矩阵李群上的混合减少
Mixture Reduction on Matrix Lie Groups
AI总结：
本文提出在矩阵李群上用于混合滤波的集中高斯分布（CGDs）减少方法，通过重新参数化计算KL散度并合并混合组件，用于多目标跟踪滤波研究。
摘要：
许多物理系统在矩阵李群上演化，为这类流形设计的混合滤波是解决挑战性估计问题的必要工具。然而，混合滤波面临组件数量持续增长的问题，因此需要适当的混合减少技术。本文提出了一种用于矩阵李群上分布的混合减少方法，称为集中高斯分布（CGDs）。这包括适当重新参数化CGD参数以计算KL散度，选择并合并混合组件。此外，我们还引入了在李群上的多目标跟踪滤波器作为所提减少方法的混合滤波研究示例。特别是，我们实现了在矩阵李群上的概率假说密度滤波器。我们使用最优子图案分配度量在由100个随机生成多目标场景组成的合成数据集上验证了滤波器性能。
英文摘要：
Many physical systems evolve on matrix Lie groups and mixture filtering designed for such manifolds represent an inevitable tool for challenging estimation problems. However, mixture filtering faces the issue of a constantly growing number of components, hence require appropriate mixture reduction techniques. In this letter we propose a mixture reduction approach for distributions on matrix Lie groups, called the concentrated Gaussian distributions (CGDs). This entails appropriate reparametrization of CGD parameters to compute the KL divergence, pick and merge the mixture components. Furthermore, we also introduce a multitarget tracking filter on Lie groups as a mixture filtering study example for the proposed reduction method. In particular, we implemented the probability hypothesis density filter on matrix Lie groups. We validate the filter performance using the optimal subpattern assignment metric on a synthetic dataset consisting of 100 randomly generated multitarget scenarios.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
