_Final.pdf,2010.
[3] 肖伟,刘文祥,徐博,等. LPV-200下中国区域内ARAIM可用性评估[J].全球定位系统, 2014(5):32-36. XIAO Wei, LIU Wenxiang, XU Bo, et al. The current ARAIM availability in China according to LPV-200[J]. GNSS World of China, 2014(5):32-36.
[4] RIPPL M, SPLETTER A, GUNTHER C. Parametric performance study of advanced receiver autonomous integrity monitoring (ARAIM) for combined GNSS constellations[C]//Proceedings of 2011 International Technical Meeting of the Institute of Navigation. San Diego, CA:[s.n.], 2011:285-295.
[5] MARTINI I, RIPPL M, MEURER M. Advanced RAIM architecture design and user algorithm performance in a real GPS, GLONASS and Galileo scenario[C]//Proceedings of the 26th International Technical Meeting of the Satellite Division of the Institute of Navigation. Nashville:[s.n.],2013:2624-2636.
[6] El-MOWAFY A. ARAIM for vertical guidance using GPS and BeiDou[J]. Journal of Global Positioning Systems, 2013, 12(1):28-37.
[7] 王尔申,杨迪,宏晨,等. ARAIM技术研究进展[J].电信科学, 2019(8):128-138. WANG Ershen, YANG Di, HONG Chen, et al. Research progress of ARAIM technology[J]. Telecommunications Science, 2019(8):128-138.
[8] BROWN R G, MCBURNEY P W. Self-contained GPS integrity check using maximum solution separation[J]. Navigation, 1988, 35(1):41-53.
[9] BLANCH J, WALTER T, ENGE P, et al. Advanced RAIM user algorithm description:integrity support message processing, fault detection, exclusion, and protection level calculation[C]//Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2012). Nashville:[s.n.], 2012:2828-2849.
[10] JOERGER M, STEVANOVIC S, CHAN F C, et al. Integrity risk and continuity risk for fault detection and exclusion using solution separation ARAIM[C]//Proceedings of the 26th International Technical Meeting of the Satellite Division of the Institute of Navigation. Nashville:[s.n.], 2013:2702-2722.
[11] BLANCH J, WALTER T,ENGE P. Optimal Positioning for Advanced RAIM[J]. Navigation, 2014, 60(4):279-289.
[12] 宋恺. GNSS自主完好性检测算法研究[D].南京:南京航空航天大学, 2017. SONG Kai. Research on GNSS integrity monitoring algorithm[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2017.
[13] 郑学恩,许承东,范国超,等.应用遗传算法的多星座保护级别优化方法[J].北京理工大学学报, 2018, 38(10):60-64. ZHENG Xueen, XU Chengdong, FAN Guochao, et al. Multi-constellation protection level optimization method using genetic algorithm[J]. Journal of Beijing Institute of Technology, 2018, 38(10):60-64.
[14] 荆帅,战兴群,苏先礼. ARAIM算法应用于LPV-200服务[J].测控技术, 2012, 31(11):75-79. JING Shuai, ZHAN Xingqun, SU Xianli. Exporation of advanced RAIM to provide LPV-200 service[J]. Measurement&Control Technology, 2012, 31(11):75-79.
[15] EU-U.S. Cooperation on satellite navigation working group. C-ARAIM technical subgroup milestone 3 report[EB/OL].[2020-06-20]. https://www.gps.gov/policy/cooperation/europe/2016/working-group-c/ARAIM-milestone-3-report.pdf,2016.
[16] 石国春.关于序列二次规划(SQP)算法求解非线性规划问题的研究[D].兰州:兰州大学, 2009. SHI Guochun. Research on algorithm of sequential quadratic programming for nonlinear programming problems[D]. Lanzhou:Lanzhou University, 2019.
[17] 高光良.序列二次规划法在航空发动机加力过程最优控制中的应用研究[D].西安:西北工业大学, 2005. GAO Guangliang. Application research of sequential quadratic programming method in optimal control of aero engine afterburning process[D]. Xi'an:Northwestern Polytechnical University, 2005.
[18] MENG Q, LIU J, ZENG Q, et al. Improved ARAIM fault modes determination scheme based on feedback structure with probability accumulation[J]. GPS Solutions, 2019, 23(1):16.
[19] 曹海洋. GNSS完好性监测理论与方法研究[D].西安:长安大学, 2013. CAO Haiyang. Theory and technique research on GNSS integrity[D]. Xi'an:Chang'an University, 2013.
[20] ZHANG Yabin, WANG Li, FAN Lihong, et al. MHSS ARAIM algorithm combined with gross error detection[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1):36-44.
[21] 范云飞. GNSS接收机自主完好性监测算法研究[D].沈阳:沈阳航空航天大学, 2016. FAN Yunfei. Research on GNSS receiver autonomous integrity monitoring algorithm[D]. Shenyang:Shenyang Aerospace University, 2016.
[22] LI W, SILONG L, RUI T, et al. ARAIM with BDS in the Asia-Pacific region[J]. Advances in Space Research, 2018, 62(3):707-720.
[23] 张亚彬,王利,范丽红,等.组合粗差探测的MHSS ARAIM算法[J].测绘学报,2019, 48(1):9-17. DOI:10.11947/j.AGCS.2019.20170367. ZHANG Yabin, WANG Li, FAN Lihong, et al.Study on MHSS ARAIM algorithm combined with gross error detection[J]. Acta Geodaetica et Cartographica Sinica,2019,48(1):9-17. DOI:10.11947/j.AGCS.2019.20170367.
[24] GEMBICHI F W. Vector optimization for control with performance and parameter sensitivity indices[D]. Cleveland:Case Western Reserve University, 1974.
[25] BRAYTON R, DIRECTOR S, HACHTEL G, et al.A new algorithm for statistical circuit design based on quasi-newton methods and function splitting[J]. Transactions on Circuits and Systems, 1979, 26(9):784-794.
[26] POWELL M. A fast algorithm for nonlinearly constrained optimization calculations[J]. Mathematical Programming, 1978, 45(3):547-566.
[27] 阳凯,郭承军.基于完好性与连续性风险的最优垂直保护门限计算[J].计算机工程, 2017(1):50-54. YANG Kai, GUO Chengjun. Calculation of optimal vertical protection level based on integrity risk and continuity risk[J]. Computer Engineering, 2017(1):50-54.
[28] 王尔申,张淑芳,蔡明,等.遗传粒子滤波的GPS接收机自主完好性监测[J].西安电子科技大学学报, 2015, 42(1):136-141. WANG Ershen, ZHANG Shufang, CAI Ming, et al. GPS receiver autonomous integrity monitoring algorithm using the genetic particle filter[J]. Journal of Xidian University, 2015, 42(1):136-141.
[29] 何尚录,白利华.解一类最大值最小化问题的线性规划方法[J].兰州铁道学院学报, 1997(3):83-86. HE Shanglu, BAI Lihua. Linear programming method for solving some min-max problems[J]. Journal of Lanzhou Railway University, 1997(3):83-86.
[30] WANG Li, LUO Silong, TU Rui, et al. ARAIM with BDS in the Asia-Pacific region[J]. Advances in Space Research, 62(3):707-720.
[31] LUO Silong, WANG Li, TU Rui, et al. Satellite selection methods for multi-constellation advanced RAIM[J]. Advances in Space Research, 65(2):1503-1517.