导航辅助雷达量测增强的扩展型低空飞行器跟踪

李坤坤; 黎克波; 曹锐; 刘远贺; 胡爽

doi:10.13700/j.bh.1001-5965.2025.0267

导航辅助雷达量测增强的扩展型低空飞行器跟踪

doi: 10.13700/j.bh.1001-5965.2025.0267

李坤坤¹,
黎克波^{2, 3, ,},
曹锐¹,
刘远贺⁴,
胡爽¹

1.
中国人民解放军 63660部队，洛阳 471099
2.
国防科技大学空天科学学院，长沙 410072
3.
太空系统运行与控制全国重点实验室，长沙 410073
4.
空军航空大学，长春 130000

基金项目:

国家自然科学基金面上项目(12472359)

详细信息

通讯作者:
E-mail：likeboreal@nudt.edu.cn

中图分类号: V217⁺.1；TN959.1
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- 被引次数: 0
出版历程
- 收稿日期: 2025-05-09
- 录用日期: 2025-06-20
- 网络出版日期: 2025-06-25
- 整期出版日期: 2026-09-01

Extended low-altitude aircraft tracking via navigation-assisted radar measurement augmentations

LI Kunkun¹,
LI Kebo^{2, 3
, ,},
CAO Rui¹,
LIU Yuanhe⁴,
HU Shuang¹

1.
Unit 63660 of Chinese People’s Liberation Army，Luoyang 471099，China
2.
College of Aerospace Science and Engineering，National University of Defense Technology，Changsha 410072，China
3.
State Key Laboratory of Space System Operation and Control，Changsha 410073，China
4.
Aviation University of Air Force，Changchun 130000，China

Funds:

The General Program of National Natural Science Foundation of China (12472359)

More Information

Corresponding author: E-mail：likeboreal@nudt.edu.cn

摘要

摘要:
合作式浮低空飞行器飞行测试中，单站高分辨雷达对飞行器表面部分观测时存在雷达量测稀疏(乃至缺失)、空间完备性差，致使飞行器跟踪精度欠佳的问题，对此，提出一种融合飞行器导航信息辅助雷达量测增强的飞行器跟踪方法。根据飞行器结构扩展特点，利用随机矩阵模型建模其近似为椭圆体的三维扩展形态；分别建立飞行器部分观测模型及雷达测量模型，进一步设计多种利用飞行器导航信息辅助雷达稀疏量测数据增强策略，以提升量测数据量及空间完备性；基于贝叶斯滤波框架实现部分观测下的飞行器状态估计。仿真实验结果表明：所提方法不仅提升了受试飞行器的跟踪精度及飞行态势感知精度，还兼有多源测控信息融合利用度高及计算成本低等优点。
- 低空飞行器 /
- 扩展目标跟踪 /
- 随机矩阵 /
- 部分观测 /
- 稀疏量测 /
- 数据增强
Abstract:
In the flight test of cooperative aircraft floating at low altitudes, a single-station high-resolution radar can get sparse (even missing) and spatially incomplete measurements, while the radar observes a partial surface of the aircraft. This will lead to poor tracking accuracy for the tested aircraft. To solve this problem, this paper proposes a tracking method using augmented radar measurements by fusing aircraft navigation information. First, a symmetric positive definite random matrix is used to approximate the aircraft’s three-dimensional extension shape, which is roughly ellipsoidal, based on the structurally extended characteristic of the aircraft identified by the high-resolution radar. Subsequently, the partially observed aircraft model and the radar measurement model are both established. Further, multiple strategies are designed to augment sparse radar measurements using assisted aircraft navigation information, such that the radar measurement data is improved in both amount and spatial completeness. Finally, an implementation of aircraft state estimation under partial observation is given within the Bayesian filtering framework. The outcomes of the simulation experiment show that the proposed method improves the tested aircraft’s tracking accuracy and, consequently, awareness accuracy for its flight condition. Moreover, the proposed method has the advantages of high fusion usage of multi-source measurement information and a low computational cost.
- low-altitude aircraft /
- extended target tracking /
- random matrix /
- partial observation /
- sparse measurements /
- data augmentation

