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Adaptive PHD-BOF: A Slow-Moving Targets Tracking Method with Air Surveillance Radar
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摘要: 以旋翼无人机为代表的低空目标可采用慢速巡航模式，使自身回波落于雷达多普勒盲区内，以躲避雷达检测跟踪。此外，低空环境中存在的复杂地固杂波，更进一步加剧了雷达对慢速目标的检测跟踪任务难度。为解决上述问题，该文基于随机有限集框架，提出一种基于低空监视雷达的慢速目标跟踪方法。首先基于贝叶斯占用滤波思想，将雷达监视区域分割为沿角度-距离向的均匀网格，并依据慢速目标与地固杂波的动力学特性差异设计自适应滤波参数模块；之后，基于概率假设密度滤波器对多普勒盲区内的网格数据进行统一的滤波处理；最后，利用聚类方法从滤波结果中提取感兴趣目标的信息，实现对慢速目标的检测跟踪。在包含多个慢速目标、环境噪声、面杂波及地固点杂波的典型低空监视场景下，结合实测背景杂波数据的实验证明了所提算法对多个低空慢速目标跟踪的有效性、稳健性及性能优势。Abstract: Low-altitude targets, represented by rotor unmanned aerial vehicles, can typically adopt a slow-cruise mode. As a result, their echoes fall within the Doppler blind zone (DBZ) and evade radar detection and tracking. The cluttered low-altitude environment adds to further complexity. To address this issue, this study proposes a method grounded in the framework of random finite set and designed for tracking slow-moving targets with a low-altitude surveillance radar. Inspired by the Bayesian occupancy filter, the proposed method initially models the radar field of view (FoV) as a grid map. It is uniformly partitioned along the angle-range axis, ensuring that each cell captures a specific segment of the FoV. Then, adaptive filtering parameter modules are meticulously designed by leveraging the distinct dynamic characteristics of slow-moving targets and ground clutter. Subsequently, a probability hypothesis density filter is deployed to conduct unified filtering on the grid map situated within the DBZ. The final step involves the use of clustering methods to extract information about the target of interest. Simulation results validate the effectiveness, robustness, and superior performance of the proposed method across typical surveillance scenarios involving multiple slow-moving targets, noise, and clutter.
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图 10 不同算法滤波结果极坐标下表示(聚类处理后)
Figure 10. The filter results of different algorithms after cluster denoted by polar coordinate system
图 13 100次蒙特卡罗实验的OSPA平均误差(消融实验)
Figure 13. Average of OSPA errors in 100 Monte Carlo trials(ablation experiment)
图 14 100次蒙特卡罗实验的OSPA平均误差(不同SNR)
Figure 14. Average of OSPA errors in 100 Monte Carlo trials under different SNR
1 算法伪代码
1. Algorithm pseudo-code
自适应PHD-BOF预测步 $ {B_k} \leftarrow {Z_k} \cap \hat O_k^\neg $ for $n = 1$ to ${n_k}$ do for $j = 1$ to ${N_b}$ do $ {\boldsymbol{x}}_{k|k}^{n,j}{\text{～}}\mathcal{U}( \cdot |{S_{{l_n}}}) \cdot {f_0}({\boldsymbol{v}}) $ end for end for $ {v_{k + 1|k}} \leftarrow {v_{k|k}} + {N_b} \cdot {n_k} $ 步骤2. 计算存活概率 for $l = 1$ to L do if $l \in {\bar O_k}$then $ {p_S}(l) \leftarrow {\dot p_S} $ else $ {p_S}(l) \leftarrow {\tilde p_S} $ end if end for 步骤3. 