This paper presents a new derivation of the variational Poisson multi-Bernoulli (V-PMB) filter for multi-target estimation proposed in [#Williams15]. The proposed derivation is based on considering an augmented space that includes the set of target states with their track indices and the global hypothesis variable. Then, we show that the V-PMB projection performs a coordinate descent Kullback-Leibler divergence (KLD) minimisation on this augmented space to fit the best possible PMB density to the Poisson multi-Bernoulli mixture (PMBM) posterior. We also show that this V-PMB projection keeps the probability hypothesis density of the posterior. The paper also includes a comparison with the PMBM filter and other PMB filter variants, including a track-oriented Murty-based implementation, a track-oriented loopy belief propagation implementation and a global nearest neighbour implementation, showing the benefits of the V-PMB filter compared to the other PMB filters when targets get in close proximity and then separate.

翻译：本文针对文献[#Williams15]中提出的多目标估计变分泊松多伯努利（V-PMB）滤波器，提出了一种新的推导方法。该推导基于考虑一个增广空间，该空间包含目标状态及其轨迹索引以及全局假设变量。然后，我们证明V-PMB投影通过在该增广空间上执行坐标下降Kullback-Leibler散度（KLD）最小化，为泊松多伯努利混合（PMBM）后验密度拟合出最佳可能的PMB密度。我们还证明，该V-PMB投影保留了后验的概率假设密度。本文还包含与PMBM滤波器及其他PMB滤波器变体的比较，包括基于轨迹导向的Murty实现、基于轨迹导向的环路置信传播实现和全局最近邻实现，结果表明当目标接近并随后分离时，V-PMB滤波器相比其他PMB滤波器具有优势。