The paper considers the problem of distributed adaptive linear parameter
estimation in multi-agent inference networks. Local sensing model information
is only partially available at the agents and inter-agent communication is
assumed to be unpredictable. The paper develops a generic mixed time-scale
stochastic procedure consisting of simultaneous distributed learning and
estimation, in which the agents adaptively assess their relative observation
quality over time and fuse the innovations accordingly.
We consider the weight design problem for the consensus algorithm under a
finite time horizon. We assume that the underlying network is random where the
links fail at each iteration with certain probability and the link failures can
be spatially correlated. We formulate a family of weight design criteria
(objective functions) that minimize n, n = 1,...,N (out of N possible) largest
(slowest) eigenvalues of the matrix that describes the mean squared consensus
error dynamics.