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量测噪声不确定情况下的水下多目标稳健方位跟踪

张博轩 杨益新 侯翔昊

张博轩, 杨益新, 侯翔昊. 量测噪声不确定情况下的水下多目标稳健方位跟踪[J]. 声学学报, 2023, 48(4): 605-617. doi: 10.15949/j.cnki.0371-0025.2023.04.027
引用本文: 张博轩, 杨益新, 侯翔昊. 量测噪声不确定情况下的水下多目标稳健方位跟踪[J]. 声学学报, 2023, 48(4): 605-617. doi: 10.15949/j.cnki.0371-0025.2023.04.027
ZHANG Boxuan, YANG Yixin, HOU Xianghao. Robust underwater multi-target direction-of-arrival tracking with uncertain measurement noise[J]. ACTA ACUSTICA, 2023, 48(4): 605-617. doi: 10.15949/j.cnki.0371-0025.2023.04.027
Citation: ZHANG Boxuan, YANG Yixin, HOU Xianghao. Robust underwater multi-target direction-of-arrival tracking with uncertain measurement noise[J]. ACTA ACUSTICA, 2023, 48(4): 605-617. doi: 10.15949/j.cnki.0371-0025.2023.04.027

量测噪声不确定情况下的水下多目标稳健方位跟踪

doi: 10.15949/j.cnki.0371-0025.2023.04.027
基金项目: 国家自然科学基金项目(12104113)、特色学科基础研究项目(G2022WD0235)和中央高校基本科研业务费专项资金资助
详细信息
    通讯作者:

    杨益新, yxyang@nwpu.edu.cn

  • PACS: 43.30, 43.60

Robust underwater multi-target direction-of-arrival tracking with uncertain measurement noise

  • 摘要:

    提出了使用Sage-Husa算法估计量测噪声的集势化概率假设密度(CPHD)滤波方位跟踪方法, 实现了量测噪声不确定情况下多水下声学目标的稳健方位跟踪。首先, 将水下目标方位的变化建模为Singer模型, 利用传统目标方位估计方法的结果作为量测值, 将方位估计误差看作量测噪声, 建立了方位量测模型。然后, 给出了CPHD滤波水下多目标方位跟踪算法, 该算法利用上一时刻的方位跟踪结果和目标方位变化模型预测目标方位, 并利用量测值和量测模型对预测值进行更新得到方位跟踪结果。最后, 考虑到量测噪声方差为决定跟踪性能的重要参数, 利用改进的Sage-Husa算法在跟踪过程中实时自适应地估计不确定量测噪声的方差, 从而实现了多目标的稳健方位跟踪。经海试数据验证, 所提出算法将目标方位测量的平均最优子模式分配(OSPA)误差从10°以上降低至2°, 显著提高了方位测量精度。所提水下多目标稳健方位跟踪方法能够有效提高量测噪声不确定情况下的方位跟踪性能。

     

  • 图 1  仿真目标方位轨迹和量测值

    图 2  箱线图标记示意图

    图 3  目标方位跟踪结果 (a) KF-JPDA; (b) PHD滤波; (c) CPHD滤波; (d) SH-CPHD滤波

    图 4  KF-JPDA, PHD滤波, CPHD滤波和SH-CPHD滤波蒙特卡洛实验结果OSPA误差箱线图 (a) ${\sigma _r} = 2.5^\circ $; (b) ${\sigma _r} = 5^\circ $; (c) ${\sigma _r} = 10^\circ $

    图 5  SH-PHD滤波蒙特卡洛实验结果OSPA误差箱线图 (a) $ \delta = 2.5^\circ $; (b) $ \delta = 5^\circ $; (c) $ \delta = 10^\circ $

    图 6  水平线列阵真实布放位置

    图 7  海上实验目标方位量测、跟踪结果和OSPA误差 (a) 目标方位量测; (b) KF-JPDA跟踪结果; (c) PHD滤波跟踪结果; (d) CPHD滤波跟踪结果; (e) SH-CPHD滤波跟踪结果; (f) OSPA误差

