论文标题
具有边缘测量的网络系统的分布式加权最小二乘估计
Distributed Weighted Least-squares Estimation for Networked Systems with Edge Measurements
论文作者
论文摘要
本文研究了带有附加噪声的互连线性测量网络的分布加权最小二乘（WLS）估计的问题。考虑了两种类型的测量值：单个节点的自我测量和连接节点的边缘测量。网络中的每个节点都通过使用其自己的测量和从其邻居传输的信息进行分布式估计。我们研究了两种分布式估计算法：最近提出的分布式WLS算法和所谓的高斯信仰传播（BP）算法。我们首先建立了两种算法的等效性。然后，我们证明了一个关键结果，该结果表明信息矩阵始终在某些非常温和的状态下始终是对角的占主导地位。使用这两个结果以及高斯BP算法的一些已知收敛性，我们表明上述分布式WLS算法可逐渐渐近地给出了全球最佳的WLS估计值。还提出了对其收敛速率的界限。
This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes, and edge measurements for the connecting nodes. Each node in the network carries out distributed estimation by using its own measurement and information transmitted from its neighbours. We study two distributed estimation algorithms: a recently proposed distributed WLS algorithm and the so-called Gaussian Belief Propagation (BP) algorithm. We first establish the equivalence of the two algorithms. We then prove a key result which shows that the information matrix is always generalised diagonally dominant, under some very mild condition. Using these two results and some known convergence properties of the Gaussian BP algorithm, we show that the aforementioned distributed WLS algorithm gives the globally optimal WLS estimate asymptotically. A bound on its convergence rate is also presented.
