基于简化欧拉螺线航迹模型的固定翼飞机雷达发现概率计算方法

  • 王浩宇 ,
  • 关晶心 ,
  • 陆孝强 ,
  • 宋磊
展开
  • 北京航空航天大学

收稿日期: 2026-03-04

  修回日期: 2026-05-26

  网络出版日期: 2026-05-28

Radar Detection Probability Calculation for Fixed-Wing Aircraft Based on a Sim-plified Clothoid Trajectory Model

  • WANG Hao-Yu ,
  • GUAN Jing-Xin ,
  • LU Xiao-Qiang ,
  • SONG Lei
Expand

Received date: 2026-03-04

  Revised date: 2026-05-26

  Online published: 2026-05-28

摘要

飞机的隐身性能是实现战场突防的关键,而雷达发现概率是评估飞机隐身性能的重要指标。固定翼飞机飞行中航迹与姿态高度耦合并共同影响雷达视线的时域演变,从而影响雷达发现概率计算。传统“直线-圆弧”航迹模型难以准确描述固定翼飞机的航迹与姿态变化,因此本文提出一种基于简化欧拉螺线(Clothoid)的动态隐身评估方法。通过建立满足飞行力学约束的解析航迹模型,重点解决了传统“直线-圆弧”法因曲率不连续引起的姿态非物理阶跃。仿真验证表明,该方法能够更精确地复现从滚转建立到稳定盘旋的真实运动历程,有效解决了因曲率突变引起的时域RCS失真,确保了对隐身平台时域RCS峰值特征捕捉的完整性与准确性。该研究为固定翼飞机的动态隐身性能评估提供了一种兼顾物理保真度与计算效率的方法。

本文引用格式

王浩宇 , 关晶心 , 陆孝强 , 宋磊 . 基于简化欧拉螺线航迹模型的固定翼飞机雷达发现概率计算方法[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2026.33535

Abstract

Aircraft stealth performance is crucial for successful battlefield penetration, and the probability of radar detection serves as a vital metric for evaluating this capability. During the flight of fixed-wing aircraft, trajectory and attitude are highly coupled, jointly influencing the time-domain evolution of the radar line of sight (LOS) and subsequently affecting the calculation of radar detection probability. The traditional "straight-line and circular-arc" trajectory model struggles to accurately describe the trajectory and attitude variations of fixed-wing aircraft. Consequently, this paper proposes a dynamic stealth evaluation method based on simplified Clothoids (Euler spirals). By establishing an analytical trajectory model that satisfies flight mechanics constraints, this study primarily resolves the non-physical attitude jumps caused by curvature dis-continuities inherent in the traditional "straight-line and circular-arc" method. Simulation validations demonstrate that the proposed method can more precisely reproduce the actual motion history from roll initiation to steady turning. It effectively eliminates the time-domain Radar Cross Section (RCS) distortion caused by abrupt curvature changes, ensuring completeness and accuracy in capturing the time-domain RCS peak characteristics of stealth platforms. This research provides an approach that successfully balances physical fidelity and computational efficiency for the dynamic stealth performance evaluation of fixed-wing aircraft.

