无人机与民航客机碰撞概率研究
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摘要
近年来民用航空机场终端管制区附近存在无人机入侵空域问题,为解决无人机造成的飞行隐患,保证飞行安全,该文建立了无人机与民航客机碰撞概率模型,并研究不同类型无人机与民航客机的碰撞概率。假设民航客机定位误差服从正态分布,在直角坐标系下,考虑无人机与民航客机的体积因素,以及由此对碰撞概率造成的影响,建立无人机与民航客机水平投影面和垂直投影面的运动学模型。当两个投影面上的相对运动距离同时小于保护间隔时碰撞发生,建立碰撞概率模型,使用分裂步θ方法求解该模型。使用MATLAB工具对模型进行算例仿真实验,并将实验结果与理论计算值进行对比,验证了模型的合理性,得到了碰撞概率随参数变化的关系。
In recent years,there has been a problem of the invasion of unmanned aerial vehicles(UAV)in the airspace near the terminal control area. A probabilistic model of the collision between the unmanned aerial vehicles and the civil aircraft is established,and the different types of UAV are studied in order to solve the problem of flying accidents caused by collision probability with airliner and UAV. Assuming that the civil aircraft positioning error obeys the normal distribution,in the Cartesian coordinate system,considering the volume factor of the UAV and the civil aircraft,and the impact on the collision probability,this paper establishes a kinematic model of the surface based on the the UAV and the civil aircraft horizontal projection plane and vertical projection. When the relative motion distance on the two projection planes is smaller than the guard interval,a collision probability model is established,and the model is solved by the splitting step method. Using the MATLAB tools to simulate the model,the results are compared with the theoretical values to verify the rationality of the model,and the relationship of collision probability and parameters.
In recent years,there has been a problem of the invasion of unmanned aerial vehicles(UAV)in the airspace near the terminal control area. A probabilistic model of the collision between the unmanned aerial vehicles and the civil aircraft is established,and the different types of UAV are studied in order to solve the problem of flying accidents caused by collision probability with airliner and UAV. Assuming that the civil aircraft positioning error obeys the normal distribution,in the Cartesian coordinate system,considering the volume factor of the UAV and the civil aircraft,and the impact on the collision probability,this paper establishes a kinematic model of the surface based on the the UAV and the civil aircraft horizontal projection plane and vertical projection. When the relative motion distance on the two projection planes is smaller than the guard interval,a collision probability model is established,and the model is solved by the splitting step method. Using the MATLAB tools to simulate the model,the results are compared with the theoretical values to verify the rationality of the model,and the relationship of collision probability and parameters.
引文
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[13] Federal Aviation Administration. Aeronautical information manual-official guide to basic flight information and ATC procedures[R]. Washington,D.C.:,2012.
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[15] Bai Xianzong,Ma Chaowei,Chen Lei,et al. Maximum collision probability considering variable size,shape,and orientation of covariance ellipse[J]. Advances in Space Research,2016,58(6):950-966.
[16] Lin Yucong,Srikanth Saripalli. Sampling-based path planning for UAV collision avoidance IEEE transactions on intelligent transportation systems[J]. IEEE Transactions on Intelligent Transportation Systems,2017(99):1-14.
[17] Lancovs D. Building,verifying and validating a collision avoidance model for unmanned aerial vehicles[J]. Procedia Engineering,2017,178:155-161.
[2] 王俊勇.监管应比无人机先起飞[N]. 杭州日报,2017-01-18(002).
[3] 栾爽.无人机法律规制问题论纲[J]. 南京航空航天大学学报(社会科学版),2017(1):32-37.Luan Shuang. Thesis of legal regulation of unmanned aerial vehicle[J]. Journal of Nanjing University of Aeronautics & Astronautics(Social Sciences),2017(1):32-37.
[4] 朱路. 无人机攻击问题国际人道法研究[J]. 南京理工大学学报(社会科学版),2013,26(6):36-43.Zhu Lu. Drone attacks from the perspective of international humanitarian laws[J]. Journal of Nanjing University of Science and Technology(Social Sciences Edition),2013,26(6):36-43.
[5] Prandini M,Lygeros J,Nilim A,et al. Randomized algorithms for probabilistic aircraft conflict detection[C]//Proceedings of the 38th IEEE Conference on Decision and Control. Berkeley,CA,USA:IEEE,1999:2444-2449.
[6] Shepherd R,Cassell R,Thapa R,et al. A reduced aircraft separation risk assessment model[C]//Guidance,Navigation,and Control Conference. New Orleans,USA:American Institute of Aeronautics and Astronautics,1997:1418-1433.
[7] 梁海军,杨红雨,肖朝,等. 3维坐标系下的飞行冲突探测算法[J]. 四川大学学报(工程科学版),2013,45(2):88-93.Liang Haijun,Yang Hongyu,Xiao Chao,et al. Flight conflict detection algorithm based on the three dimensional coordinate system[J]. Journal of Sichuan University(Engineering Science Edition),2013,45(2):88-93.
[8] 石磊,吴仁彪,黄晓晓. 基于总体冲突概率和三维布朗运动的冲突探测算法[J]. 电子与信息学报,2015(2):360-366.Shi Lei,Wu Renbiao,Huang Xiaoxiao. Conflict detection algorithm based on overall conflict probability and three dimensional brownian motion[J]. Journal of Electronics & Information Technology,2015(2):360-366.
[9] 王松涛,吕宗平,张兆宁. 基于环境要素的自由飞行条件下航空器碰撞风险模型[J]. 中国科技论文,2016,11(19):2183-2186.Wang Songtao,Lv Zongping,Zhang Zhaoning. Study of the collision risk model involving flight environment conditions under free flight[J]. China Science Paper,2016,11(19):2183-2186.
[10] 党淑雯,王康乐. 飞机平行航路侧向碰撞风险预测仿真[J]. 计算机应用,2017,37(S1):115-117.Dang Shuwen,Wang Kangle. Prediction and simulation of aircraft lateral collision risk on parallel route[J]. Journal of Computer Applications,2017,37(S1):115-117.
[11] Yang L,Kuchar J. Prototype conflict alerting system for free flight[J]. Journal of Guidance,Control,and Dynamics,1997,20(4):768-773.
[12] Enstedt M,Wellander N. A spectral expansion-based Fourier split-step method for uncertainty quantification of the propagation factor in a stochastic environment[J]. Radio Science,2016,51(11):1783-1791.
[13] Federal Aviation Administration. Aeronautical information manual-official guide to basic flight information and ATC procedures[R]. Washington,D.C.:,2012.
[14] 刘云平,李先影,王田苗,等. 四旋翼无人机偏航飞行过程量化稳定性分析[J]. 南京理工大学学报,2016,40(5):520-526.Liu Yunping,Li Xianying,Wang Tianmiao,et al. Quantitative stability of quadrotor unmanned aerial vehicle during yawing[J]. Journal of Nanjing University of Science and Technology,2016,40(5):520-526.
[15] Bai Xianzong,Ma Chaowei,Chen Lei,et al. Maximum collision probability considering variable size,shape,and orientation of covariance ellipse[J]. Advances in Space Research,2016,58(6):950-966.
[16] Lin Yucong,Srikanth Saripalli. Sampling-based path planning for UAV collision avoidance IEEE transactions on intelligent transportation systems[J]. IEEE Transactions on Intelligent Transportation Systems,2017(99):1-14.
[17] Lancovs D. Building,verifying and validating a collision avoidance model for unmanned aerial vehicles[J]. Procedia Engineering,2017,178:155-161.
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