    图 8  海上实验添加噪声后目标方位量测、跟踪结果和OSPA误差 (a) 目标方位量测; (b) KF-JPDA跟踪结果; (c) PHD滤波跟踪结果; (d) CPHD滤波跟踪结果; (e) SH-CPHD滤波跟踪结果; (f) OSPA误差

    1. 初始化GM模型分量和集势分布$\{ w_0^{\left( i \right)},{\boldsymbol{m}}_0^{\left( i \right)},{\boldsymbol{P}}_0^{\left( i \right)}\} _{i = 1}^{{J_0}}$和${p_0}\left( n \right)$; for $ k = 1:K $预测: 2. 根据式(8)计算预测集势分布$ {p_{k|k - 1}}\left( n \right) $; 3. 计算存活目标分量:  for $ i = 1:{J_{k - 1}} $  $ w_{s,k|k - 1}^{\left( i \right)} = {p_{s,k}}w_{k - 1}^{\left( i \right)} $, ${\boldsymbol{m}}_{s,k|k - 1}^{\left( i \right)}{\text{ = }}{{\boldsymbol{F}}_{k - 1}}{\boldsymbol{m}}_{k - 1}^{\left( i \right)}$,   $ {\boldsymbol{P}}_{s,k|k - 1}^{\left( i \right)} = {{\boldsymbol{G}}_k}\boldsymbol{Q}_k{\boldsymbol{G}}_k^{\text{T}} + {{\boldsymbol{F}}_{k - 1}}{\boldsymbol{P}}_{k - 1}^{\left( i \right)}{\boldsymbol{F}}_{k - 1}^{\text{T}} $;  end4. 添加新生目标分量$\left\{ w_{\gamma ,k}^{\left( i \right)},{\boldsymbol{m}}_{\gamma ,k}^{\left( i \right)},{\boldsymbol{P}}_{\gamma ,k}^{\left( i \right)}\right\} _{i = {J_{k - 1}} + 1}^{i = {J_{k - 1}} + {J_{\gamma ,k}}}$; 5. ${J_{k|k - 1}} = {J_{k - 1}} + {J_{\gamma ,k}}$, 将预测分量表示为$\left\{ w_{k|k - 1}^{\left( i \right)},{\boldsymbol{m}}_{k|k - 1}^{\left( i \right)}, {\boldsymbol{P}}_{k|k - 1}^{\left( i \right)}\right\} _{i = 1}^{i = {J_{k|k - 1}}}$; 更新: 6. 根据式(15)计算更新集势分布$ {p_k}\left( n \right) $; 7. 更新目标分量:   for $ i = 1:{J_{k|k - 1}} $    $w_k^{\left( i \right)} = \dfrac{{\left\langle {\varPsi _k^1\left[ {{{\boldsymbol{w}}_{k|k - 1}},{{\boldsymbol{Z}}_k}} \right],{p_{k|k - 1}}} \right\rangle }}{{\left\langle {\varPsi _k^0\left[ {{{\boldsymbol{w}}_{k|k - 1}},{{\boldsymbol{Z}}_k}} \right],{p_{k|k - 1}}} \right\rangle }}\left( {1 - {p_{D,k}}} \right)w_{k - 1}^{\left( i \right)}$,     ${\boldsymbol{m}}_k^{\left( i \right)} = {\boldsymbol{m}}_{k|k - 1}^{\left( i \right)}$, ${\boldsymbol{P}}_k^{\left( i \right)} = {\boldsymbol{P}}_{k|k - 1}^{\left( i \right)}$;   end
      for $ m = 1:{m_k} $    for $ i = 1:{J_{k|k - 1}} $    8. 利用式(29)给出的Sage-Husa算法估计量测噪声方差$ \widehat \sigma _{r,k}^2 $;      $ {\boldsymbol{S}}_{k|k - 1}^{\left( i \right)} = {{\boldsymbol{H}}_k}{\boldsymbol{P}}_{k|k - 1}^{\left( i \right)}{\boldsymbol{H}}_k^{\text{T}} + \widehat \sigma _{r,k}^2 $, ${\boldsymbol{K}}_k^{\left( i \right)} = {\boldsymbol{P}}_{k|k - 1}^{\left( i \right)}{\boldsymbol{H}}_k^{\text{T}}{\left[ {{\boldsymbol{S}}_{k|k - 1}^{\left( i \right)}} \right]^{{{ - }}1}}$,     $ w_k^{\left( {{J_{k|k - 1}} + (m - 1){m_k} + i} \right)} = {p_{D,k}}w_{k|k - 1}^{\left( i \right)}q_k^{\left( i \right)}\left( {{{{z}}_m}} \right) $,     $ \dfrac{{\left\langle {\varPsi _k^1\left[ {{w_{k|k - 1}},{{\boldsymbol{Z}}_k}\backslash \left\{ {{{{z}}_m}} \right\}} \right],{p_{k|k - 1}}} \right\rangle }}{{\left\langle {\varPsi _k^0\left[ {{w_{k|k - 1}},{{\boldsymbol{Z}}_k}} \right],{p_{k|k - 1}}} \right\rangle }} \dfrac{{\left\langle {1,{\kappa _k}} \right\rangle }}{{{\kappa _k}\left( {{{{z}}_m}} \right)}} $      ${\boldsymbol{m}}_k^{\left( {{J_{k|k - 1}} + (m - 1){m_k} + i} \right)} = {\boldsymbol{m}}_{k|k - 1}^{\left( i \right)} + {\boldsymbol{K}}_k^{\left( i \right)}\left( {{{\textit{z}}_m} - {\boldsymbol{\eta }}_{k|k - 1}^{\left( i \right)}} \right)$,      ${\boldsymbol{P}}_k^{\left( {{J_{k|k - 1}} + (m - 1){m_k} + i} \right)} = \left[ {{\boldsymbol{I}} - {\boldsymbol{K}}_k^{\left( i \right)}{{\boldsymbol{H}}_k}} \right]{\boldsymbol{P}}_{k|k - 1}^{\left( i \right)}$;     end  end9. $ {J_{k|k}} = {J_{k|k - 1}} + {J_{k|k - 1}}{m_k} $, 对$ {J_{k|k}} $个分量进行修剪, 合并和限制, 得到新的$ {J_k} $个分量; 10. 将更新后的分量表示为$\{ w_k^{\left( i \right)},{\boldsymbol{m}}_k^{\left( i \right)},{\boldsymbol{P}}_k^{\left( i \right)}\} _{i = 1}^{i = {J_k}}$; 11. 目标数估计$ {\widehat N_k} $为$ {p_k}\left( n \right) $最大值对应的n; 12. 目标状态估计为权值最大的$ {\widehat N_k} $个分量对应的${\boldsymbol{m}}_k^{\left( i \right)}$。end
    下载: 导出CSV

