跑道侵入与冲突检测的共形几何代数描述  

Conformal geometric algebraic description of runway incursion and conflict detection

作　　者：焦卫东[1] 王瑞冬 姚军强 庞艳丽 JIAO Weidong;WANG Ruidong;YAO Junqiang;PANG Yanli(Tianjin Key Laboratory for Advanced Signal Processing,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学天津市智能信号与图像处理重点实验室,天津300300

出　　处：《航空学报》2022年第5期475-484,共10页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金委员会-中国民航局民航联合研究基金(U1533115)。

摘　　要：提出一种基于共形几何代数(CGA)的跑道侵入与跑道冲突检测描述方法,以弥补欧氏空间中跑道侵入与冲突检测算法的计算结构复杂、语义不清晰及动态计算效率低等不足。首先,建立跑道保护区的共形几何代数描述,基于共形几何代数的外积运算,通过判断飞行器与跑道保护区(RPZ)各边界所在面的位置关系检测跑道侵入。然后,对飞行器保护区进行共形几何代数描述,基于共形几何代数的内积运算,通过判断飞行器保护区是否相交检测跑道冲突。最后,基于ADS-B数据,构造跑道侵入与冲突场景,利用卡尔曼滤波算法预测航迹,通过实验验证了所提方法的有效性:本文跑道侵入与冲突检测算法的运算速度比欧氏空间方法分别快1.5倍和2.2倍以上,可以更快速地准确检测跑道侵入与跑道冲突。To overcome the problems of complex calculation structure,unclear semantics and low dynamic calculation efficiency of the algorithms in Euclidean space,a description method of the runway incursion and conflict detection is proposed based on Conformal Geometric Algebra(CGA).First,the boundary planes of the Runway Protection Zone(RPZ) are expressed as formation of CGA.Based on the CGA outer product operation,the runway intrusion is detected by judging the position relationship between the aircraft and each boundary of the RPZ.Then,the aircraft protection zone is described by CGA.Based on the CGA inner product operation,the conflict is detected by judging whether the aircraft protection zones intersect or not.Finally,based on the ADS-B data,the runway intrusion and conflict scenes are constructed,and the Kalman filter algorithm is used to predict the track.Effectiveness of the proposed method is verified by experiments.The results show that compared with that of the Euclidean space method,the operation speed of our algorithm is 1.5 times and 2.2 times faster,demonstrating the efficiency and accuracy of the proposed method.

关 键 词：共形几何代数 外积 跑道侵入 内积 冲突检测 

分 类 号：V328.3[航空宇航科学与技术—人机与环境工程]