Motion Parameter Estimation Combined Smoothing Filter Algorithm Based on Gaussian Mixture Probability Hypothesis Density
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摘要: 针对高斯混合概率假设密度(GM-PHD)滤波器在目标速度未知或不准确时，目标状态估计性能较差，该文提出一种基于GM-PHD的运动参数估计组合平滑滤波算法。该算法通过目标状态提取速度信息，经过中值平滑和线性平滑组合处理提升速度估计准确性，然后将速度反馈给GM-PHD滤波器的状态转移方程，提高状态预测精度。仿真结果表明，目标速度未知或不准确时，所提算法能够明显改善GM-PHD滤波器状态估计性能。
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关键词:
- 目标跟踪 /
- 高斯混合概率假设密度滤波 /
- 参数估计 /
- 组合平滑
Abstract: Considering poor performance of target state estimation for Gaussian Mixture Probability Hypothesis Density(GM-PHD) filter when the target velocity is unknown or inaccurate, a combined smoothing filtering algorithm for motion parameter estimation based on GM-PHD is proposed. The velocity information is extracted from the target state, and the accuracy of velocity estimation is improved through the combined processing of median smoothing and linear smoothing. Then, the velocity is fed back to the state transition equation of the GM-PHD filter to improve the accuracy of state prediction. Simulation results show that the proposed algorithm can significantly improve the state estimation performance of GM-PHD filter when the target velocity is unknown or inaccurate. -
表 1 基于GM-PHD滤波器运动参数估计组合平滑算法
初始化$\tilde {\boldsymbol{v}} = \left[ {0,0,0,0} \right]$，$\Delta \tilde {\boldsymbol{v}} = \left[ {0,0,0,0} \right]$； 步骤1 由$\left\{ {w_{k - 1}^{\left( i \right)},{\boldsymbol{m}}_{k - 1}^{\left( i \right)},{\boldsymbol{p}}_{k - 1}^{\left( i \right)}} \right\}$进行GM-PHD滤波得到
$\left\{ {w_k^{\left( i \right)},{\boldsymbol{m}}_k^{\left( i \right)},{\boldsymbol{p}}_k^{\left( i \right)}} \right\}$；步骤2 从${\boldsymbol{m}}_{k - 1}^{\left( i \right)}$及${\boldsymbol{m}}_k^{\left( i \right)}$中获取$\left[ {x_{k - 1}^{\left( i \right)},y_{k - 1}^{\left( i \right)},z_{k - 1}^{\left( i \right)}} \right]$及
$\left[ {x_k^{\left( i \right)},y_k^{\left( i \right)},z_k^{\left( i \right)}} \right]$；步骤3 速度初步获取：根据式(14)～式(16)得到$\tilde{\dot{x}}_{k}^{\left( i \right)},\tilde{\dot{y}}_{k}^{\left( i \right)},\tilde{\dot{z}}_{k}^{\left( i \right)}$
后，送入组合平滑滤波器；步骤4 组合平滑处理：获得中值输出${{\boldsymbol{l}}_v}\left( k \right)$，再根据式(17)获得
$\bar {\boldsymbol{v}}_k^{\left( i \right)}$；步骤5 误差反馈：根据式(18)计算差值$\Delta \tilde {\boldsymbol{v}}_k^{\left( i \right)}$，经过中值滤波输
出${{\boldsymbol{l}}_{\Delta v}}\left( k \right)$，进行线性平滑输出$\Delta \bar {\boldsymbol{v}}_k^{\left( i \right)}$；步骤6 根据式(19)计算平滑滤波器的输出$\hat {\boldsymbol{v}}_k^{\left( i \right)}$； 步骤7 根据式(20)和式(21)更新$\tilde {\boldsymbol{m}}_k^{\left( i \right)}$和$\left\{ {w_k^{\left( i \right)},\tilde {\boldsymbol{m}}_k^{\left( i \right)},{\boldsymbol{p}}_k^{\left( i \right)}} \right\}$； 步骤8 下一时刻，重复步骤2～8。 
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表 2 实验参数设置
仿真参数 值 迭代时间间隔${{\mathit{\Delta}} _k}\left( s \right)$ 0.1 目标新生概率${p_{b,k}}$ 0.1 目标检测概率${p_{D,k}}$ 0.98 目标存活概率${p_{S,k}}$ 0.99 剪枝阈值$T$ 4 合并阈值$U$ 0.5 最大高斯分量数目${J_{\rm{max}}}$ 100 蒙特卡罗次数 100 杂波数$lc$ 20 过程噪声协方差${{\boldsymbol{Q}}_k}$ $1{0^{ - 2}}{{\boldsymbol{I}}_6}$
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表 3 不同过程噪声下算法的平均OSPA距离
过程噪声(q) 0.005 0.01 0.050 0.100 0.500 速度未知GM-PHD 15.0502 14.4323 15.1557 15.1504 16.8850 (平滑前)本文算法 11.0243 7.0980 4.8090 5.0435 7.9587 (无差值补偿)本文算法 10.9665 7.1931 4.9964 5.0335 7.8285 (组合平滑)本文算法 10.7054 6.9934 4.7873 4.9872 7.5573 速度已知GM-PHD 10.9928 7.2449 5.0565 4.9300 7.9385
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