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EKF和UKF在双观测站纯方位目标跟踪中的应用

成春彦 李亚安

成春彦, 李亚安. EKF和UKF在双观测站纯方位目标跟踪中的应用[J]. 水下无人系统学报, xxxx, x(x): x-xx doi: 10.11993/j.issn.2096-3920.202203014
引用本文: 成春彦, 李亚安. EKF和UKF在双观测站纯方位目标跟踪中的应用[J]. 水下无人系统学报, xxxx, x(x): x-xx doi: 10.11993/j.issn.2096-3920.202203014
CHENG Chun-yan, LI Ya-an. Applications of EKF and UKF Algorithms in Bearings-only Target Tracking of Double Observation Stations[J]. Journal of Unmanned Undersea Systems. doi: 10.11993/j.issn.2096-3920.202203014
Citation: CHENG Chun-yan, LI Ya-an. Applications of EKF and UKF Algorithms in Bearings-only Target Tracking of Double Observation Stations[J]. Journal of Unmanned Undersea Systems. doi: 10.11993/j.issn.2096-3920.202203014

EKF和UKF在双观测站纯方位目标跟踪中的应用

doi: 10.11993/j.issn.2096-3920.202203014
基金项目: 国家自然科学基金项目资助(11874302).
详细信息
    作者简介:

    成春彦(1996-), 男, 在读硕士, 主要研究方向为水下目标跟踪

  • 中图分类号: TJ630.1; U764.7; TB566

Applications of EKF and UKF Algorithms in Bearings-only Target Tracking of Double Observation Stations

  • 摘要: 为了对水下运动目标进行实时跟踪, 以静止双观测站纯方位跟踪系统为研究对象, 分别结合扩展卡尔曼滤波(EKF)算法和无迹卡尔曼滤波(UKF)算法的原理, 对基于EKF和UKF算法的双观测站纯方位跟踪系统进行了仿真分析及比较。结果表明, 基于2种算法的双观测站纯方位系统都能适用于水下运动目标实时跟踪, 但后者具有更快的收敛速度和更好的鲁棒性。同时, 分别分析了双站距离以及方位角量测误差对实时跟踪效果的影响, 仿真结果表明, 2个观测站距离过近或者过远都会降低目标跟踪的效果, 基于EKF和UKF算法的双观测站系统在两站距离800 m时分别能够得到更加满意的跟踪效果; 随着方位角量测误差的增大, 基于2种算法的双观测站系统的跟踪性能都会下降, 但UKF算法在EKF算法跟踪失效时仍然具有较好的跟踪性能。

     

  • 图  1  目标-观测站几何态势

    Figure  1.  Geometrical situation between target and observation stations

    图  2  R = 1°时EKF和UKF的目标跟踪航迹图

    Figure  2.  Target tracking trajectory of EKF and UKF with R = 1°

    图  3  R = 1°时EKF和UKF在xy方向目标位置的RMSE

    Figure  3.  RMSE of position in x and y directions of EKF and UKF with R = 1°

    图  4  R = 1°时EKF和UKF在xy方向目标速度的RMSE

    Figure  4.  RMSE of velocity in x and y directions of EKF and UKF with R = 1°

    图  5  EKF的位置均方根误差平均值折线图

    Figure  5.  Average of the positional RMSE with EKF

    图  6  EKF的速度均方根误差平均值折线图

    Figure  6.  Average of RMSE about velocity with EKF

    图  7  UKF的位置均方根误差平均值折线图

    Figure  7.  Average of the positional RMSE with UKF

    图  8  UKF的速度均方根误差平均值折线图

    Figure  8.  Average of RMSE about velocity with UKF

    图  9  R = 4°时EKF、UKF算法的目标跟踪航迹

    Figure  9.  Target tracking trajectory of EKF and UKF with R = 4°

    图  10  R = 4°时EKF、UKF算法的位置和速度RMSE

    Figure  10.  Position and Velocity RMSE of EKF and UKF with R = 4°

    图  11  EKF和UKF在不同方位角量测误差时的位置平均RMSE

    Figure  11.  Positional average RMSE of EKF and UKF with different bearing measurement error

    图  12  R = 8°时EKF、UKF算法的目标跟踪航迹

    Figure  12.  Target tracking trajectory of EKF and UKF with R = 8°

    图  13  R = 8°时EKF、UKF算法的位置和速度RMSE

    Figure  13.  RMSE about position and velocity of EKF and UKF with R = 8°

    表  1  EKF的位置均方根误差平均值

    Table  1.   Average of the positional RMSE with EKF

    两站距离/
    m
    x方向位置平均RMSE/my方向位置平均RMSE/m位置平均
    RMSE/m
    10041.3514.3443.78
    20035.9617.4240.00
    30031.9117.4336.40
    40028.2216.0532.51
    50026.4116.7631.29
    60025.7916.1130.41
    70020.5817.2426.85
    80019.6815.5025.05
    90018.5417.7525.71
    1 00020.5819.4428.32
    1 10019.4217.7026.29
    1 20022.5718.7929.37
    1 30030.2921.7337.28
    1 40033.9022.4540.66
    1 50033.5120.6439.36
    下载: 导出CSV

