Distributed signal estimation in a wireless sensor network with partially-overlapping node-specific interests or source observability

We study a distributed node-specific signal estimation problem where the node-specific desired signals and/or the sensor observations can have partially-overlapping latent signal subspaces. First, we provide the minimum number of linear combinations of observed sensor signals that each node can broadcast to still let all other nodes achieve the network-wide Linear Minimum Mean-Square Error (LMMSE) estimate of their node-specific desired signals. Later, for a fully-connected wireless sensor network, we derive a distributed algorithm that, under some settings, allows each node to achieve the LMMSE estimate of its node-specific desired signals by broadcasting the smallest number of signals. Unlike the existing algorithms, the proposed algorithm deals with the problem of partially-overlapping node-specific interests and incomplete observability of all latent sources at the nodes. Finally, the effectiveness of the proposed technique is shown through numerical simulations.