基于混合式惯导系统构型优化的弹道导弹落点精度研究

  • 康林 ,
  • 王新龙 ,
  • 陈万春 ,
  • 雷文贵
展开
  • 1. 北京航空航天大学宇航学院
    2. 北京航空航天大学

收稿日期: 2025-09-22

  修回日期: 2025-11-10

  网络出版日期: 2025-11-10

Research on Ballistic Missile Impact Point Accuracy Based on Hybrid Inertial Navigation System Configuration Optimization

  • KANG Lin ,
  • WANG Xin-Long ,
  • CHEN Wan-Chun ,
  • LEI Wen-Gui
Expand

Received date: 2025-09-22

  Revised date: 2025-11-10

  Online published: 2025-11-10

摘要

为了提升弹道导弹落点精度,本文提出了一种高效的混合式惯导构型优化方法。该方法基于摄动法构建了混合式惯导误差快速计算模型,将落点圆概率误差计算时间大幅缩减至秒级,为射前快速构型寻优奠定了坚实基础。进一步深入分析惯性元件敏感轴指向对导航精度的影响,并以圆概率误差为性能指标,采用四元数描述构型参数,建立了能够避免计算奇异性并覆盖全姿态空间的优化模型。对该模型的仿真验证与机理分析表明,所提方法可使弹道导弹落点精度提升约20%~30%,且无需增加硬件成本或改变飞行弹道,在特定飞行轨迹下,相比静态最优构型表现出更高精度。这一提升主要得益于对惯性元件残余安装误差的有效抑制,从而在不同发射方向下均能实现导航精度的显著提升,验证了该方法的有效性与普适性。

本文引用格式

康林 , 王新龙 , 陈万春 , 雷文贵 . 基于混合式惯导系统构型优化的弹道导弹落点精度研究[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2025.32815

Abstract

To improve the impact point accuracy of ballistic missiles, this paper presents an efficient configuration optimization method for a hybrid inertial navigation system (INS). A rapid error computation model for the hybrid INS is developed based on the perturbation method, reducing the computation time of the circular error probable (CEP) to seconds-level and enabling fast pre-launch configuration optimization. Furthermore, the influence of the sensitive-axis orientation of inertial components on navigation accuracy is investigated. Using CEP as the performance metric and representing configuration parameters with quaternions, an optimization model is established that avoids computational singularities while fully covering the attitude space. Simulation and mechanistic analysis indicate that the proposed approach can improve missile impact accuracy by approximately 20%–30% without additional hardware cost or trajectory modification, and, for certain flight trajectories, achieves higher accuracy than static optimal configurations. This improvement primarily results from the effective suppression of residual installation errors in inertial components, thereby significantly enhancing navigation accuracy across different launch directions and validating the effectiveness and generality of the proposed method.

