论文标题
线性复杂性Gibbs采样，用于广义标记的多重bernoulli滤波
Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering
论文作者
论文摘要
在单对象过滤中类似于高斯的多个多对象系统应用中，会出现广义标记的多伯努利（GLMB）密度。但是，计算GLMB滤波密度需要解决NP硬化问题。为了减轻这种计算瓶颈，我们开发了用于GLMB密度计算的线性复杂性Gibbs采样框架。具体而言，我们提出了一个钢化GIBBS采样器，该采样器利用GLMB过滤密度的结构，以实现$ \ Mathcal {o}（t（p+m））$复杂性，其中$ t $是算法，$ p $和$ m $的迭代次数，是数量假设的对象和测量值。此创新使GLMB过滤器实现可以从$ \ Mathcal {O}（tp^{2} M）$复杂度到$ \ Mathcal {o}（T（p+m+m+\ log t）+pm）$。此外，所提出的框架为跟踪性能和计算负载之间的权衡提供了灵活性。建立了提出的Gibbs采样器的收敛性，并提供了数值研究以验证所提出的GLMB滤波器实现。
Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $\mathcal{O}(T(P+M))$ complexity, where $T$ is the number of iterations of the algorithm, $P$ and $M$ are the number hypothesized objects and measurements. This innovation enables the GLMB filter implementation to be reduced from an $\mathcal{O}(TP^{2}M)$ complexity to $\mathcal{O}(T(P+M+\log T)+PM)$. Moreover, the proposed framework provides the flexibility for trade-offs between tracking performance and computational load. Convergence of the proposed Gibbs sampler is established, and numerical studies are presented to validate the proposed GLMB filter implementation.
