Graph Filter Transfer for Time-Varying Signal Estimation Between Two Networks

This paper presents a filter transfer method for estimating time-varying graph signals, i.e., Kalman filtering between two different 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 the signal values at all nodes requires huge resources, particularly in terms of energy consumption. To alleviate the issue, one may extract one cluster from the network and perform intra-cluster analysis based on the statistics in the cluster. The statistics are then utilized to estimate the signals from another cluster. This leads to the requirement for transferring a set of parameters in the Kalman filter from one cluster to another. In this paper, we propose a cooperative Kalman filter between two networks. The proposed Kalman filter alternately estimates signals in time between the two 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, we validate the effectiveness of the proposed method.