基于自适应滑动窗口的飞行器轨迹实时平滑算法

刘楚斌 ,  刘雪峰 ,  赵伟 ,  李伟 ,  张强

弹道学报 ›› 2026, Vol. 38 ›› Issue (3) : 9 -18.

PDF (1364KB)
弹道学报 ›› 2026, Vol. 38 ›› Issue (3) : 9 -18. DOI: 10.12115/ddxb.2025.04001

基于自适应滑动窗口的飞行器轨迹实时平滑算法

作者信息 +

Real-time Smoothing Algorithm for Aircraft Trajectory Based on Adaptive Sliding Window

Author information +
文章历史 +
PDF (1395K)

摘要

为实现对飞行器目标的自动跟踪,需要给测量设备提供高精度的中心引导数据。针对目前飞行器测量数据误差导致的中心引导数据抖动剧烈和跳点野值多的问题,提出一种基于自适应滑动窗口的飞行器轨迹数据实时平滑算法。该算法先通过粗差探测算法对原始数据进行预处理,有效剔除异常野值;再采用自适应滑动窗口机制,根据数据特征动态调整窗口参数,实现轨迹数据的动态实时滤波,兼顾平滑效果与处理效率。为精准评估滤波性能,选取变量差分法、最小二乘拟合残差法、最大平滑度和边缘效应四项指标,对平滑前后的测量数据进行量化统计分析。通过仿真数据与3组实际飞行试验数据开展算法验证,结果表明,相较于传统滤波算法,该文算法鲁棒性更强、运算速度更快、实时性更优,能够有效抑制轨迹数据震荡,大幅减少跳点野值干扰。经该算法处理后的中心引导数据精度高、稳定性好,可满足飞行器自动跟踪中对数据精度和实时性的要求,具备较好的工程应用价值。

Abstract

To achieve automatic tracking of aircraft targets, it is necessary to provide high-precision central guidance data for measurement equipment. Aiming at the problems of severe jitter in central guidance data and numerous outlier jump points caused by current aircraft measurement data errors, a real-time smoothing algorithm for aircraft trajectory data based on adaptive sliding window was proposed. The algorithm first adopts the gross error detection algorithm to preprocess raw measurement data for effective outlier elimination. On this basis, an adaptive sliding window strategy was employed to dynamically adjust the window parameters according to data characteristics, realizing dynamic real-time filtering of trajectory data while balancing smoothing performance and computational efficiency. Four evaluation indicators including the variable difference method, least-squares fitting residual method, maximum smoothness and edge effect were selected to quantitatively analyze measurement data before and after smoothing. The algorithm was validated through simulation data and three groups of actual flight-test data. The result shows that the proposed algorithm features stronger robustness, higher computing speed and superior real-time capability compared with traditional filtering approaches. It can effectively suppress trajectory oscillation and eliminate most jump outliers. The processed central guidance data exhibits high precision and favorable stability, which fully satisfies the stringent requirements on precision and real-time performance for aircraft automatic tracking, and possesses promising practical engineering value.

关键词

飞行器 / 轨迹 / 平滑滤波 / 粗差剔除 / 测量设备

Key words

aircraft / trajectory / smoothing filtering / gross error elimination / measurement equipment

引用本文

引用格式 ▾
刘楚斌,刘雪峰,赵伟,李伟,张强. 基于自适应滑动窗口的飞行器轨迹实时平滑算法[J]. 弹道学报, 2026, 38(3): 9-18 DOI:10.12115/ddxb.2025.04001

登录浏览全文

4963

注册一个新账户 忘记密码

参考文献

[1]

浦发, 芮筱亭. 外弹道学[M]. 北京: 国防工业出版社 1989.

[2]

PU Fa, RUI Xiaoting. External ballistics[M]. Beijing: National Defense Industry Press 1989. (in Chinese)

[3]

陈建, 向露, 严明, 等. 基于 BP 神经网络和拓展卡尔曼滤波的轨迹追踪[J]. 计算机仿真, 2024, 41(1): 508-512.

[4]

CHEN Jian, XIANG Lu, YAN Ming, et al. Trajectory tracking based on BP neural network and extended Kalman filter[J]. Computer Simulation, 2024, 41(1): 508-512. (in Chinese)

[5]

范旭, 陈国光, 白敦卓. Kalman 弹道滤波器的快速收敛性研究[J]. 导航与控制, 2018, 17(2): 73-78.