计算${D_{k + 1|k}}({\boldsymbol{x}})$的权矢量 for $i = 1$ to ${v_{k + 1|k}}$ do if $i \le {v_{k|k}}$ then $ {\boldsymbol{x}}_{k + 1|k}^i \sim {f_{k + 1|k}}( \cdot |{\boldsymbol{x}}_{k|k}^i) $ $ \omega _k^i \leftarrow \omega _{k|k}^i $ else $ {\boldsymbol{x}}_{k + 1|k}^i \sim {f_{k + 1|k}}( \cdot |{\boldsymbol{x}}_{k|k}^{n,j}) $ $ \omega _k^i \leftarrow u/{N_b} $ end if $ \omega _{k + 1|k}^i \leftarrow {p_S}({l^i}) \cdot \omega _k^i $// $ {l^i} $为$ {\boldsymbol{x}}_{k|k}^i $的单元索引 end for 自适应PHD-BOF更新步 输入：$ {Z_{k + 1}},{O_C},\{ \omega _{k + 1|k}^i,{\boldsymbol{x}}_{k + 1|k}^i\} _{i = 1}^{{v_{k + 1|k}}} $ 输出：$ \{ \omega _{k + 1|k + 1}^i\} _{i = 1}^{{v_{k + 1|k}}} $ 步骤1. 计算$ {\tau _{k + 1}}({\boldsymbol{z}}) $ for $m = 1$ to ${m_{k + 1}}$ do if $m \in {O_C}$ then $ {p_D}(m) \leftarrow {\stackrel \frown{p} _D} $ else $ {p_D}(m) \leftarrow {\bar p_D} $ end if $\tau _{k + 1}^{{{\boldsymbol{z}}_m}} \leftarrow {p_D}(m) \cdot \omega _{k + 1|k}^{{{\boldsymbol{z}}_m}}$ // $ {{\boldsymbol{z}}_m} $为${Z_{k + 1}}$的第m个单元 end for for $i = 1$ to ${v_{k + 1|k}}$ do if $ h({\boldsymbol{x}}_{k + 1|k}^i) \in {S_{{Z_{k + 1}}}} $ then $ {{\boldsymbol{z}}_m} \leftarrow l:h({\boldsymbol{x}}_{k + 1|k}^i) \in {S_l} $ $ \tau _{k + 1}^{{{\boldsymbol{z}}_m}} \leftarrow \tau _{k + 1}^{{{\boldsymbol{z}}_m}} + {p_D}({\boldsymbol{x}}_{k + 1|k}^i) \cdot \omega _{k + 1|k}^i $ end if end for 步骤2. 计算权矢量${D_{k + 1|k + 1}}({\boldsymbol{x}})$ for $i = 1$ to ${v_{k + 1|k}}$ do 计算$ {L_{{Z_{k + 1}}}}({\boldsymbol{x}}_{k + 1|k}^i) $根据式(24) $ \omega _{k + 1|k + 1}^i \leftarrow \omega _{k + 1|k}^i \cdot {L_{{Z_{k + 1}}}}({\boldsymbol{x}}_{k + 1|k}^i) $ end for 
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表 1 滤波器参数设置
Table 1. Parameters of the filter
参数 数值 参数 数值 参数 数值 L 10000 ${\dot p_S}$ 0.01 $\alpha $ 2.5 d 2 ${\tilde p_S}$ 0.99 ${k_T}$ 0.05 ${N_b}$ 60 ${\stackrel \frown{p} _D}$ 0.1 $ {\stackrel \frown{\rho } _0} $ 0.01 ${N_{{\text{eff}}}}$ 1200 ${\bar p_D}$ 0.95 $ {\bar \rho _0} $ 0.3 u 0.001 ${\lambda _c}$ 0.1 ${\sigma _{\text{V}}}$ 0.1
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表 2 雷达系统参数
Table 2. Parameters of radar system
参数 数值 参数 数值 参数 数值 参数 数值 距离范围 $[{R_{\min }},{R_{\max }}]$ $ [300\; {\text{m}},1800 \;{\text{m}}] $ 距离分辨力$\Delta r$ 15 m 脉冲重复周期 20 μs 带宽B 10 MHz 角度范围 $[{\theta _{\min }},{\theta _{\max }}]$ [–60°, 60°] 角度分辨力$ \Delta \theta $ 1.2° 载频${f_0}$ 3 GHz 波长$\lambda $ 0.1 m 速度范围 $ [ - {v_{{m} {\text{dv}}}},{v_{{m} {\text{dv}}}}] $ $ [ - 4.5 \;{\text{m/s}},4.5 \;{\text{m/s}}] $ 信噪比 25 dB 脉冲数 500 CPI 0.01 s 距离单元数${N_r}$ 100 噪声标准差$ \sigma $ 1 采样快拍数 512 扫描时间${T_s}$ 1 s 方位单元数 ${N_\theta }$ 100 脉宽$\tau '$ 2 us 阵元数${N_a}$ 64 扫描帧数N 300
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表 3 对象状态真值
Table 3. Truth of object state
身份 初始状态 新生时刻 死亡时刻 T1 $ [ - 500,700,2,3] $ 1 250 T2 $ [ - 480,600, - 2,1] $ 1 300 T3 $ [300,600,2,2] $ 1 300 T4 $ [200,900,2,2] $ 1 300 C1 $[ - 350,550]$ 1 300 C2 $[ - 700,900]$ 1 300 C3 $ [0,1040] $ 1 300
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