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图 1 坐标系示意图

Figure 1. Schematic diagram of coordinate systems

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图 2 3种雷达量测数据增强策略示意图

Figure 2. Schematic diagrams of three augmentation strategies for radar measurements

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图 3 受试飞行器典型低空测试航迹示意图

Figure 3. Schematic diagram of typical test trajectory of low-altitude aircraft

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图 4 转弯阶段1雷达稀疏量测数据增强结果

Figure 4. Augmentation results for sparse radar measurements in turning phase 1

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图 5 飞行器位置、扩展形态估计局部结果

Figure 5. Partial estimation results for position, and extension shape of aircraft

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图 6 飞行器速度估计结果

Figure 6. Estimation results for velocity of aircraft

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图 7 飞行器运动状态估计RMSE

Figure 7. Estimation RMSE for kinematic state of aircraft

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图 8 飞行器扩展形态参数估计平均结果

Figure 8. Average estimation results for extension shape parameters of aircraft

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图 9 平均单帧运算时间曲线

Figure 9. Curves of average computational time per scan

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表 1 4种矩阵运算的浮点运算数^[32]

Table 1. Flops of four kinds of matrix operations^[32]

矩阵运算	示例矩阵对象	浮点运算数
加减法	$ {\boldsymbol{M}}_{1}\in {\bf{R}}^{n\times m} $,$ {\boldsymbol{M}}_{2}\in {\bf{R}}^{n\times m} $	$ {O}(nm) $
乘法	$ {\boldsymbol{M}}_{1}\in {\bf{R}}^{n\times m} $,$ {\boldsymbol{M}}_{2}\in {\bf{R}}^{m\times l} $	$ {O}(2nml-nl) $
求逆	$ {\boldsymbol{M}}_{1}\in {\bf{R}}^{n\times n} $	$ {O}({n}^{3}) $
Cholesky分解	$ {\boldsymbol{M}}_{1}\in {\bf{R}}^{n\times n} $	$ {O}({n}^{3}/3) $

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表 2 3种量测数据增强策略的复杂度

Table 2. Flops of three kinds of measurements data augmentation strategy

增强策略	浮点运算量
1	$ {O}(51{n}_{k}) $
2	$ {O}(12{n}_{k}) $
3	$ {O}(51{n}_{k}) $

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表 3 飞行器运动状态估计RMSE比较

Table 3. Comparison of estimation RMSE for kinematic state of aircraft

数据质量	位置RMSE/m		位置RMSE提升/%	速度RMSE/(m·s⁻¹)		速度RMSE提升/%
数据质量	不增强	增强	位置RMSE提升/%	不增强	增强	速度RMSE提升/%
1	13.668	0.039	99.71	38.392	1.468	96.18
2	13.926	0.151	98.92	38.607	5.683	85.28
3	14.304	0.152	98.94	40.515	6.023	85.13

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表 4 飞行器扩展形态参数估计AED比较

Table 4. Comparison of estimation AED for extension shape parameters of aircraft

数据质量	长半轴长/m		减少比/%	短半轴长/m		减少比/%	主轴指向/（°）		减少比/%
数据质量	不增强	增强	减少比/%	不增强	增强	减少比/%	不增强	增强	减少比/%
1	−4.847	−1.686	65.22	−1.135	0.217	80.88	11.623	1.082	90.69
2	−4.848	−1.698	64.98	−1.130	0.219	80.62	11.655	1.117	90.42
3	−4.904	−1.705	65.23	−1.254	0.206	83.57	11.909	1.278	89.27

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表 5 平均单帧运算时间和平均单帧量测数比较

Table 5. Comparison of average single-frame computational times and average single-frame measurement count

方法	平均单帧运算时间/s	平均单帧量测数/个
不增强	0.013	6.419
增强	0.021	63.853

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