    表  1  噪声方差增大时间段KF-JPDA, PHD滤波, CPHD滤波和SH-CPHD滤波的平均OSPA误差

    ${\sigma _r} = 2.5^\circ $${\sigma _r} = 5^\circ $${\sigma _r} = 10^\circ $
    KF-JPDA平均OSPA误差 (°)3.563.804.05
    PHD平均OSPA误差 (°)6.627.557.73
    CPHD平均OSPA误差 (°)4.565.206.33
    SH-CPHD平均OSPA误差 (°)1.261.592.10
    下载: 导出CSV

    表  2  KF-JPDA、PHD滤波、CPHD滤波和SH-CPHD滤波每一时间步的平均运行时间

    ${\sigma _r} = 2.5^\circ $${\sigma _r} = 5^\circ $${\sigma _r} = 10^\circ $
    KF-JPDA平均运行时间 (ms)1.501.521.56
    PHD平均运行时间 (ms)0.440.420.44
    CPHD平均运行时间 (ms)0.680.660.65
    SH-CPHD平均运行时间 (ms)0.710.720.72
    下载: 导出CSV

    表  3  噪声方差增大时间段SH-PHD滤波的平均OSPA误差

    $\delta = 2.5^\circ $$\delta = 5^\circ $$\delta = 10^\circ $
    平均OSPA误差 (°)1.251.431.98
    平均运行时间 (ms)0.660.670.66
    下载: 导出CSV

    表  4  海上实验目标方位跟踪结果每一时间步的平均OSPA误差和平均运行时间

    KF-JPDAPHDCPHDSH-CPHD
    平均OSPA误差 (°)3.422.672.241.97
    平均运行时间 (ms)4.200.730.850.92
    下载: 导出CSV

