Analysis of the Impact of Aircraft Kinematic State on Radar Detection Probability

doi:10.3969/j.issn.1009-086x.2026.02.009

Abstract

Abstract:

Maintaining a low detection probability by defense radars in vital areas is a fundamental requirement for aircraft route planning during aerial surveys. This necessitates considering and assessing the variations in radar detection probability caused by the kinematic state uncertainty of the aircraft itself. To this end， analysis method based on unscented transformation （UT） is proposed to evaluate the impact of aircraft kinematic state uncertainty on detection probability. Relevant models regarding aircraft detection by radar are presented. The UT method is introduced to establish an process for the propagation of aircraft kinematic state （involving position， and attitude） uncertainty and their impact on radar detection probability. A simulation experiment scenario is designed wherein an aerial survey aircraft is detected by a single-pulse defense radar. The Monte Carlo method is employed to verify the high analysis accuracy of the UT method. Additionally， the patterns regarding how varying degrees of aircraft kinematic state uncertainty affect detection probability are analyzed. Furthermore， comparisons with the traditional linear covariance analysis method demonstrate that the UT method possesses both simplicity and high computational efficiency.

Key words: aircraft, route planning, kinematic state uncertainty, detection probability, unscented transformation（UT）

摘要：

飞行器航测时保持要地防御雷达对其低检测概率是其航线规划的基本要求，这需要考虑和评估飞行器自身运动状态不确定性引起的雷达检测概率变化，对此提出一种基于无迹变换(unscented transformation, UT)的飞行器运动状态不确定性影响检测概率的分析方法。给出飞行器被雷达检测的相关模型；引入UT方法建立了飞行器位置、姿态等运动状态不确定性传播影响检测概率的分析流程；设计一个航测飞行器被单脉冲防御雷达探测的仿真实验场景，通过Monte Carlo方法检验了UT方法具有较高的分析准确性，并分析了飞行器运动状态不同程度不确定性影响检测概率的规律，此外与传统线性协方差分析方法比较说明了UT方法具有简捷高效的计算效率。

关键词: 飞行器, 航线规划, 运动状态不确定性, 检测概率, 无迹变换

CLC Number:

TN957

Kunkun LI, Haiqing LUO, Zijing LIU, Tianxiang LIU. Analysis of the Impact of Aircraft Kinematic State on Radar Detection Probability[J]. Modern Defense Technology, 2026, 54(2): 100-109.

李坤坤, 罗海清, 刘子敬, 刘天翔. 飞行器运动状态对雷达检测概率的影响分析[J]. 现代防御技术, 2026, 54(2): 100-109.

Figures/Tables 10

Fig. 1 Schematic diagram of ellipsoidal aircraft

Fig. 2 Schematic diagram of coordinate systems

Fig. 3 Planform of aircraft route for aerial survey

Fig. 4 Variation curves of theoretical flight attitudes of aircraft

Fig. 5 Variation curves for parameters like aircraft RCS， incident radar angle， detection SNR and aerial survey range

Fig. 6 Variation curves of detection probability subject to low degree of aircraft kinematic state uncertainty

Fig. 7 Variation curves of detection probability subject to medium degree of aircraft kinematic state uncertainty

Fig. 8 Variation curves of detection probability subject to high degree of aircraft kinematic state uncertainty

Fig. 9 Variation curves of 3σPD subject to various degrees of aircraft kinematic state uncertainty

