  In distributed processing, agents generally collect data generated by the
same underlying unknown model (represented by a vector of parameters) and then
solve an estimation or inference task cooperatively. In this paper, we consider
the situation in which the data observed by the agents may have risen from two
different models. Agents do not know beforehand which model accounts for their
data and the data of their neighbors. The objective for the network is for all
agents to reach agreement on which model to track and to estimate this model
cooperatively. In these situations, where agents are subject to data from
unknown different sources, conventional distributed estimation strategies would
lead to biased estimates relative to any of the underlying models. We first
show how to modify existing strategies to guarantee unbiasedness. We then
develop a classification scheme for the agents to identify the models that
generated the data, and propose a procedure by which the entire network can be
made to converge towards the same model through a collaborative decision-making
process. The resulting algorithm is applied to model fish foraging behavior in
the presence of two food sources.
