Chen Xiangbing, Zhou Jie
Division of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China.
College of Mathematics, Sichuan University, Chengdu 610064, China.
Entropy (Basel). 2022 Dec 9;24(12):1802. doi: 10.3390/e24121802.
In the paper, we characterize local estimates from multiple distributed sensors as posterior probability densities, which are assumed to belong to a common parametric family. Adopting the information-geometric viewpoint, we consider such family as a Riemannian manifold endowed with the Fisher metric, and then formulate the fused density as an informative barycenter through minimizing the sum of its geodesic distances to all local posterior densities. Under the assumption of multivariate elliptical distribution (MED), two fusion methods are developed by using the minimal Manhattan distance instead of the geodesic distance on the manifold of MEDs, which both have the same mean estimation fusion, but different covariance estimation fusions. One obtains the fused covariance estimate by a robust fixed point iterative algorithm with theoretical convergence, and the other provides an explicit expression for the fused covariance estimate. At different heavy-tailed levels, the fusion results of two local estimates for a static target display that the two methods achieve a better approximate of the informative barycenter than some existing fusion methods. An application to distributed estimation fusion for dynamic systems with heavy-tailed process and observation noises is provided to demonstrate the performance of the two proposed fusion algorithms.
在本文中，我们将来自多个分布式传感器的局部估计表征为后验概率密度，假设这些后验概率密度属于一个共同的参数族。采用信息几何观点，我们将这样的族视为赋予费希尔度量的黎曼流形，然后通过最小化其到所有局部后验密度的测地距离之和，将融合密度表述为一个信息重心。在多元椭圆分布（MED）的假设下，通过使用最小曼哈顿距离而非MED流形上的测地距离，开发了两种融合方法，这两种方法都具有相同的均值估计融合，但协方差估计融合不同。一种方法通过具有理论收敛性的鲁棒不动点迭代算法获得融合协方差估计，另一种方法给出了融合协方差估计的显式表达式。在不同的重尾水平下，对静态目标的两个局部估计的融合结果表明，这两种方法比一些现有的融合方法能更好地逼近信息重心。给出了在具有重尾过程和观测噪声的动态系统的分布式估计融合中的应用，以证明所提出的两种融合算法的性能。