Fig. 10 Comparison of computation times of various methods

References 22

[1]	龚生阳，李哲，曹立雄，等. 飞行器飞行姿态不确定性传播分析［J］. 强度与环境， 2023， 50（1）： 22-30.
	GONG Shengyang， LI Zhe， CAO Lixiong， et al. Uncertainty Propagation Analysis for Flight Attitude of Aircraft［J］. Structure & Environment Engineering， 2023， 50（1）： 22-30.
[2]	王美凤. 机载雷达目标检测及航迹规划方法研究［D］. 西安：西安电子科技大学， 2020.
	WANG Meifeng. Research on Airborne Radar Target Detection and Track Planning Methods［D］. Xi'an： XiDian University， 2020.
[3]	COSTLEY A， CHRISTENSEN R， LEISHMAN R C， et al. Sensitivity of Single-Pulse Radar Detection to Aircraft Pose Uncertainties［J］. IEEE Transactions on Aerospace and Electronic Systems， 2023， 59（3）： 2286-2295.
[4]	陶杨，周益，蒋黄滔. 改进蚁群算法在地形跟随航线规划问题中的应用［J］. 现代防御技术， 2024， 52（1）： 34-40.
	TAO Yang， ZHOU Yi， JIANG Huangtao. Application of Improved Ant Colony Algorithm to Terrain Following Route Planning Problem［J］. Modern Defence Technology， 2024， 52（1）： 34-40.
[5]	魏维斌，兰旭辉，彭思勇，等. 基于发现概率的预警机机动部署研究［J］. 雷达科学与技术， 2024， 22（6）： 620-627.
	WEI Weibin， LAN Xuhui， PENG Siyong， et al. Research on Maneuvering Deployment of AWACS Based on Detection Probability［J］. Radar Science and Technology， 2024， 22（6）： 620-627.
[6]	何通，韦亚利，卢青，等. 无人机群协同侦察多点目标路径规划与控制［J］. 空天防御， 2025， 8（1）： 31-40.
	HE Tong， WEI Yali， LU Qing， et al. Path Planning and Control of UAV Cluster Cooperative Reconnaissance Multi-point Targets［J］. Air & Space Defense， 2025， 8（1）： 31-40.
[7]	PENG Gaoxiang， WANG Bo， LIU Lei， et al. 3-D Autonomous Entry Trajectory Planning via Hybrid Action Reinforcement Learning［J］. IEEE Transactions on Aerospace and Electronic Systems， 2025， 61（1）： 342-354.
[8]	刘海波. 针对概率盒模型的高效不确定性传播数值分析方法［D］. 长沙：湖南大学， 2019.
	LIU Haibo. Efficient Uncertainty Propagation Numerical Analysis Methods for Probability-Box Model［D］. Changsha： Hunan University， 2019.
[9]	谢博群，张哲，姜潮. 一种针对多峰随机分布的不确定性传播分析方法［J］. 中国科学（技术科学）， 2022， 52（8）： 1259-1273.
	XIE Boqun， ZHANG Zhe， JIANG Chao. An Uncertainty Propagation Analysis Method Considering Multimodal Random Distribution［J］. Scientia Sinica（Technologica）， 2022， 52（8）： 1259-1273.
[10]	杨雪榕，杨雅君，朱俊. 飞行器试验及数据统计处理方法［M］. 北京：国防工业出版社， 2024.
	YANG Xuerong， YANG Yajun， ZHU Jun. Flight Vehicle Tests and Data Statistics Processing Methods［M］. Beijing： National Defense Industry Press， 2024.
[11]	丁力全，吴楠，孟凡坤，等. 基于无迹变换的协同探测与速度方向控制制导律一体化设计［J］. 弹道学报， 2022， 34（2）： 25-32.
	DING Liquan， WU Nan， MENG Fankun， et al. Integrated Design of Collaborative Detection and Velocity Direction Control Guidance Law Based on Unscented Transformation［J］. Journal of Ballistics， 2022， 34（2）： 25-32.
[12]	YANG Yang. Square-Root Higher-Order Unscented Estimators for Robust Orbit Determination［J］. IEEE Transactions on Aerospace and Electronic Systems， 2024， 60（6）： 7820-7837.
[13]	姚卓青，沙安，龚胜平，等. 一种航天器姿态控制系统多源误差分析方法［J］. 飞行力学， 2024， 42（5）： 47-54.
	YAO Zhuoqing， SHA An， GONG Shengping， et al. A Multi-source Error Analysis Method for Spacecraft Attitude Control System［J］. Flight Dynamics， 2024， 42（5）： 47-54.
[14]	彭祺擘，刘将辉，张海联，等. 航天器入轨状态与偏差传播分析［J］. 系统工程与电子技术， 2024， 46（6）： 2117-2127.
	PENG Qibo， LIU Jianghui， ZHANG Hailian， et al. Analysis of Orbital Injection State and Deviation Propagation of Spacecraft［J］. Systems Engineering and Electronics， 2024， 46（6）： 2117-2127.
[15]	李鹏，柴华，白显宗. 基于状态转移张量的LEO目标短期误差传播及碰撞概率计算［J］. 现代防御技术， 2024， 52（5）： 106-115.
	LI Peng， CHAI Hua， BAI Xianzong. State Transition Tensors-Based Short-Term Error Propagation and Collision Probability Calculation for LEO Targets［J］. Modern Defence Technology， 2024， 52（5）： 106-115.
[16]	杨震. 非线性轨道机动瞄准与偏差演化分析方法［D］. 长沙：国防科技大学， 2018.
	YANG Zhen. Nonlinear Method for Orbit Targeting and Uncertainty Propagation［D］. Changsha： National University of Defense Technology， 2018.
[17]	QIAO Chenliang， XU Heyong， YE Zhengyin. Sensitivity and Uncertainty Analysis of the Nonlinear Flight Dynamics System of the Flexible Body［J］. Aerospace Science and Technology， 2023， 139： 108389.
[18]	程萌，周奇，魏骁，等. 面向低精度分析模型不可分层级的多保真度近似建模方法研究［J］. 中国舰船研究， 2024， 19（6）： 82-96.
	CHENG Meng， ZHOU Qi， WEI Xiao， et al. Research on Multi-fidelity Surrogate Modeling Method for Non-Hierarchical Low-Fidelity Analysis Model Problem［J］. Chinese Journal of Ship Research， 2024， 19（6）： 82-96.
[19]	CHIAPPETTA M， PIAZZOLA C， CARRATURO M， et al. Sparse-Grids Uncertainty Quantification of Part-Scale Additive Manufacturing Processes［J］. International Journal of Mechanical Sciences， 2023， 256： 108476.
[20]	MAHAFZA B R. Radar Systems Analysis and Design Using MATLAB［M］. 4th ed. New York： Chapman and Hall/CRC， 2022.
[21]	吕强，刘海军，钟珲，等. 一种主被动雷达目标跟踪测量数据融合方法［J］. 现代防御技术， 2024， 52（4）： 108-116.
	Qiang LÜ， LIU Haijun， ZHONG Hui， et al. A Fusion Method for Target Tracking Measurement Data of Active and Passive Radar［J］. Modern Defence Technology， 2024， 52（4）： 108-116.
[22]	陈克俊，刘鲁华，孟云鹤. 远程火箭飞行动力学与制导［M］. 2版. 北京：科学出版社， 2024.
	CHEN Kejun， LIU Luhua， MENG Yunhe. Launch Vehicle Flight Dynamics and Guidance［M］. 2nd ed. Beijing： Science Press， 2024.