基于几何代数的自适应典型航迹生成

中国民航大学学报 ›› 2025, Vol. 43 ›› Issue (6): 38-45.

基于几何代数的自适应典型航迹生成

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；

2. 经纬恒润（天津）研究开发有限公司汽车电子专业部，天津 300300

收稿日期:2024-02-20 修回日期:2024-06-20 出版日期:2025-12-20 发布日期:2026-01-10
作者简介:焦卫东（1973—），男，陕西咸阳人，教授，博士，研究方向为虚拟现实技术在民航中的应用.
基金资助:
国家重点研发计划项目（2020YFB1600101）

Adaptive typical trajectory generation based on geometric algebra

1. Intelligent Signal and Image Processing Key Lab of Tianjin, CAUC, Tianjin 300300, China; 2. The Automotive Electronics

Department of Jingwei Hirain (Tianjin) Research & Development Co., Ltd., Tianjin 300300, China

Received:2024-02-20 Revised:2024-06-20 Online:2025-12-20 Published:2026-01-10

1. 基于几何代数的自适应典型航迹生成.pdf(2852KB)

摘要/Abstract

摘要：

通过分析基于密度的带噪空间聚类算法（DBSCAN，density-based spatial clustering of applications with

noise）和模糊 C 均值（FCM，fuzzy C-means）聚类算法的聚类性能，本文提出一种快速的基于几何代数的自

适应典型航迹生成算法。首先，利用 K-means 聚类算法进行航班运行时间的归一化；然后，利用几何代数

优越的时空表达和计算能力，给出了航迹转弯判定、DBSCAN 聚类和 FCM 聚类的几何代数描述；最后，在几

何代数空间中对转弯运动状态和直线运动状态的航迹分别自适应地进行 DBSCAN 聚类和 FCM 聚类形成

典型航迹。实验结果表明，本文自适应典型航迹的生成速度较欧氏空间方法可提升 30%以上。

关键词:

几何代数, 基于密度的带噪空间聚类算法（DBSCAN）聚类, 模糊 C 均值（FCM）聚类, 典型航迹

Abstract:

By analyzing the performance of density-based spatial clustering of applications with noise (DBSCAN) and fuzzy

C-means (FCM) clustering, a fast adaptive typical trajectory generation method based on geometric algebra is

proposed. Firstly, the K-means clustering algorithm is used to normalize the flight operation time. Then, lever aging the superior capabilities of geometric algebra in spatiotemporal representation and computation, geometric

algebraic descriptions are formulated for trajectory turn determination, DBSCAN clustering and FCM clustering.

Finally, in the geometric algebraic space, DBSCAN clustering and FCM clustering are carried out adaptively to

form typical trajectories of turn motion state and straight motion state respectively. Experimental results show

that the adaptive typical trajectories achieve over 30% faster generation speed compared to conventional Euclidean space methods.

Key words:

geometric algebra, density-based spatial clustering of applications with noise (DBSCAN) clustering, fuzzy

C-means (FCM) clustering, typical trajectory

中图分类号:

V328.3

焦卫东, 李春阳, 武浩波, 李泰宇 .

基于几何代数的自适应典型航迹生成

[J]. 中国民航大学学报, 2025, 43(6): 38-45.

JIAO Weidong , LI Chunyang, , WU Haobo , LI Taiyu.

Adaptive typical trajectory generation based on geometric algebra

[J]. Journal of Civil Aviation University of China, 2025, 43(6): 38-45.

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