Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the target distribution by the arithmetic average (AA) of a finite number of sub-distributions which constitute a mixture. While the mixture has been widely used for single sensor filter design, it is only recent that the AA fusion demonstrates compelling performance for multi-sensor filter design. In this paper, some statistic and information-theoretic results are given on the covariance consistency, mean square error, mode-preservation capacity, and the information divergence of the AA fusion approach. In particular, based on the concept of conservative fusion, the relationship of the AA fusion with the existing conservative fusion approaches such as covariance union and covariance intersection is exposed. A suboptimal weighting approach has been proposed, which jointly with the best mixture-fit property of the AA fusion leads to a max-min optimization problem. Linear Gaussian models are considered for algorithm illustration and simulation comparison, resulting in the first-ever AA fusion-based multi-sensor Kalman filter.

翻译：有限混合模型（如高斯混合）是一种灵活且强大的概率建模工具，用于表示许多估计与学习问题中广泛涉及的多模态分布。其核心是通过有限个子分布的算术平均值（AA）来表征目标分布，这些子分布构成混合分布。尽管混合模型已广泛用于单传感器滤波器设计，但直到最近，AA融合方法才在多传感器滤波器设计中展现出令人瞩目的性能。本文给出了关于AA融合方法的协方差一致性、均方误差、模态保持能力及信息散度的若干统计与信息论结果。特别地，基于保守融合的概念，揭示了AA融合与现有保守融合方法（如协方差联合与协方差交叉）之间的关系。提出了一种次优加权方法，结合AA融合的最佳混合拟合特性，导致了一个最大最小优化问题。考虑线性高斯模型进行算法说明与仿真比较，从而首次实现了基于AA融合的多传感器卡尔曼滤波器。