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Information-driven Fully Distributed Kalman Filter for Sensor Networks in Presence of Naive Nodes

We consider the distributed Kalman filtering problem for sensor networks where each node takes the measurement, communicates with its local neighbors, and updates its local estimate and estimation error covariance at the same frequency. In such a scenario, if the target is not directly observed by neither a certain node nor its local neighbors, this node is naive about the target. The well-known Kalman Consensus filter (KCF) has been shown to perform well if there exists no naive node in the network. The case in presence of naive nodes has been considered by the generalized KCF (GKCF) and the Information Weighted Consensus filter (ICF) later on. However, all these consensus-embedded filters require some global information such as the maximum degree of the graph, or the total number of the nodes. If these global information are changing over the time, such as time-varying topologies or unexpected sensor failures in the network, the performance of the GKCF or the ICF might be degraded. With communication topology changes, node failures, or addition of new nodes, the filter performance would be adversely affected. In this paper, we consider a novel local Weighted Least Square estimator for each node that utilizes its generalized measurement formed by not only its own and local neighbors' measurements but their prior local estimates to track the target. With some approximations in the derivation of the covariance matrix, we propose the Information-driven Fully Distributed Kalman filter (IFDKF), which is able to deal with the existence of naive nodes without knowing any global information. Experimental results show that the proposed algorithm performs better than the existing algorithms in the considered realistic scenario.