If computational tractability were not an issue, multi-object estimation should integrate all measurements from multiple sensors across multiple scans. In this article, we propose an efficient numerical solution to the multi-scan multi-sensor multi-object estimation problem by computing the (labeled) multi-sensor multi-object posterior density. Minimizing the $L_{1}$-norm error from the exact posterior density requires solving large-scale multi-dimensional assignment problems that are NP-hard. An efficient multi-dimensional assignment algorithm is developed based on Gibbs sampling, together with convergence analysis. The resulting multi-scan multi-sensor multi-object estimation algorithm can be applied either offline in one batch or recursively. The efficacy of the algorithm is demonstrated using numerical experiments with a simulated dataset.

翻译：如果计算可分性不是一个问题, 多对象估计应该将多个传感器通过多个扫描进行的所有测量数据综合起来。 在本条中, 我们提出一个高效的数字解决方案, 解决多扫描多传感器多对象估计问题, 方法是计算( 标签的) 多传感器多对象后端密度。 将 $L ⁇ 1} $- norm 错误从精确的后方密度中最小化, 需要解决大规模多维分配问题, 这些问题是硬的。 高效的多维分配算法是根据Gibbs 取样以及聚合分析开发的。 由此产生的多扫描多传感器多对象估计算法可以分批或递归。 算法的效力通过模拟数据集的数字实验得到证明。