Time-Varying Graph Signal Estimation among Multiple Sub-Networks

Tsutahiro Fukuhara, Junya Hara, Hiroshi Higashi, Yuichi Tanaka
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Abstract

This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node connectivity. For a large sensor network, measuring signal values at all nodes over time requires huge resources, particularly in terms of energy consumption. To alleviate the issue, we consider a scenario that a sub-network, i.e., cluster, from the whole network is extracted and an intra-cluster analysis is performed based on the statistics in the cluster. The statistics are then utilized to estimate signal values in another cluster. This leads to the requirement for transferring a set of parameters of the sub-network to the others, while the numbers of nodes in the clusters are typically different. In this paper, we propose a cooperative Kalman filter between two sub-networks. The proposed method alternately estimates signals in time between two sub-networks. We formulate a state-space model in the source cluster and transfer it to the target cluster on the basis of optimal transport. In the signal estimation experiments of synthetic and real-world signals, we validate the effectiveness of the proposed method.
多个子网络间的时变图信号估计
本文提出了一种在多个子网络中估算时变图信号的方法。在许多传感器网络中,观测到的信号与节点(即传感器)相关联,网络的边代表节点间的连接性。为了缓解这一问题,我们考虑的方案是从整个网络中提取一个子网络(即簇),并根据簇内的统计数据进行簇内分析。然后利用这些统计数据来估计另一个簇中的信号值。这就需要将子网络的一组参数传输给其他子网络,而各集群中的节点数量通常是不同的。本文提出了一种两个子网络之间的合作卡尔曼滤波法。我们在源集群中建立了一个状态空间模型,并在最优传输的基础上将其传输到目标集群。在合成信号和实际信号的估计实验中,我们验证了所提方法的有效性。
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