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摘要: 针对基于概率假设密度算法（Probability hypothesis density，PHD）的非线性多目标跟踪精度低、滤波发散等问题，提出了一种新的PHD算法——改进的均方根嵌入式容积粒子PHD算法（Advanced square-root imbedded cubature particle PHD，ASRICP-PHD）.新的算法在初始化采样时将整个采样区域等概率划分为若干个区域，然后利用既定的准则从每个区域抽取粒子，并利用均方根嵌入式容积滤波方法对每个粒子进行滤波，来拟合重要密度函数，预测和更新多目标状态的PHD.仿真结果表明该算法能对多目标进行有效跟踪，相比拟随机采样法和伪随机采样，等概率采样的方法在多目标位置估计和数目估计上有更高的精度.
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关键词:
- 多目标跟踪 /
- 概率假设密度 /
- 均方根嵌入式容积滤波 /
- 等概率采样
Abstract: Considering the low accuracy, filter divergence and other problems of nonlinear multi-target tracking based on probability hypothesis density (PHD), a new filter named advanced square-root imbedded cubature particle PHD (ASRICP-PHD) is proposed. ASRICP-PHD divides the whole particle sampling area into several parts of equal probability, then uses a special rule to obtain particles from each part, and matches the important density function with square-root imbedded cubature particle filter, and therefore predicts and updates PHD. Simulation shows that ASRICP-PHD is able to track multiple targets effectively. Moreover, compared with quasi random sampling, the method of particle sampling based on probability has higher accuracy in terms of multi-target positions and number's estimations.1) 本文责任编委 赖剑煌 -
图 3 目标数目估计比较( $q = 0.1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 3 Comparison of number estimation ( $q = 0.1,{\lambda _k} = 5; {\rm CV}$
图 4 OSPA比较( $q = 0.1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 4 Comparison of OSPA ( $q = 0.1,{\lambda _k} = 5; {\rm CV}$
图 5 单步运行时间比较( $q = 0.1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 5 Comparison of step time ( $q = 0.1,{\lambda _k} = 5; {\rm CV}$ )
图 6 目标数目估计比较( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 6 Comparison of number estimation ( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
图 7 OSPA比较( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 7 Comparison of OSPA ( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
图 8 单步运行时间比较( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
Fig. 8 Comparison of step time ( $q = 1,{\lambda _k} = 5; {\rm CV}$ )
图 9 目标数目估计比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 9 Comparison of number estimation ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
图 10 OSPA比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 10 Comparison of OSPA ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
图 11 单步运行时间比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 11 Comparison of step time ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
图 12 目标数目估计比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 12 Comparison of number estimation ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
图 13 OSPA比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 13 Comparison of OSPA ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
图 14 单步运行时间比较( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
Fig. 14 Comparison of step time ( $q = 3,{\lambda _k} = 10; {\rm CT}$ )
表 1 初始化目标运动参数
Table 1 Motion parameters initialization
目标 位置(m) 速度(m·s-1) t0 (s) tf (s) 1 (-250, 250) (5, -5) 1 45 2 (-250, -250) (5, 5) 1 50 3 (-160, 160) (7, -9) 17 50 4 (-160, -160) (9, 7) 27 50 
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表 2 $P_f$ 分析( $offset = 40\,{\rm {m}}; {\rm CV}$ )
Table 2 Analysis of $P_f$ ( $offset = 40\,{\rm {m}}; {\rm CV}$ )
采样手段 失败次数 仿真次数 Pf QRS 20 60 0.334 EPS (N=96) 8 60 0.134 EPS (N=200) 3 60 0.05 PRS 35 60 0.584
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表 3 $P_f$ 分析( $offset = 100\,{\rm {m}}; {\rm CT}$ )
Table 3 Analysis of $P_f$ ( $offset = 100\,{\rm {m}}; {\rm CT}$ )
算法 失败次数 仿真次数 Pf ASRICP-PHD 17 60 0.28 ASRCP-PHD 32 60 0.502 HSRUP-PHD 50 60 0.83 SRGHP-PHD 55 60 0.916
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