[6]

FAN Xu, CHEN Guoguang, BAI Dunzhuo, et al. Study of the fast convergence for Kalman ballistic filter[J]. Navigation and Control, 2018, 17(2): 73-78. (in Chinese)

[7]

史金光, 徐明友, 王中原, 等. 卡尔曼滤波在弹道修正弹落点推算中的应用[J]. 弹道学报, 2008, 20(3): 41-43.

[8]

SHI Jinguang, XU Mingyou, WANG Zhongyuan, et al. Application of Kalman filtering in calculation of trajectory falling point of trajectory correction projectiles[J]. Journal of Ballistics, 2008, 20(3): 41-43. (in Chinese)

[9]

李小元, 王中原, 常思江. 在线弹道参数滤波与辨识方法分析[J]. 弹道学报, 2020, 32(2): 29-34.

[10]

LI Xiaoyuan, WANG Zhongyuan, CHANG Sijiang. Online trajectory parameter filtering and identification method analysis[J]. Journal of Ballistics, 2020, 32 (2): 29-34. (in Chinese)

[11]

李岩, 任睿, 王旭刚. 两种卡尔曼滤波模型在修正弹道数据处理中的应用比较[J]. 弹道学报, 2011, 23(1): 27-30.

[12]

LI Yan, REN Rui, WANG Xugang. Application comparison of two Kalman filtering models used in trajectory data processing of correction projectile[J]. Journal of Ballistics, 2011, 23 (1): 27-30. (in Chinese)

[13]

段鹏伟, 宫志华, 徐旭, 等. 用于实时弹道滤波的 Sage-Husa 改进算法[J]. 弹道学报, 2022, 34(2): 10-16.

[14]

DUAN Pengwei, GONG Zhihua, XU Xu, et al. Improved Sage-Husa algorithm for real-time trajectory filtering[J]. Journal of Ballistics, 2022, 34(2): 10-16. (in Chinese)

[15]

许立松, 马国梁, 闻泉, 等. 基于无迹卡尔曼滤波的火箭弹姿态估计[J]. 弹道学报, 2021, 33(4): 20-25.

[16]

XU Lisong, MA Guoliang, WEN Quan, et al. Attitude estimation of artillery rocket based on unscented Kalman filter[J]. Journal of Ballistics, 2021, 33 (4): 20-25. (in Chinese)

[17]

谢恺, 秦鹏程. 基于七维状态向量反向无迹卡尔曼滤波的弹道外推算法[J]. 兵工学报, 2018, 39(10): 1945-1950.

[18]

XIE Kai, QIN Pengcheng. Extrapolation algorithm based on the seven-state inverse unscented Kalman filter[J]. Acta Armamentarii, 2018, 39 (10): 1945-1950. (in Chinese)

[19]

雷晓云, 张志安, 杜忠华. 基于改进无迹卡尔曼滤波的弹道射程修正算法研究[J]. 兵工学报, 2018, 39(9): 1701-1710.

[20]

LEI Xiaoyun, ZHANG Zhian, DU Zhonghua. Ballistic range correction algorithm based on an improved unscented Kalman filter[J]. Acta Armamentarii, 2018, 39 (9): 1701-1710. (in Chinese)

[21]

范旭, 陈国光, 白敦卓, 等. 卡尔曼弹道滤波状态初值的最优估计方法研究[J]. 弹箭与制导学报, 2018, 38(1): 139-143.

[22]

FAN Xu, CHEN Guoguang, BAI Dunzhuo, et al. Study on the optimal estimation method of initial value of Kalman ballistic filtering state[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2018, 38 (1): 139-143. (in Chinese)

[23]

常思江, 王中原, 韩成辉. 一种基于过程噪声控制的弹道滤波方案[J]. 空军工程大学报( 自然科学版), 2011, 12(1): 51-54.

[24]

CHANG Sijiang, WANG Zhongyuan, HAN Chenghui. Investigation on a scheme for trajectory filtering based on process noise control[J]. Journal of Air Force Engineering University ( Natural Science Edition ), 2011, 12 (1): 51-54. (in Chinese)

[25]

刘玉磊, 冯新喜, 鹿传国, 等. 带渐消因子的 Quadrature 卡尔曼滤波[J]. 宇航学报, 2013, 34(10): 1370-1377.

