A coalitional game for distributed estimation in wireless sensor networks

We consider a collaborative estimation problem using dependent observations in a wireless sensor network, where each sensor aims to maximize its estimation performance in terms of Fisher information (FI) by forming coalitions with other sensors and collaborating within a coalition. The energy consumed by the sensors increases with the size of the coalition and hence we prove that grand coalition will not form. We investigate the formation of non-overlapping coalitions such that each sensor´s performance is maximized under a specific energy constraint. We decouple marginal and dependent components of FI obtained from the joint distribution by using copula theory. We introduce the concept of diversity gain and redundancy loss and demonstrate how a copula based formulation allows us to characterize these concepts. Distributed estimation problem is formulated as a coalitional game. A merge-and-split algorithm is used for finding an optimal partition. Stability of the proposed algorithm for this game is discussed. Finally, numerical results are discussed.