A track-before-detect method for neighboring targets based on auxiliary particle filter in passive sonar scenarios
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摘要:
针对无源声呐多目标方位跟踪问题, 研究了一种基于粒子滤波的检测前跟踪方法, 关注于改善邻近目标和机动目标的跟踪性能。首先, 提出了一种考虑了邻近目标影响的似然函数; 其次, 采用辅助变量利用量测信息优化粒子采样, 当算法运动模型与目标实际运动状态失配时, 这种策略具有很大优势。结合以上两点, 提出了一种检测前跟踪算法, 该算法将邻近目标划分为一组, 使用邻近目标的预测状态计算目标的似然, 计算效率较高。利用仿真生成的数据和海上采集的实际数据分别验证了该算法的性能, 并与其他多目标粒子滤波检测前跟踪算法进行比较, 证明了该算法具有良好的跟踪性能。在目标邻近和目标机动的情况下, 该算法的优势更加明显。
Abstract:The problem of multiple target tracking based on particle filter in passive sonar is studied, which becomes more difficult when there are nearby targets and maneuvering targets in the observation space. First, a likelihood function considering the influence of neighboring targets is proposed. Second, the auxiliary variable is utilized to consider the measurement information in the particle sampling process. This strategy has great advantages when the actual motion of the target is mismatched with the dynamic model of the algorithm. Then, a track-before-detect algorithm is proposed, which divides the neighboring targets into a group and calculates the likelihood of the target by using the predicted states of the neighboring targets with high computational efficiency. The performance of the proposed algorithm is verified by simulation data and data collected at sea. Compared with other multi-target particle filter track-before-detect algorithms, the proposed algorithm has better tracking performance, especially in the presence of neighboring and maneuvering targets.
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Key words:
- Bearing-only tracking /
- Track-before-detect /
- Particle filter /
- Target tracking
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图 8 观测极坐标系下跟踪结果 (a) APP-TBD; (b) PP-TBD; (c) CE-TBD; (d) CEG-TBD; (e) FIT-TBD; (f) OGRAPF-TBD
图 11 观测极坐标系下跟踪结果 (a) APP-TBD; (b) PP-TBD; (c) CE-TBD; (d) CEG-TBD; (e) FIT-TBD; (f) OGRAPF-TBD
图 13 海上实测数据跟踪结果 (a) APP-TBD算法跟踪结果; (b) PP-TBD算法跟踪结果; (c) FIT-TBD算法跟踪结果; (d) CE-TBD算法跟踪结果; (e) CEG-TBD算法跟踪结果; (f) OGRAPF-TBD算法跟踪结果
表 1 仿真实验具体结果
目标 真实方位 (°) 预测方位 (°) 估计方位 (°) IP PP APF 1 165.1 163.6 163.8 164.9 165.0 2 162.2 162.9 162.8 162.6 162.5 
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表 2 APP-TBD算法流程
输入(${ {{z} }_1},{ {{z} }_2}, \cdots ,{ {{z} }_K}$), K为总帧数 输出(${ {{\hat x} }_1},{ {{\hat x} }_2}, \cdots ,{ {{\hat x} }_K}$) 1. 初始化粒子及其权值 2. 使用式(15)对目标进行分群, 将邻近目标划分为一个群组 3. $j = 1\thicksim r$, $r$表示目标数目, 循环: 4. $n = 1\thicksim {n_p}$, ${n_p}$表示粒子总数, 循环: 5. 采样辅助变量${{{\boldsymbol{u}}} }_{k,j}^n = f\left( { {{{\boldsymbol{x}}} }_{k - 1,j}^n,{{{\boldsymbol{w}}} }_{k - 1,j}^n} \right)$ 6. 计算辅助变量的一阶权值$p({ {{{\boldsymbol{z}}} }_k}|{{{\boldsymbol{u}}} }_{k,j}^n,\widehat C_{k|k - 1}^{g - \{ j\} })$ 7. 结束循环, 归一化一阶权值 8. 根据一阶权值筛选优质粒子的编号$ {a_{j,1}},{a_{j,2}}, \cdots ,{a_{j,{n_p}}} $ 9. $n = 1\thicksim{n_p}$,循环: 10. 回溯到$k - 1$时刻, 采样优质粒子状态${{{\boldsymbol{x}}} }_{k,j}^n = f\left( { {{{\boldsymbol{x}}} }_{k - 1,j}^{ {a_{j,n} } },{{{\boldsymbol{w}}} }_{k - 1,j}^n} \right)$ 11. 计算粒子的一阶权值$p({ {{{\boldsymbol{z}}} }_k}|{{{\boldsymbol{x}}} }_{k,j}^n,\widehat C_{k|k - 1}^{g - \{ j\} })$ 12. 结束循环, 归一化一阶权值 13. 若有效粒子数目小于$0.8{n_p}$, 则进行重采样 14. 结束循环 15. 使用式(22)计算粒子的权值 16. 使用式(35)估计目标状态；返回步骤2, 开始下一帧
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表 3 算法属性对比
算法 似然函数 考虑邻近
目标考虑量测
信息使用遗传
算子FIT-TBD FIT 否 否 否 CE-TBD CE 否 否 否 CEG-TBD CE 否 否 是 OGRAPF-TBD CE 否 否 是 PP-TBD PSF 是 否 否 APP-TBD PSF 是 是 否
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