Title: A second-order PHD filter with mean and variance in target number Show Chinese title

Title: 带有目标数均值和方差的二阶PHD滤波器

Abstract: The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters. Show Chinese abstract

Abstract: 概率假设密度（PHD）和基数化PHD（CPHD）滤波器由于其低复杂度和在杂波环境中估计目标数量和状态的能力，是多目标跟踪问题的流行解决方案。 PHD滤波器传播目标数量的一阶矩（即均值），而CPHD则传播目标数量的基数分布，尽管计算成本更高。 引入Panjer点过程，本文提出了一种二阶PHD滤波器，传播目标数量的二阶矩（即方差）以及其均值。 该算法在建模选择上比PHD滤波器更加灵活，其计算成本显著低于CPHD滤波器。 本文在统计模拟中比较了三种滤波器，结果表明所提出的滤波器对目标数量的变化（即目标出生和死亡）反应比CPHD滤波器更快。 此外，为了研究状态空间不同区域中估计目标数量之间的相关性，引入了一种新的多目标滤波器统计量，并对三种滤波器的幽灵效应进行了定量分析。