    表  5  海上实验添加噪声后每一时间步的平均OSPA误差和平均运行时间

    KF-JPDAPHDCPHDSH-CPHD
    平均OSPA误差 (°)4.264.223.712.06
    平均运行时间 (ms)4.250.720.860.90
    下载: 导出CSV
  • [1] Yan H, Fan H H. Signal-selective DOA tracking for wideband cyclostationary sources. IEEE Trans. Signal Process., 2007; 55(5): 2007—2015 doi: 10.1109/TSP.2007.893204
    [2] Chen W, Zhang W, Wu Y, et al. Joint algorithm based on interference suppression and Kalman filter for bearing-only weak target robust tracking. IEEE Access, 2019; 7: 131653—131662 doi: 10.1109/ACCESS.2019.2940956
    [3] Kong D, Chun J. A fast DOA tracking algorithm based on the extended Kalman filter. IEEE 2000 National Aerospace and Electronics Conference, Dayton, USA, 2000: 235—238
    [4] Zhang B, Hou X, Yang Y. Robust underwater direction-of-arrival tracking with uncertain environmental disturbances using a uniform circular hydrophone array. J. Acoust. Soc. Am., 2022; 151(6): 4101—4113 doi: 10.1121/10.0011730
    [5] Orton M, Fitzgerald W. A Bayesian approach to tracking multiple targets using sensor arrays and particle filters. IEEE Trans. Signal Process., 2002; 50(2): 216—223 doi: 10.1109/78.978377
    [6] Saucan A A, Chonavel T, Sintes C, et al. CPHD-DOA tracking of multiple extended sonar targets in impulsive environments. IEEE Trans. Signal Process., 2016; 64(5): 1147—1160 doi: 10.1109/TSP.2015.2504349
    [7] Masnadi-Shirazi A, Rao B D. A covariance-based superpositional CPHD filter for multisource DOA tracking. IEEE Trans. Signal Process., 2018; 66(2): 309—323 doi: 10.1109/TSP.2017.2768025
    [8] Zhao J, Gui R, Dong X. A new measurement association mapping strategy for DOA tracking. Digit. Signal Process., 2021; 118: 103228 doi: 10.1016/j.dsp.2021.103228
    [9] Yardim C, Michalopoulou Z H, Gerstoft P. An overview of sequential Bayesian filtering in ocean acoustics. IEEE J. Ocean. Eng., 2011; 36(1): 71—89 doi: 10.1109/JOE.2010.2098810
    [10] 郭鑫, 葛凤翔, 郭良浩. 改进的自适应Kalman滤波及其在水声机动目标跟踪中的应用. 声学学报, 2011; 36(6): 611—618 doi: 10.15949/j.cnki.0371-0025.2011.06.002
    [11] 孙旭, 李然威, 胡鹏. 目标机动未知下的有源声呐跟踪滤波方法. 声学学报, 2016; 41(3): 371—378 doi: 10.15949/j.cnki.0371-0025.2016.03.012
    [12] 胡友峰, 孙进才. 水下无源目标运动分析的修正扩展卡尔曼滤波方法. 声学学报, 2002; 27(5): 449—454 doi: 10.3321/j.issn:0371-0025.2002.05.013
    [13] Koteswara Rao S, Raja Rajeswari K, Lingamurty K S. Unscented Kalman filter with application to bearings-only target tracking. IETE J. Res., 2009; 55(2): 63—67 doi: 10.4103/0377-2063.53236
    [14] 王平波, 刘杨. 基于改进自适应IMM-UKF算法的水下目标跟踪. 电子与信息学报, 2022; 44(6): 1999—2005 doi: 10.11999/JEIT211128