参考文献

[1]RAO G A, MAHULIKAR S P.Integrated review of stealth technology and its role in airpower[J].The Aeronautical Journal, 2002, 106(1066):629-642
[2]傅莉, 崔哲, 邓洪伟.航空发动机后向统计特性分析方法[J].航空发动机, 2024, 50(1):72-78
[3]FU L, CUI Z, DENG H W,.Statistical Characteristics Analysis Method of Aeroengine Backward RCS[J].Aeroengine, 2024, 50(1):72-78
[4]庄亚强, 王毅增, 刘俊良.隐身无人机的RCS统计特性研究[J].微波学报, 2020, 36(S01):-
[5]ZHUANG Y Q, WANG Z Y, LIU J L, Research on Statistical Characteristic of Stealth UAV[J].Journal of Microwaves, 2020, 36(S01)(in chinses).
[6]YING L, ZHE W, PEILIN H, et al.A New Method for Analyzing Integrated Stealth Ability of Penetration Aircraft[J].Chinese Journal of Aeronautics, 2010, 23(2):187-193
[7]ZHOU L, CHEN X, HUANG J, et al.Adjoint-Based RCS Surface Sensitivity Calculation and Aero/RCS Optimization[C]//FU S. 2023 Asia-Pacific Internation-al Symposium on Aerospace Technology (APISAT 2023) Proceedings. Singapore: Springer Nature Sin-gapore, 2024: 1715-1730.
[8]黄亚林, 张晨新, 刘凯越, 等.基于动态的隐身目标检测研究[J].微波学报, 2017, 33(1):58-62
[9]HUANG Y L, ZHANG C X, LIU K Y, et al.A Study on Detection of Stealth Target Based on Dynamic RCS[J].Journal of Microwaves, 2017, 33(1):58-62
[10]马前阔, 张小宽.基于改进混合对数正态分布模型的隐身飞机动态统计特性分析[J].系统工程与电子技术, 2022, 44(1):34-39
[11]MA Q K, ZHANG X K.Dynamic RCS statistical characteristics analysis of stealth aircraft based on improved hybrid lognormal distribution model[J].Systems Engineering and Electronics, 2022, 44(1):34-39
[12]SEN K, AKSIMSEK S, KARA A.Dynamic RCS Modeling and Aspect Angle Analysis for Highly Ma-neuverable UAVs[J].Aerospace, 2024, 11(9):775-
[13]ZHUANG Y Q, ZHANG C X, ZHANG X K.A Novel Simulation Approch of Aircraft Dynamic RCS[J]. Progress In Electromagnetics Research M, 2014, 36: 85-91.
[14]陈世春, 黄沛霖, 姬金祖.从探测概率的角度评价飞机的隐身性能[J].航空学报, 2015, 36(4):1150-1161
[15]CHEN S C, HUANG P L, JI J Z.Evaluating Aircraft’s Stealth Performance From the Perspective of detection Probability[J].Acta Aeronautica et Astronautica Sinica, 2015, 36(4):1150-1161
[16]XU Q, GE J, YANG T, et al.A trajectory design meth-od for coupling aircraft radar cross-section character-istics[J]. Aerospace Science and Technology, 2020, 98: 105653.
[17]YUE K, CHEN S, SHU C.Calculation of Aircraft Target’s Single-Pulse Detection Probability[J].Journal of Aerospace Technology and Management, 2015, 7(3):314-322
[18]GUAN J, HUANG J, SONG L, et al.Stealth Aircraft Penetration Trajectory Planning in 3D Complex Dy-namic Environment Based on Sparse A* Algorithm[J].Aerospace, 2024, 11(1):87-
[19]LU X, HUANG J, WU Y, et al.Influence of stealth aircraft dynamic RCS peak on radar detection proba-bility[J].Chinese Journal of Aeronautics, 2023, 36(3):137-145
[20]卿朝进, 何林锶, 王子龙, 等.基于发现概率地对空雷达干扰源分配的改进型遗传算法[J].火力与指挥控制, 2025, 50(02):21-28
[21]QING C, HE L, WANG Z, et al.Improved Genetic Algorithm for Jamming Source Allocation ofGround to Air Radar Based on Detection Probability[J].Fire Control & Command Control, 2025, 50(02):21-28
[22]卿朝进, 何林锶, 王子龙, 等.基于发现概率的箔条干扰弹投放策略研究[J].雷达科学与技术, 2024, 22(06):672-680
[23]QING C, HE L, WANG Z, et al.Research on Chaff Jamming Shell Launch Strategy Based on Detection Probability[J].Radar Science and Technology, 2024, 22(6):672-680
[24]KARAMAN S, FRAZZOLI E.Sampling-based algo-rithms for optimal motion planning[J].The Interna-tional Journal of Robotics Research, 2011, 30(7):846-894
[25]杨冲.一种二维平面运动目标航迹仿真方法[J].陕西科技大学学报自然科学版, 2014, 32(3):153-157
[26]YANG C.Simulation method for two-dimensional plane moving target track[J].Journal of Shaanxi Uni-versity of Science & Technology, 2014, 32(3):153-157
[27]杨莉, 安红.作战飞机机动飞行航迹仿真建模研究[J].微计算机信息, 2011, 27(11):132-134
[28]YANG L, AN H.Research on combat airplane ma-neuvering flight path simulation[J].Microcomputer Information, 2011, 27(11):132-134
