A New Sequential Monte Carlo Implementation of Cardinality Balanced Multi-target Multi-Bernoulli Filter
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摘要: 为提升多伯努利滤波器序贯蒙特卡罗(Sequential Monte Carlo, SMC)实现中粒子采样的有效性,提出一种CBMeMBer辅助粒子滤波(Auxiliary particle filter, APF)实现的新方法.首先,利用多伯努利后验概率密度选择适合于CBMeMBer滤波器的辅助变量去重新定义采样问题.分别选择量测和先验密度分量作为辅助变量,确保最终的状态粒子能够集中在真实目标量测对应航迹的伯努利概率密度上进行采样,以使粒子向似然函数的峰值区移动,得到更为精确的多目标多伯努利(Multi-target multi-Bernoulli, MeMBer)后验概率密度的估计.同时,文中深入研究并给出了在量测更新和漏检情况下辅助变量以及多目标状态采样分布函数的设计,并研究利用渐近更新(Progressive correction, PC)算法对先验密度分量的量测更新进行迭代逼近计算,以提高最终分布函数求解的准确度.最后,针对两个典型非线性多目标跟踪问题的应用验证了算法的有效性.Abstract: To improve the effectiveness of particle sampling in the sequential Monte Carlo(SMC) implementation of the multi-Bernoulli filter, this paper proposes a new SMC implementation of the CBMeMBer filter using the so called auxiliary particle filter(APF). First, according to the posterior multi-Bernoulli density, this paper redefines the sampling problem by introducing some auxiliary random variables suited to the CBMeMBer filter. The measurement and the prior density component are chosen accordingly as auxiliary variables. As a result, this method can sample particles concentrating on the high likelihood state space and the Bernoulli probability density of track corrected by the actual target measurement. Therefore, a more accurate posterior probability density of multi-target multi-Bernoulli(MeMBer) can be obtained. Meanwhile, the sampling distribution functions of those auxiliary random variables and the multi-target states are designed for the legacy tracks and the measurement-corrected tracks. Moreover, this paper corrects iteratively the prior density component based on the progressive correction(PC) algorithm in order to improve the solving accuracy of sampling distribution functions. Finally, simulation results show the effectiveness of the proposed approach as applied to two typical nonlinear tracking problems.
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图 2 传统SMC-CBMeMBer滤波器的目标跟踪效果
Fig. 2 Target tracking with the traditional SMC-CBMeMBer filter
图 7 传统SMC-CBMeMBer滤波器的BOT跟踪效果
Fig. 7 Bearings-only tracking with the traditional SMC-CBMeMBer filter
表 1 不同采样规模下的性能比较
Table 1 Tracking performance versus sampling size
$L_s$ 100 300 500 1000 1500 BF OSPA~(m) 32.43 23.64 20.53 17.42 17.04 时间(s) 0.41 1.78 3.05 7.31 11.31 APF OSPA(m) 17.18 16.41 16.26 16.18 16.12 时间(s) 1.27 4.19 7.23 18.78 33.70 
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