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摘要: 针对杂波环境下的目标跟踪问题, 提出了一种基于变分贝叶斯的概率数据关联算法(Variational Bayesian based probabilistic data association algorithm, VB-PDA). 该算法首先将关联事件视为一个随机变量并利用多项分布对其进行建模, 随后基于数据集、目标状态、关联事件的联合概率密度函数求取关联事件的后验概率密度函数, 最后将关联事件的后验概率密度函数引入变分贝叶斯框架中以获取状态近似后验概率密度函数. 相比于概率数据关联算法, VB-PDA算法在提高算法实时性的同时在权重Kullback-Leibler (KL)平均准则下获取了近似程度更高的状态后验概率密度函数. 相关仿真实验对提出算法的有效性进行了验证.Abstract: Aiming at the problem of target tracking in clutter, this paper proposes a variational Bayesian based probabilistic data association algorithm (VB-PDA). Firstly, associated events are regarded as a random variable and modelled by the multi-nomial distribution. Then, the joint probability density function of data set, target state and associated events is constructed and the posterior probability density function of associated events is obtained by using this joint probability density function. Finally, the posterior probability density function of associated events is introduced into the framework of variational Bayesian to obtain the approximate posterior probability density function of state. Compared with the probabilistic data association algorithm, the VB-PDA algorithm obtains a state posterior probability density function with higher approximation degree based on the weight Kullback-Leibler (KL) average criterion while improving real-time performance. The simulation experiments verify the effectiveness of proposed algorithm.
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图 1 场景 1 下 3 种算法的位置 RMSE
Fig. 1 The RMSE of position from three algorithms in scenario 1
图 2 仿真场景 1 下 3 种算法的速度 RMSE
Fig. 2 The RMSE of velocity from three algorithms in scenario 1
图 3 仿真场景 2 下 3 种算法的位置 RMSE
Fig. 3 The RMSE of position from three algorithms in scenario 2
图 4 仿真场景 2 下 3 种算法的速度 RMSE
Fig. 4 The RMSE of velocity from three algorithms in scenario 2
表 1 一步状态更新过程中所需的加减运算与乘除运算次数
Table 1 The number of addition and subtraction operations and multiplication and division operations required in the process of one-step state update
算法 加减法运算次数 乘除法运算次数 PDA $\begin{aligned} &{r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - {n_{k + 1} } + 2) + \\ &\qquad r({n_{k + 1} } + 1 + 2m) + 2{n_{k + 1} } - 1 +\\ & \qquad m{n_{k + 1} } - m\end{aligned}$ $\begin{aligned} & {r^3} + {r^2}(2{n_{k + 1} } + m + 3) + \\ &\qquad r(2m + 1) + m{n_{k + 1} } + 1 \end{aligned}$ DW-PDA $\begin{aligned} & {r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - {n_{k + 1} } + 2)\; + \\ &\qquad r({n_{k + 1} } + 1 + 2m) + 4{n_{k + 1} } - 3 + \\ &\qquad m{n_{k + 1} } - m\end{aligned}$ $\begin{aligned} &{r^3} + {r^2}(2{n_{k + 1} } + m + 3)+ \\ &\qquad r(2m + 1) + m{n_{k + 1} } + 4{n_{k + 1} } + 1\end{aligned}$ VB-PDA $\begin{aligned} & {r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - 2{n_{k + 1} } + 1)\; + \\ & \qquad2mr + 2{n_{k + 1} } - 1 + m{n_{k + 1} } - m \end{aligned}$ $\begin{aligned} & {r^3} + {r^2}m + r(2m + 1)+\; \\ &\qquad m{n_{k + 1} } + 1 + {m^2} \end{aligned}$ 
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表 2 场景 1 下 3 种算法的 TRMSE
Table 2 The TRMSE of three algorithms in scenario 1
算法 位置 TRMSE (m) 速度 TRMSE (m/s) PDA 6.892 0.873 DW-PDA 6.792 0.839 VB-PDA 6.742 0.872
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表 3 场景 1 下一次蒙特卡洛仿真实验所需的计算时间
Table 3 The computational time at one Monte Carlo simulation experiment in scenario 1
算法 计算时间 (ms) PDA 56.52 DW-PDA 58.72 VB-PDA 46.70
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表 4 仿真场景2下3种算法的TRMSE
Table 4 The TRMSE of three algorithms in scenario 2
算法 位置TRMSE (m) 速度TRMSE (m/s) IMM-PDA 8.409 1.874 IMM-DW-PDA 8.101 1.818 IMM-VB-PDA 7.967 1.784
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