[29]朱金冬, 张方齐, 赵彤, 等.任务规划系统机动模型与航线设计[J].航空工程进展, 2022, 13(4):73-82
[30]滕鹏, 黄俊, 张斌.三维航迹的B样条曲线拟合算法[J]. 火力与指挥控制, 2007(9): 115-118.
[31]TENG P, HUANG J, ZHANG B.Study on the three-dimensional trajectory optimization by using the method of B-spline curve fitting[J].Fire Control & Command Control, 2007, 32(9):115-118
[32]黄俊, 滕鹏, 于雷, 等.战斗机航迹可飞性过载检验算法[J]. 飞行力学, 2008(3): 22-25.
[33]HUANG J, TENG P, YU L.Algorithm of overloading verification for some fighter's trajectory[J].Flight Dy-namics, 2008, 26(3):2-26
[34]YU Z, QI N, HUO M, 等.Fast Cooperative Trajectory Generation of Unmanned Aerial Vehicles Using a Bezier Curve-Based Shaping Method[J]. IEEE Access, 2022, 10: 1626-1636.
[35]NIKOLAIEV M, NOVOTARSKYI M.An Enhanced Adaptive B-spline Smoothing Approach for UAV Path Planning[J]. International Journal of Intelligent Sys-tems and Applications, 17(4): 1.
[36]QIN C, ZHAO N, WANG Q, et al.Minimum Snap Trajectory Planning and Augmented MPC for Morph-ing Quadrotor Navigation in Confined Spac-es[J].Drones, 2025, 9(4):304-
[37]HUO F, ZHU S, DONG H, et al.A new approach to smooth path planning of Ackerman mobile robot based on improved ACO algorithm and B-spline curve[J]. Robotics and Autonomous Systems, 2024, 175: 104655.
[38]BASSOLILLO S R, RASPAOLO G, BLASI L, et al.Path Planning for Fixed-Wing Unmanned Aerial Vehi-cles: An Integrated Approach with Theta* and Clo-thoids[J].Drones, 2024, 8(2):62-
[39]BINNINGER A, SORKINE-HORNUNG O.Smooth Interpolating Curves with Local Control and Mono-tone Alternating Curvature[J].Computer Graphics Fo-rum, 2022, 41(5):25-38
[40]ALNUAIMI M.Performance comparison of clothoid and dubins path generation algorithms[C]//AIAA AVIATION 2022 Forum. Chicago, IL & Virtual: American Institute of Aeronautics and Astronautics, 2022: 3972
[41]MAHULIKAR S P, SONAWANE H R, ARVIND RAO G.Infrared signature studies of aerospace vehicles[J].Progress in Aerospace Sciences, 2007, 43(7):218-245
[42]方振平.航空飞行器飞行动力学[M]. 航空飞行器飞行动力学, 2005.
[43]FANG Z P.Aircraft Flight Dynamics[M]. Beijing: Bei-hang University Press. 2005: 92-95.
[44]STENGEL R F.Some Effects of Parameter Variations on the Lateral-Directional Stability of Aircraft[J].Journal of Guidance and Control, 1980, 3(2):124-131
[45]BRANDSE J, MULDER M, VAN PAASSEN M M.Clothoid-Augmented Trajectories for Perspective Flight-Path Displays[J].The International Journal of Aviation Psychology, 2007, 17(1):1-29
[46]丁鹭飞, 耿富录, 陈建春.雷达原理.第5版[M]. 北京: 电子工业出版社, 2014.
[47]Din L F, Geng F L, Chen J C.Radar Principles[M]. Beijing: Publishing House of Electronics Industry. 2014: 190
[48]吴凤鸣, 余志勇, 杜兆阳, 等.雷达探测能力评估模型研究[J].雷达科学与技术, 2019, 17(6):689-694
[49]KANTER I.Exact Detection Probability for Partially Correlated Rayleigh Targets[J].Aerospace & Elec-tronic Systems IEEE Transactions on, 1986, AES-22(2):184-196
[50]SWERLING P.Detection of fluctuating pulsed signals in the presence of noise[J].IRE Transactions on In-formation Theory, 1957, 3(3):175-178
[51]刘万萌, 童创明, 王童, 等.飞机运动特征对动态序列的影响分析[J].火力与指挥控制, 2017, 42(7):33-38
[52]LIU W M, TONG C M, WANG T, et al.Analysis of the impact of aircraft movement feature on dynamic RCS series[J].Fire Control & Command Control, 2017, 42(7):33-38
[53]YE H, CHEN M, WU Q.Flight Envelope Protection Control Based on Reference Governor Method in High Angle of Attack Maneuver[J]. Mathematical Problems in Engineering, 2015, 2015: 1-15.
[54]ZHOU Z, HUANG J.Hybrid Deflection of Spoiler Influencing Radar Cross-Section of Tailless Fighter[J].Sensors, 2021, 21(24):8459-
[55]LI Z, YONG C, DUO L.Multi-effectors distribution of flying wing with stealthy optimization[C]//2017 36th Chinese Control Conference (CCC). 2017: 2864-2869.
文章导航

/