基于高斯积分的航空器冲突概率计算方法

doi:10.16265/j.cnki.issn1003-3033.2018.08.021

中国安全科学学报 ›› 2018, Vol. 28 ›› Issue (8): 123-128.doi: 10.16265/j.cnki.issn1003-3033.2018.08.021

基于高斯积分的航空器冲突概率计算方法

郝敬堂¹ 实验师, 苏志刚^1,2 教授

1 中国民航大学中欧航空工程师学院,天津 300300;
2 中国民航大学智能信号与图像处理天津市重点实验室,天津 300300

收稿日期:2018-05-11 修回日期:2018-07-07 出版日期:2018-08-28 发布日期:2020-11-25
作者简介:郝敬堂(1989—),男,河南淇县人,硕士,实验师,主要从事空中交通管理信息采集与处理方面的研究。E-mail:jthao_siae@126.com。
基金资助:
中央高校基本科研业务费中国民航大学专项项目(3122017111)。

Method for calculating probability of conflict between aircrafts based on Gaussian quadrature

HAO Jingtang¹, SU Zhigang^1,2

1 Sino-European Institute of Aviation Engineering,Civil Aviation University of China,Tianjin 300300,China;
2 Tianjin Key Laboratory for Advanced Signal Processing,Civil Aviation University of China,Tianjin 300300,China

Received:2018-05-11 Revised:2018-07-07 Online:2018-08-28 Published:2020-11-25

摘要/Abstract

摘要： 为推进新一代空管系统冲突探测技术的应用,保障航空器飞行安全,首先,通过分析现有概率型冲突探测算法的计算难点,构建改进的冲突概率模型;其次,利用勒让德(Legendre)多项式递推公式及牛顿迭代法,实现任意点数高斯-勒让德(Gauss-Legendre)积分的求解,进而通过高斯求积公式计算该模型的冲突概率;最后,仿真模拟相向飞行、交叉飞行以及转弯飞行3种相遇模型,验证该冲突概率计算方法的普遍适用性。结果表明:该方法可以精确估计向前看时间段内航空器之间的冲突概率,积分点数越多,计算精度越高;与扩展区域近似法及蒙特卡罗(Monte Carlo)方法相比,较少点数的冲突概率计算方法有更好的计算精度与效率。

关键词: 空中交通管制, 冲突探测, 航迹误差, 高斯积分, 冲突概率

Abstract: In order to promote the application of conflict detection technology in the next generation air traffic control system and protect flight safety more effectively,firstly,an improved conflict probability model was built after analyzing the computational difficulties of the traditional conflict detection algorithm.Then,Gauss-Legendre quadrature of any order was implemented by using recursive formula for Legendre polynomials and Newton's iteration method.On this basis,improved conflict probability model was calculated by using Gaussian quadrature formula to obtain the conflict probability.Finally,an opposite movement model,a crossover movement model and a turn movement model were considered,the universal applicability of the conflict probability calculation method was verified by simulation experiments.The results show that conflict probability in the forward looking period can be accurately estimated by using the proposed method,that the more the points,the higher the calculation accuracy,and that compared with the extended region approximation method and the Monte Carlo method,conflict probability calculation method with few Gaussian-points has better calculation accuracy and efficiency.

Key words: air traffic control, conflict detection, track error, Gaussian quadrature, conflict probability

中图分类号:

X949

郝敬堂实验师, 苏志刚. 基于高斯积分的航空器冲突概率计算方法[J]. 中国安全科学学报, 2018, 28(8): 123-128.

HAO Jingtang, SU Zhigang. Method for calculating probability of conflict between aircrafts based on Gaussian quadrature[J]. China Safety Science Journal, 2018, 28(8): 123-128.