    表  2  EKF的速度均方根误差平均值

    Table  2.   Average of RMSE about velocity with EKF

    两站距离/
    m
    x方向速度平均RMSE/(m·s−1)y方向速度平均RMSE/(m·s−1)速度平均
    RMSE/(m·s−1)
    1000.119 30.247 60.274 9
    2000.142 20.259 40.295 8
    3000.150 80.256 20.297 3
    4000.151 50.247 70.290 4
    5000.161 50.238 40.288 0
    6000.161 90.225 00.277 3
    7000.179 50.229 40.291 3
    8000.180 30.207 40.274 8
    9000.200 80.213 50.293 1
    1 0000.215 50.212 90.303 0
    1 1000.215 80.189 20.287 1
    1 2000.230 60.182 20.291 3
    1 3000.252 10.198 80.321 0
    1 4000.261 80.195 40.326 7
    1 5000.261 60.172 50.313 5
    下载: 导出CSV

    表  3  UKF的位置均方根误差平均值

    Table  3.   Average of the positional RMSE with UKF

    两站距离/mx方向位置平均RMSE/my方向位置平均RMSE/m位置平均RMSE/m
    10032.4310.4134.06
    20031.0510.4932.81
    30028.8811.7831.29
    40026.3011.9628.89
    50026.2212.0828.90
    60019.8512.3223.37
    70020.6213.0224.40
    80018.2712.4722.11
    90018.3212.9822.45
    100020.7814.0425.10
    110021.4714.3225.81
    120023.7815.7528.52
    130031.2716.7835.50
    140032.4218.5637.36
    150033.7319.1938.81
    下载: 导出CSV

    表  4  UKF的速度均方根误差平均值

    Table  4.   Average of RMSE about velocity with UKF

    两站距离/mx方向速度平均RMSE/(m·s−1)y方向速度平均RMSE/(m·s−1)速度平均
    RMSE/(m·s−1)
    1000.160 60.205 60.260 9
    2000.167 90.208 00.275 6
    3000.169 00.204 10.276 3
    4000.151 10.228 90.274 3
    5000.165 80.223 50.278 3
    6000.175 30.222 70.283 5
    7000.186 90.222 40.281 3
    8000.173 00.207 10.269 9
    9000.193 00.200 90.278 5
    10000.212 70.203 20.294 3
    11000.229 50.197 10.302 7
    12000.230 30.184 20.295 2
    13000.251 10.178 20.308 1
    14000.260 70.192 70.324 2
    15000.260 40.151 90.301 5
    下载: 导出CSV

    表  5  EKF在不同方位角量测误差时的位置平均RMSE

    Table  5.   Average of RMSE about position with different bearing measurement error in EKF

    R/(°)x方向位置平均RMSE/my方向位置平均RMSE/m位置平均
    RMSE/m
    120.0516.9326.26
    238.0529.0547.95
    360.6440.2072.84
    471.3047.1585.48
    578.0756.5396.39
    692.7866.90114.50
    7116.6778.82140.97
    8131.0786.97157.40
    9137.3099.63170.10
    10139.63108.20176.64
    下载: 导出CSV

    表  6  EKF在不同方位角量测误差时的速度平均RMSE

    Table  6.   Average of RMSE about velocity with different bearing measurement error in EKF

    R/(°)x方向速度平均RMSE/(m·s−1)y方向速度平均RMSE/(m·s−1)速度平均
    RMSE/(m·s−1)
    10.187 00.219 60.287 5
    20.200 70.309 00.368 2
    30.211 10.348 50.408 0
    40.212 40.36850.425 3
    50.242 60.402 50.470 0
    60.262 50.413 60.490 2
    70.290 80.414 50.506 7
    80.297 70.421 70.516 2
    90.335 00.490 00.594 2
    100.336 80.512 30.613 1
    下载: 导出CSV

    表  7  UKF在不同方位角量测误差时的位置平均RMSE

    Table  7.   Average of RMSE about position with different bearing measurement error in UKF

    R/(°)x方向位置平均RMSE/my方向位置平均RMSE/m位置平均RMSE/m
    118.4812.6722.41
    235.3519.9740.62
    342.8029.5551.78
    455.6535.2465.87
    561.4441.8774.35
    665.6046.4780.39
    768.4256.4888.72
    873.6959.4294.67
    987.0764.40108.30
    1093.4771.74117.83
    下载: 导出CSV

    表  8  UKF在不同方位角量测误差时的速度平均RMSE

    Table  8.   Average of RMSE about velocity with different bearing measurement error in UKF

    R/(°)x方向速度平均RMSE/(m·s−1)y方向速度平均RMSE/(m·s−1)速度平均
    RMSE/(m·s−1)
    10.172 50.203 30.266 6
    20.180 50.226 60.289 7
    30.216 80.236 70.321 0
    40.200 80.226 50.302 7
    50.204 70.240 20.315 6
    60.196 70.261 20.327 2
    70.205 50.269 90.339 6
    80.231 90.268 50.354 6
    90.258 30.304 20.402 2
    100.263 10.329 10.421 7
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-28
  • 修回日期:  2022-05-24
  • 网络出版日期:  2022-07-25

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