School of Mathematics and Statistics, Kashi University, Kashi, Xinjiang, China.
Division of Mathematics, Sichuan University Jinjiang College, Meishan, Sichuan, China.
PLoS One. 2024 Sep 27;19(9):e0307587. doi: 10.1371/journal.pone.0307587. eCollection 2024.
In this contribution, we use Gaussian posterior probability densities to characterize local estimates from distributed sensors, and assume that they all belong to the Riemannian manifold of Gaussian distributions. Our starting point is to introduce a proper Lie algebraic structure for the Gaussian submanifold with a fixed mean vector, and then the average dissimilarity between the fused density and local posterior densities can be measured by the norm of a Lie algebraic vector. Under Gaussian assumptions, a geodesic projection based algebraic fusion method is proposed to achieve the fused density by taking the norm as the loss. It provides a robust fixed point iterative algorithm for the mean fusion with theoretical convergence, and gives an analytical form for the fused covariance matrix. The effectiveness of the proposed fusion method is illustrated by numerical examples.
在本贡献中，我们使用高斯后验概率密度来描述分布式传感器的局部估计，并假设它们都属于具有固定均值向量的高斯分布的黎曼流形。我们的出发点是为具有固定均值向量的高斯子流形引入一个适当的李代数结构，然后可以通过李代数向量的范数来度量融合密度与局部后验密度之间的平均差异。在高斯假设下，我们提出了一种基于测地线投影的代数融合方法，通过取范数作为损失来实现融合密度。它为均值融合提供了一个具有理论收敛性的稳健固定点迭代算法，并给出了融合协方差矩阵的解析形式。数值示例说明了所提出的融合方法的有效性。