参考文献

[1] 中国民用航空局空中交通管理局.民航空管系统“十三五”发展规划[R],2017.
[2] JILKOV V P,LI Xiaorong,LEDET J H.Improved estimation of conflict probability for aircraft collision avoidance[C].Proceedings of 17^th International Conference on Information Fusion,2014:1-7.
[3] TANG Jun.Review:analysis and improvement of traffic alert and collision avoidance system[J].Institute of Electrical and Electronics Engineers Access,2017,5:21419-21429.
[4] PAGLIONEM,YOUNG C M,TORRESS,et al.Operational impact of trajectory prediction accuracy on air traffic automation tools[C].Proceeding of the Institute of Electrical and Electronics Engineers/American Institute of Aeronautics and Astronautics 36^th Digital Avionics Systems Conference,2017:1-10.
[5] PAIELLI R A,ERZBERGER H.Trajectory specification for terminal air traffic:conflict detection and resolution[C].Proceedings of 17^th,American Institute of Aeronautics and Astronautics,Aviation Technology,Integration,and Operations Conference,2017:1-19.
[6] PAIELLI R A,ERZBERGER H.Conflict probability estimation for free flight[J].Journal of Guidance,Control and Dynamics,1997,20(3):588-596.
[7] PAIELLI R A,ERZBERGER H.Conflict probability estimation generalized to non-level flight[J].Journal of Guidance Control and Dynamics1999,7(3):195-222.
[8] PRANDINI M,HU Jianghai,LYGEROS J,et al.A probabilistic approach to aircraft conflict detection[J].IEEE Trans.on Intelligent Transportation Systems,2000,1(4):199-220.
[9] 翟文鹏,吴昊,王莉莉,等.用粒子滤波改进的飞行冲突探测算法研究[J].中国安全科学学报,2014,24(6):105-108.
ZHAI Wenpeng,WU Hao,WANG Lili,et al.Particle filtering-based flight conflict detection algorithm[J].China Safety Science Journal,2014,24(6):105-108.
[10] JILKOV V P,LEDET J H,LI Xiaorong.Improved conflict resolution method for unmanned aircraft sense-and-avoid[C].Proceeding of the 19^th International Conference on Information Fusion,2016:1-8.
[11] LIU Zhaoxuan,CAI Kaiquan,ZHU Xi,et al.Large scale aircraft conflict resolution based on location network[C].Proceedings of the IEEE/AIAA 36^th Digital Avionics Systems Conference,2017:1-8.
[12] 高扬,王向章,郑涤滨.机场终端区航空器飞行冲突风险预测方法研究[J].中国安全科学学报,2017,27(1):157-162.
GAO Yang,WANG Xiangzhang,ZHENG Dibin.Research on method for predicting risk of aircraft flight conflict in airport terminal[J].China Safety Science Journal,2017,27(1):157-162.
[13] 张兆宁,余晟.自由飞行下基于航空器定位误差修正的碰撞风险研究[J].安全与环境学报,2017,17(5):1633-1636.
ZHANG Zhaoning,YU Sheng.On the collision risk in rectification of the aircraft positioning error under the free flight condition[J].Journal of Safety and Environment,2017,17(5):1633-1636.
[14] 彭良福,颜悦,石佳奇,等.通航飞机避碰区域防撞模型的等效性研究[J].中国安全科学学报,2016,26(8):95-99.
PENG Liangfu,YAN Yue,SHI Jiaqi,et al.Equivalence study on collision avoidance zone based models for general aviation aircraft collision avoidance[J].China Safety Science Journal,2016,26(8):95-99.
[15] 刘洋,向锦武,罗漳平,等.低空自由飞行短期冲突探测算法[J].北京航空航天大学学报,2017,43(9):1873-1881.
LIU Yang,XIANG Jinwu,LUO Zhangping,et al.Short-term conflict detection algorithm for free flight in low-altitude airspace[J].Journal of Beijing University of Aeronautics and Astronautics,2017,43(9):1873-1881.
[16] YANG Yang,ZHANG Jun,CAI Kaiquan,et al.Multi-aircraft conflict detection and resolution based on probabilistic reach sets[J].IEEE Transactions on Control Systems Technology,2016,25(1):309-316.

基于高斯积分的航空器冲突概率计算方法

Method for calculating probability of conflict between aircrafts based on Gaussian quadrature

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