  We study a distributed node-specific parameter estimation problem where each
node in a wireless sensor network is interested in the simultaneous estimation
of different vectors of parameters that can be of local interest, of common
interest to a subset of nodes, or of global interest to the whole network. We
assume a setting where the nodes do not know which other nodes share the same
estimation interests. First, we conduct a theoretical analysis on the
asymptotic bias that results in case the nodes blindly process all the local
estimates of all their neighbors to solve their own node-specific parameter
estimation problem. Next, we propose an unsupervised diffusion-based LMS
algorithm that allows each node to obtain unbiased estimates of its
node-specific vector of parameters by continuously identifying which of the
neighboring local estimates correspond to each of its own estimation tasks.
Finally, simulation experiments illustrate the efficiency of the proposed
strategy.
