Robust underwater multi-target direction-of-arrival tracking with uncertain measurement noise
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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。
Abstract:A robust direction-of-arrival (DOA) tracking method with uncertain measurement noise for underwater multiple acoustic targets is proposed based on the cardinalized probability hypothesis density (CPHD) filter and the Sage-Husa algorithm. Firstly, the varying of the DOA is modeled as Singer model. The DOA estimates provided by traditional DOA estimation methods and the estimation error are treated as measurement and measurement noise, respectively, to establish the measurement model. Based on this, the multi-target DOA tracking is performed based on the CPHD filter. In this step, the DOAs are predicted by using the tracking results at the previous time step and the varying model of the DOA, the predicted values are then modified through the measurement and measurement model to obtain the DOA tracking results. Finally, the modified Sage-Husa algorithm is used to estimate the variance of uncertain measurement noise adaptively in real time of tracking since the measurement noise variance is an important parameter to determine the tracking performance. In this manner, a robust underwater multi-target DOA tracking method is proposed. The experimental result shows that the proposed algorithm reduces the average optimal sub-patten assignment (OSPA) error of the measurements of DOAs from more than 10° to 2°, and the measurements of DOAs are significantly improved. The proposed robust underwater multi-target DOA tracking method improves the tracking performance in the scenario of uncertain measurement noise.
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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 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 
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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 (°) 3.56 3.80 4.05 PHD平均OSPA误差 (°) 6.62 7.55 7.73 CPHD平均OSPA误差 (°) 4.56 5.20 6.33 SH-CPHD平均OSPA误差 (°) 1.26 1.59 2.10
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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) 1.50 1.52 1.56 PHD平均运行时间 (ms) 0.44 0.42 0.44 CPHD平均运行时间 (ms) 0.68 0.66 0.65 SH-CPHD平均运行时间 (ms) 0.71 0.72 0.72
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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 (°) 1.25 1.43 1.98 平均运行时间 (ms) 0.66 0.67 0.66
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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-JPDA PHD CPHD SH-CPHD 平均OSPA误差 (°) 3.42 2.67 2.24 1.97 平均运行时间 (ms) 4.20 0.73 0.85 0.92
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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-JPDA PHD CPHD SH-CPHD 平均OSPA误差 (°) 4.26 4.22 3.71 2.06 平均运行时间 (ms) 4.25 0.72 0.86 0.90
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