融合金字塔栅格与测向交叉的低空无人机定位

张宏展; 韩鹏; 赵可; 陈鹏

doi:10.3963/j.jssn.1674-4861.2025.03.015

融合金字塔栅格与测向交叉的低空无人机定位

doi: 10.3963/j.jssn.1674-4861.2025.03.015

张宏展^{1, 2, ,},
韩鹏³,
赵可⁵,
陈鹏⁵

1.
福州外语外贸学院大数据学院福州 350202
2.
福州外语外贸学院现代服务业大数据应用福建省高校工程研究中心福州 350202
3.
中国民航大学空中交通管理学院天津 300300
4.
燃谷科技（南京）有限公司南京 210012
5.
中国科学院大学集成电路学院北京 101400

基金项目:

国家自然科学基金项目 52102419

国家重点研发计划项目 2022YFB4300904

北京市重点研发项目 E1JS03C001

详细信息

通讯作者:
张宏展（1974—），博士，副教授. 研究方向：低空交通管理、空间大数据处理. E-mail：534924882@qq.com

中图分类号: X951
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出版历程
- 收稿日期: 2024-09-10
- 网络出版日期: 2025-10-11

Low-altitude UAV Positioning Fusing Pyramid Grid and Direction-finding Cross-location

ZHANG Hongzhan^{1, 2
, ,},
HAN Peng³,
ZHAO Ke⁵,
CHEN Peng⁵

1.
College of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, China
2.
Engineering Research Center of Big Data Application in Modern Service Industry of Fujian Provincial Universities, Fuzhou University of International Studies and Trade, Fuzhou 350202, China
3.
School of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China
4.
Rangu Technology (Nanjing) Co., Ltd, Nanjing 210012, China
5.
College of Integrated Circuit, University of Chinese Academy of Sciences, Beijing 101400, China

摘要

摘要: 针对传统地面测向设备在低空空域监视中无法获取航空器高度数据的问题，研究了融合高斯金字塔空域栅格模型与地面测向设备的低成本算法，实现低空无人机三维位置（含高度）实时精准预测。利用立方米级最优粒度三维栅格技术，将可通达空域离散化为可计算空域，奠定计算基础；在高斯滤波下采样中引入湍流强度动态关联的三维高斯核函数，创新性地构建高斯金字塔多尺度空域模型，利用三线性插值上采样保障数据连续性与精度；将实时天气、地理信息及环境因素映射至空域栅格，设计基于环境参数方差的动态权重函数，建立动态加权的可信度矩阵。在金字塔栅格空间中，结合测向交叉定位数据，遍历空域栅格概率集合，计算无人机经纬度及高度，实现三维定位。在某测试区域内部署2台测向设备进行实验验证。结果表明：①定位精度：在最小分辨率8 m的三维栅格下，经纬度定位最大偏差为20 m（目标转向时），高度预测平均偏差为4.37 m（标准差7.87），显著优于对比方法；②计算效率：算法平均内存占用仅55 MB，在i9-13900H处理器下CPU平均利用率仅为9%，显著低于对比方法；③适用性：仅需低成本地面测向设备支持，无需机载设备。本文算法在立方米级偏差范围内实现了低成本、较高精度的低空无人机三维实时定位，可为低空监视设施建设受限场景提供有效解决方案。
- 无人机 /
- 低空空域 /
- 测向交叉定位 /
- 高度预测 /
- 高斯金字塔 /
- 可信度矩阵
Abstract: To address the issue that traditional ground-based direction-finding equipment cannot acquire aircraft altitude data during low-altitude airspace surveillance, this study investigates a low-cost algorithm integrating Gaussian pyramid airspace grid models with ground-based direction-finding equipment, enabling real-time and precise 3D position (including altitude) prediction for low-altitude UAVs. The accessible airspace is discretized into a computable airspace using cubic-meter-level optimal granularity 3D grid technology, laying the computational foundation. During Gaussian filtering downsampling, a 3D Gaussian kernel function dynamically correlated with turbulence intensity is introduced, innovatively con-structing a multi-scale Gaussian pyramid airspace model. Trilinear interpolation upsampling ensures data continuity and precision. Real-time weather conditions, geographic information, and environmental factors are mapped to the airspace grid, establishing a dynamically weighted credibility matrix via a dynamic weighting function based on the variance of environmental parameters. Within the pyramid grid space, combined with direction-finding cross-location data, the algorithm traverses the airspace grid probability set to calculate latitude/longitude and altitude of the UAV, achieving 3D localization. Experimental validation is conducted by deploying two detection devices in a test area. The results demonstrate that: ① Positioning Ac-curacy: In a 3D grid with a minimum resolution of 8 m, the maximum latitude/longitude deviation is 20 m (during target turning), and the average altitude prediction deviation is 4.37 m (standard deviation: 7.87), significantly outperforming comparative methods. ② Computational Efficiency: The algorithm averages only 55 MB memory usage and 9% CPU utilization on an i9-13900H processor, markedly lower than comparative methods. ③ Applicability: It requires only low-cost ground-based direction-finding equipment without onboard devices. The proposed algorithm achieves low-cost, high-precision 3D real-time localization for low-altitude UAVs within cubic-meter-level deviations, providing an effective solution for scenarios with constrained low-altitude surveillance infrastructure deployment.
- unmanned aerial vehicle /
- low-altitude airspace /
- direction finding cross-location /
- height prediction /
- gaussian pyramid /
- credibility matrix

