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低复杂度自适应容积卡尔曼滤波算法

李春辉 马健 杨永建 甘轶

李春辉, 马健, 杨永建, 等 . 低复杂度自适应容积卡尔曼滤波算法[J]. 北京航空航天大学学报, 2022, 48(4): 716-724. doi: 10.13700/j.bh.1001-5965.2020.0642
引用本文: 李春辉, 马健, 杨永建, 等 . 低复杂度自适应容积卡尔曼滤波算法[J]. 北京航空航天大学学报, 2022, 48(4): 716-724. doi: 10.13700/j.bh.1001-5965.2020.0642
LI Chunhui, MA Jian, YANG Yongjian, et al. Low-complexity adaptive cubature Kalman filter algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(4): 716-724. doi: 10.13700/j.bh.1001-5965.2020.0642(in Chinese)
Citation: LI Chunhui, MA Jian, YANG Yongjian, et al. Low-complexity adaptive cubature Kalman filter algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(4): 716-724. doi: 10.13700/j.bh.1001-5965.2020.0642(in Chinese)

低复杂度自适应容积卡尔曼滤波算法

doi: 10.13700/j.bh.1001-5965.2020.0642
基金项目: 

空军工程大学校长基金 XZJ2020039

详细信息
    通讯作者:

    马健, E-mail: majiankgd@163.com

  • 中图分类号: TN953

Low-complexity adaptive cubature Kalman filter algorithm

Funds: 

Air Force Engineering University President's Fund XZJ2020039

More Information
  • 摘要:

    确定采样型滤波算法中的容积卡尔曼滤波(CKF)算法滤波性能优良,但是却难以克服目标模型不确定性或者目标状态突变带来的影响。构造强跟踪CKF能有效改善算法的自适应性,但是在求解渐消因子时大大增加了计算量。为此,提出一种低复杂度自适应CKF算法,通过设立基于新息的自适应修正判决准则和修正方式,直接对状态预测值进行修正,使滤波算法能及时跟上目标真实状态,以提高滤波精度。使用浮点操作数计算并分析了CKF算法、强跟踪CKF算法及所提算法的复杂度,同时将3种算法应用在建模不准确的目标跟踪中,并进行仿真验证。仿真结果表明:在目标建模不匹配的情况下,低复杂度自适应CKF算法和强跟踪CKF算法都能保持较好的滤波精度和数值稳定性,同时所提算法在算法复杂度上有明显改善。

     

  • 图 1  基于新息的修正判决准则

    Figure 1.  Amending judgment criteria based on innovation sequence

    图 2  低复杂度自适应CKF算法流程

    Figure 2.  Flowchart of low-complexity adaptive CKF algorithm

    图 3  三种算法的复杂度比较(l=8)

    Figure 3.  Comparison of three algorithms complexity (l=8)

    图 4  三种算法的复杂度比较(n=8)

    Figure 4.  Comparison of three algorithms complexity (n=8)

    图 5  单次仿真中的目标运动轨迹

    Figure 5.  Target motion trajectory in single simulation

    图 6  x轴位置均方根误差

    Figure 6.  RMSE of position in x axis

    图 7  y轴位置均方根误差

    Figure 7.  RMSE of position in y axis

    图 8  x轴位置平均均方根误差

    Figure 8.  Mean RMSE of position in x axis

    图 9  y轴位置平均均方根误差

    Figure 9.  Mean RMSE of position in y axis

    表  1  三种算法复杂度计算结果

    Table  1.   Computational results of complexity of three algorithms

    算法 算法复杂度/flops
    CKF 20n3/3+10n2+10n2l+8nl2+2nl+l3+3l2+l
    强跟踪CKF 26n3/3+10n2+16n2l+10nl2-nl+l3+8l2+3l
    低复杂度自适应CKF 20n3/3+11n2+10n2l+8nl2+2nl+l3+3l2+3l+n
    下载: 导出CSV

    表  2  不同算法平均均方根误差对比

    Table  2.   Comparison of mean RMSE among different algorithms

    算法 平均RMSE/m
    x轴位置 y轴位置
    CKF 35.732 5 35.062 5
    强跟踪CKF 8.416 2 8.389 1
    低复杂度自适应CKF 8.405 5 8.384 5
    下载: 导出CSV

    表  3  不同算法运行时间对比

    Table  3.   Comparison of running time among different algorithms

    算法 平均运行时间/(10-2s) 运行时间增加百分比
    CKF 2.677 6 0
    强跟踪CKF 3.468 3 29.53
    低复杂度自适应CKF 2.712 1 1.29
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-11-17
  • 录用日期:  2021-01-15
  • 网络出版日期:  2022-04-20

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