    [15] Leong P H, Arulampalam S, Lamahewa T A, et al. A Gaussian-sum based cubature Kalman filter for bearings-only tracking. IEEE Trans. Aerosp. Electron. Syst., 2013; 49(2): 1161—1176 doi: 10.1109/TAES.2013.6494405
    [16] 石桂欣, 鄢社锋, 郝程鹏, 等. 不完全量测下长基线系统的水下目标跟踪算法. 声学学报, 2019; 44(4): 480—490 doi: 10.15949/j.cnki.0371-0025.2019.04.009
    [17] 金盛龙, 李宇, 黄海宁. 水下多目标方位的联合检测与跟踪. 声学学报, 2019; 44(4): 503—512 doi: 10.15949/j.cnki.0371-0025.2019.04.011
    [18] Sage A P, Husa G W. Adaptive filtering with unknown prior statistics. Joint Automatic Control Conference, IEEE, Boulder, USA, 1969: 760—769
    [19] Li X, Willett P, Baum M, et al. PMHT approach for underwater bearing-only multisensory-multitarget tracking in clutter. IEEE J. Oceanic Eng., 2016; 41(4): 831—839 doi: 10.1109/JOE.2015.2506220
    [20] 谢志华, 蒋丞, 吴俊超, 等. 水下目标多平台协同定位和跟踪方法. 声学学报, 2021; 46(6): 1028—1038 doi: 10.15949/j.cnki.0371-0025.2021.06.022
    [21] 李晓花, 李亚安, 鲁晓锋, 等. 强干扰环境下水下纯方位PMHT多目标跟踪. 西北工业大学学报, 2020; 38(2): 359—365 doi: 10.3969/j.issn.1000-2758.2020.02.017
    [22] 杨峰, 王永齐, 梁彦, 等. 基于概率假设密度滤波方法的多目标跟踪技术综述. 自动化学报, 2013; 39(11): 1944—1956 doi: 10.3724/SP.J.1004.2013.01944
    [23] Mahler R P S. Multitarget Bayes filtering via first-order multitarget moments. IEEE Trans. Aerosp. Electron. Syst., 2003; 39(4): 1152—1178 doi: 10.1109/TAES.2003.1261119
    [24] Clark D E, Panta K, Vo B N. The GM-PHD filter multiple target tracker. 9th International Conference on Information Fusion, Florence, Italy, 2006: 1–8
    [25] Vo B N, Singh S, Doucet A. Sequential Monte Carlo methods for multitarget filtering with random finite sets. IEEE Trans. Aerosp. Electron. Syst., 2005; 41(4): 1224—1245 doi: 10.1109/TAES.2005.1561884
    [26] Mahler R. PHD filters of higher order in target number. IEEE Trans. Aerosp. Electron. Syst., 2007; 43(4): 1523—1543 doi: 10.1109/TAES.2007.4441756
    [27] Vo B T, Vo B N, Cantoni A. Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Trans. Signal Proces., 2007; 55(7): 3553—3567 doi: 10.1109/TSP.2007.894241
    [28] 刘伯胜, 黄益旺, 陈文剑, 等. 水声学原理. 第3版. 哈尔滨: 哈尔滨工程大学出版社, 2010: 268—272
    [29] 韩崇昭, 朱洪艳, 段战胜, 等. 多源信息融合. 第2版. 北京: 清华大学出版社. 2010: 327—332
    [30] Song Y, Hu Z, Li T, et al. Performance evaluation metrics and approaches for target tracking: a survey. Sensors, 2022; 22(3): 793 doi: 10.3390/s22030793
    [31] Booth N O, Hodgkiss W S, Ensberg D E. SWellEx-96 experiment acoustic data. UC San Diego Library Digital Collections, 2015
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出版历程
  • 收稿日期:  2022-09-06
  • 修回日期:  2022-12-12
  • 网络出版日期:  2023-07-13
  • 刊出日期:  2023-07-11

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