HTML全文

图 1 交通信号协调控制策略动态决策流程可通达空域-可计算空域映射关系

Figure 1. The dynamic decision-making process of air traffic signal coordination control strategy: relationship of accessible airspace and computable airspace mapping

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图 2 可计算空域金字塔模型

Figure 2. Computable spatial pyramid model

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图 3 目标经纬度位置

Figure 3. Target latitude and longitude position

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图 4 测试部署图

Figure 4. Test deployment diagram

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图 5 测试区域地理空间基准数据

Figure 5. Geospatial reference data for the Test Area

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图 6 无线电对可信度影响数据

Figure 6. Data on the Impact of Radio on Reliability

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图 7 测向设备可信度均值

Figure 7. Mean device reliability

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图 8 预测路径和实际飞行路径对比

Figure 8. Comparison between predicted and actual flight paths

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图 9 预测高度和实际飞行高度对比

Figure 9. Comparison between predicted and actual flight height

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表 1 1号测向设备和2号测向设备主要参数

Table 1. Main parameters of No. 1 and No. 2 direction-finding equipment

参数	1号测向设备	2号测向设备
扫描频段/G	2.4，5.8	2.4，5.8
侦测距离/km	≥2	≥2
接收灵敏度/dBm	≥-110	≥-110
扫描范围（/ °）	360	360
角度误差（/ °）	≤2	≤2
纬度（°）	32.086 836	32.081 165
经度（/ °）	118.764 62	118.872 475
高度/m	65	52

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表 2 天气状况对传感器可信度影响表

Table 2. Weather factor impact table

天气	无线电类	红外类	可见光类
晴天	1.0	1.0	1.0
多云	1.0	1.0	1.0
阴天	1.0	1.0	0.6
大雨、暴雨	0.8	0.3	0.2
中雨	0.9	0.5	0.4
小雨	0.95	0.7	0.6
大雪	0.8	0.4	0.2
中雪	0.85	0.6	0.3
小雪	0.9	0.8	0.4
大雾	0.8	0.2	0.1
雾	0.95	0.5	0.3

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表 3 温度因素对传感器可信度影响表

Table 3. Temperature factor impact table

温度（/℃）	无线电类	红外类	可见光类
≤-20	0.9	1.0	0.9
> -20—10	1.0	1.0	1.0
> -10~0	1.0	1.0	1.0
> 0-10	1.0	1.0	1.0
> 10 - 20	1.0	1.0	1.0
> 20 - 30	1.0	0.8	1.0
> 30 - 40	1.0	0.7	1.0
> 40	0.9	0.6	0.9

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表 4 湿度因素对传感器可信度影响表

Table 4. Humidity factor impact table

湿度（/ %）	无线电类	红外类	可见光类
≤10	1.0	1.0	0.9
> 10~20	1.0	1.0	1.0
> 20~30	1.0	1.0	1.0
> 30~40	1.0	1.0	1.0
> 40~50	1.0	1.0	1.0
> 50~60	1.0	0.9	0.95
> 60~70	1.0	0.85	0.9
> 70~80	0.95	0.8	0.85
> 80	0.9	0.7	0.8

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表 5 本文算法与前沿方法性能对比

Table 5. Metrics comparison: proposed algorithm vs. State-of-the-art methods

对比方法	高度平均偏差/m	平面定位误差/m	计算资源占用/MB		设备成本
对比方法	高度平均偏差/m	平面定位误差/m	内存/MB	CPU/%	设备成本
本文算法	4.37	≤20（转向时）	55	9	低（纯地面设备）
徐海源融合TDOA/DOA	5.2	12	82	15	高（需机载应答器）
Pang随机分形搜索	6.8*	18	210	25	高（离线算力需求）
徐鹏豪测向交叉定位	未提供	15	48	12	低
*注：Pang原文未提高度偏差，6.8 m为根据其航迹优化误差推算值。

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