[26]

LIU Yulei, FENG Xinxì, LU Chuanguo, et al. A fading quadrature Kalman filter for nonlinear systems[J]. Journal of Astronautics, 2013, 34(10): 1370-1377. (in Chinese)

[27]

刘也, 余安喜, 朱焗波, 等. 弹道目标跟踪中的滤波方法综述[J]. 宇航学报, 2013, 34(11): 1417-1426.

[28]

LIU Ye, YU Anxi, ZHU Jubo, et al. Survey of filter algorithms for ballistic target real-time tracking[J]. Journal of Astronautics, 2013, 34(11): 1417-1426. (in Chinese)

[29]

何昕, 王经义. 基于S-G 滤波算法的航空器着陆阶段滑行轨迹修正研究[J]. 现代计算机, 2024, 30(8): 108-109.

[30]

HE Xin, WANG Jingyi. Research on aircraft taxi trajectory correction during landing stage based on S-G filter algorithm[J]. Modern Computer, 2024, 30(8): 108-109. (in Chinese)

[31]

姜海玲, 姚奕旭, 洪绣超, 等. 基于 SG 滤波去噪的时间序列谐波分析重建算法研究[J]. 吉林师范大学学报(自然科学版), 2021, 42(3): 133-140.

[32]

JIANG Hailing, YAO Yixu, HONG Xiuchao, et al. Research on reconstruction algorithm of time series harmonic analysis based on SG filter and denoising[J]. Journal of Jilin Normal University ( Natural Science Edition ), 2021, 42 (3): 133-140. (in Chinese)

[33]

SCHAFER R W. On the frequency-domain properties of Savitzky-Golay filters[C] // 2011 Digital Signal Processing and Signal Processing Education Meeting ( DSP/SPE ). Sedona, AZ, USA: IEEE, 2011: 54-59.

[34]

赵立兴, 唐英干, 王洪瑞. 一种自适应窗口滤波算法研究[J]. 燕山大学学报, 2013, 37(4): 372-376.

[35]

ZHAO Lixing, TANG Yinggan, WANG Hongrui, et al. Research on a novel adaptive window for image filtering algorithm[J]. Journal of Yanshan University, 2013, 37 (4): 372-376. (in Chinese)

[36]

申程, 张连超, 张卓, 等. 轻量化弹道解算系统火控修正和瞄准线滤波预测[J]. 兵工学报, 2024, 45(2): 429-442.

[37]

SHEN Cheng, ZHANG Lianchao, ZHANG Zhuo, et al. Fire control correction and line-of-sight filtering prediction of lightweight ballistic calculation system[J]. Acta Armamentarii, 2024, 45(2): 429-442. (in Chinese)

[38]

王开园, 许志, 唐硕, 等. 一种基于飞行任务的临近空间短距滑翔飞行器弹道预示方法[J]. 宇航学报, 2021, 42(1): 50-60.

[39]

WANG Kaiyuan, XU Zhi, TANG Shuo, et al. A trajectory prediction method for near space short-range glide vehicle based on flight mission[J]. Journal of Astronautics, 2021, 42(1): 50-60. (in Chinese)

[40]

崔乃刚, 张龙, 王小刚, 等. 自适应高阶容积卡尔曼滤波在目标跟踪中的应用[J]. 航空学报, 2015, 36(12): 3885-3895.

[41]

CUI Naigang, ZHANG Long, WANG Xiaogang, et al. Application of adaptive high-degree cubature Kalman filter in target tracking[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(12): 3885-3895. (in Chinese)

[42]

刘也, 余安喜, 朱焗波, 等. 基于半参数建模的弹道目标实时滤波[J]. 宇航学报, 2011, 32(10): 2169-2174.

[43]

LIU Ye, YU Anxi, ZHU Jubo, et al. Real-time filter for trajectory target tracking based on semi-parameter modeling[J]. Journal of Astronautics, 2011, 32(10): 2169-2174. (in Chinese)

AI Summary AI Mindmap
PDF (1364KB)

0

访问

0

被引

详细

导航
相关文章

AI思维导图

/

〈 〉