In target tracking and sensor fusion contexts it is not unusual to deal with a large number of Gaussian densities that encode the available information (multiple hypotheses), as in applications where many sensors, affected by clutter or multimodal noise, take measurements on the same scene. In such cases reduction procedures must be implemented, with the purpose of limiting the computational load. In some situations it is required to fuse all available information into a single hypothesis, and this is usually done by computing the barycenter of the set. However, such computation strongly depends on the chosen dissimilarity measure, and most often it must be performed making use of numerical methods, since in very few cases the barycenter can be computed analytically. Some issues, like the constraint on the covariance, that must be symmetric and positive definite, make it hard the numerical computation of the barycenter of a set of Gaussians. In this work, Fixed-Point Iterations (FPI) are presented for the computation of barycenters according to several dissimilarity measures, making up a useful toolbox for fusion/reduction of Gaussian sets in applications where specific dissimilarity measures are required.
翻译:在目标跟踪和感应聚合背景下,处理大量编码现有信息的高斯密度(多重假设)并不罕见,如许多传感器受到杂乱或多式噪音影响的应用中,在同一场景进行测量;在这类情况下,为了限制计算负载,必须实施减少程序;在某些情况下,需要将所有可用信息整合到一个单一假设中,这通常是通过计算成套数据中位器完成的。然而,这种计算在很大程度上取决于所选择的不同度量,而且往往必须使用数字方法进行,因为在极少数情况下,可以用分析方式计算中位器。有些问题,如对共变的制约,必须具有对称性和积极确定性,使一组高官中位器的数值计算变得困难。在这项工作中,根据若干不同度度度度度量度度量,提出固定点透镜(FPI),用于计算中位器的计算,根据若干不同度度度度度度度度度度度度量,提出一个有用的工具箱,用以计算不同度度度度度量度,其中要求的定点/递增度措施。