参考文献

[1] 秦永元. 惯性导航[M]. 第三版. 北京: 科学出版社, 2020: 1-7. QIN Y Y. Inertial Navigation[M]. 3rd ed. Beijing: Science Press, 2020: 1-7 (in Chinese). [2] 张士峰, 李俊, 杨华波. 惯性制导工具误差分离技术综述[J]. 航空学报, 2023, 44(15): 175-194. ZHANG S F, LI J, YANG H B. Review of inertial guidance instrumental error separation techniques[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(15): 175-194 (in Chinese). [3] 贺杰, 黄显林, 李学峰. Sins制导工具误差补偿研究[J]. 航空学报, 2007(1): 182-186. HE J, HUANG X L, LI X F. Study on SINS guidance instrument error compensation[J]. Acta Aeronautica et Astronautica Sinica, 2007(1): 182-186 (in Chinese). [4] ZHANG Z, ZHANG H, HAO Y, et al. A review on MEMS silicon resonant accelerometers[J]. Journal of Microelectromechanical Systems, 2024, 33(2): 174-208. [5] JIANG L, QUAN W, LI R, et al. A parametrically modulated dual-axis atomic spin gyroscope[J]. Applied Physics Letters, 2018, 112(5). [6] 徐明. 美国“和平卫士”式导弹[J]. 航天, 1994(6): 14-16. XU M. The US “Peacekeeper” missile[J]. Aerospace, 1994(6): 14-16 (in Chinese). [7] IEEE standard specification format guide and test procedure for single-degree-of-freedom rate-integrating gyros[J]. IEEE Std 517-1974, 1974: 1-60. [8] 吴梦旋. 惯性仪表高阶误差模型系数在精密离心机上的测试方法[D]. 哈尔滨工业大学, 2018. WU M X. Test method for high order error model coefficients of inertial instruments on precision centrifuge[D]. Harbin Institute of Technology, 2018 (in Chinese). [9] 孙闯, 任顺清. 陀螺加速度计交叉二次项的线振动台测试方法[J]. 导航定位与授时, 2017, 4(5): 105-110. SUN C, REN S Q. Measurement method for cross-quadratic coefficient of PIGA on linear vibration table[J]. Navigation, Positioning & Timing, 2017, 4(5): 105-110 (in Chinese). [10] 陈东生, 魏宗康, 房建成. 验证石英加速度计误差模型的火箭橇试验[J]. 中国惯性技术学报, 2009, 17(2): 236-239+245. CHEN D S, WEI Z K, FANG J C. Verifying QFPA’s error model based on rocket sled testing[J]. Journal of Chinese Inertial Technology, 2009, 17(2): 236-239+245 (in Chinese). [11] SECER G, BARSHAN B. Improvements in deterministic error modeling and calibration of inertial sensors and magnetometers[J]. Sensors and Actuators A: Physical, 2016, 247: 522-538. [12] KHANKALANTARY S, RANJBARAN S, EBADOLLAHI S. Simplification of calibration of low-cost MEMS accelerometer and its temperature compensation without accurate laboratory equipment[J]. Measurement Science and Technology, 2021, 32(4): 045102. [13] 朱建丰, 徐世杰. 基于误差椭球理论的惯性部件构型分析[J]. 导弹与航天运载技术, 2008(2): 40-45. ZHU J F, XU S J. Configuration analysis of inertial units based on error ellipsoid theory[J]. Missiles and Space Launch Vehicles, 2008(2): 40-45 (in Chinese). [14] JAFARI M. Optimal redundant sensor configuration for accuracy increasing in space inertial navigation system[J]. Aerospace Science and Technology, 2015, 47: 467-472. [15] HE Q, YU H, LIANG D, et al. Enhancing pure inertial navigation accuracy through a redundant high-precision accelerometer-based method utilizing neural networks[J]. Sensors, 2024, 24(8): 2566. [16] GAO C, WEI G, WANG L, et al. A systematic calibration modeling method for redundant INS with multi-sensors non-orthogonal configuration[J]. Micromachines, 2022, 13(10): 1684. [17] 程建华, 董金鲁, 陈岱岱. 一种对称斜置式四陀螺惯导冗余配置方案[J]. 传感器与微系统, 2015, 34(2): 16-19+27. CHENG J H, DONG J L, CHEN D D. Symmetrical and sideling redundancy configuration scheme of SINS using four gyroscopes[J]. Sensor and Microsystems, 2015, 34(2): 16-19+27. (in Chinese) [18] 陈世年. 控制系统设计[M]. 北京: 宇航出版社, 1996. CHEN S N. Control System Design[M]. Beijing: Astronautic Publishing House, 1996 (in Chinese). [19] 冯培德. 论混合式惯性导航系统[J]. 中国惯性技术学报, 2016, 24(3): 281-284, 290. FENG P D. On hybrid inertial navigation system[J]. Journal of Chinese Inertial Technology, 2016, 24(3): 281-284, 290 (in Chinese). [20] 王蕾, 王玮, 刘增军, 等. 混合式惯性导航系统全数字平台技术研究[J]. 兵工学报, 2018, 39(7): 1316-1322. WANG L, WANG W, LIU Z J, et al. Research on the digital platform for hybrid inertial navigation system[J]. Acta Armamentarii, 2018, 39(7): 1316-1322 (in Chinese). [21] 尤太华, 禹春梅, 杜建邦. 混合式惯导原理及其在弹载环境下应用[J]. 航天控制, 2020, 38(1): 23-29. YOU T H, YU C M, DU J B. Principle and application of Hybrid-INS in the missile borne environment[J]. Aerospace Control, 2020, 38(1): 23-29 (in Chinese). [22] SHKEL A M, WANG Y. Navigation error analysis in strapdown inertial navigation[M]//Pedestrian Inertial Navigation with Self-Contained Aiding. IEEE, 2021: 47-64. [23] ZHOU X, WANG Z, LI D, et al. Guidance systematic error separation method based on nonlinear combinatorial model[C]//2018 37th Chinese Control Conference (CCC). 2018: 4685-4690. [24] HE J, HUANG X lin. Modeling, identification and compensation of sins guidance instrument error[C]//2006 International Conference on Machine Learning and Cybernetics. 2006: 2479-2484. [25] 杨洪森. 弹载SINS/双星组合导航系统建模与仿真精度分析[D]. 国防科学技术大学, 2006. YANG H S. Modeling and accuracy assessment on missile-borne SINS/Double-Satellite integrated navigation system[D]. National University of Defense Technology, 2006 (in Chinese). [26] 郑伟, 汤国建. 扰动引力场中弹道导弹飞行力学[M]. 北京: 国防工业出版社, 2009. ZHENG W, TANG G J. Flight Mechanics of Ballistic Missiles in Perturbed Gravity Field[M]. Beijing: National Defense Industry Press, 2009 (in Chinese). [27] 温永智, 谢愈, 吴杰, 等. 基于环境函数矩阵法的惯导精度快速评估[J]. 弹箭与制导学报, 2011, 31(3): 56-58. WEN Y Z, XIE Y, WU J, et al. Rapid accuracy assessment of INS based on environment function matrix method[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2011, 31(3): 56-58 (in Chinese). [28] 张金槐. 远程火箭精度分析与评估[M]. 长沙: 国防科技大学出版社, 1995. ZHANG J H. Analysis and Assessment of Long-Range Rocket Accuracy[M]. Changsha: National University of Defense Technology Press, 1995 (in Chinese). [29] YANG Y. Spacecraft attitude determination and control: Quaternion based method[J]. Annual Reviews in Control, 2012, 36(2): 198-219. [30] EL-HAKEM HEGAZY S A, KAMEL A M, ARAFA, I I, et al. INS Stochastic Noise Impact on Circular Error Probability of Ballistic Missiles[J]. NAVIGATION: Journal of the Institute of Navigation, 2022, 69(2): navi.523. [31] 魏宗康, 高荣荣, 周姣, 等. 基于椭圆概率误差的落点精度评定方法[J]. 导弹与航天运载技术, 2020(2): 58-63. WEI Z K, GAO R R, ZHOU J, et al. An accuracy evaluation method of fall points based on elliptic error probable[J]. Missiles and Space Launch Vehicles, 2020(2): 58-63 (in Chinese). [32] 徐明. “民兵Ⅲ”号洲际弹道导弹[J]. 航天, 1994(5): 12-14. XU M. “Minuteman III" intercontinental ballistic missile[J]. Aerospace, 1994(5): 12-14 (in Chinese).
文章导航

/