Title: FADE: Fast and Asymptotically efficient Distributed Estimator for dynamic networks,
Abstract: Consider a set of agents that wish to estimate a vector of parameters of
their mutual interest. For this estimation goal, agents can sense and
communicate. When sensing, an agent measures (in additive gaussian noise)
linear combinations of the unknown vector of parameters. When communicating, an
agent can broadcast information to a few other agents, by using the channels
that happen to be randomly at its disposal at the time.
To coordinate the agents towards their estimation goal, we propose a novel
algorithm called FADE (Fast and Asymptotically efficient Distributed
Estimator), in which agents collaborate at discrete time-steps; at each
time-step, agents sense and communicate just once, while also updating their
own estimate of the unknown vector of parameters.
FADE enjoys five attractive features: first, it is an intuitive estimator,
simple to derive; second, it withstands dynamic networks, that is, networks
whose communication channels change randomly over time; third, it is strongly
consistent in that, as time-steps play out, each agent's local estimate
converges (almost surely) to the true vector of parameters; fourth, it is both
asymptotically unbiased and efficient, which means that, across time, each
agent's estimate becomes unbiased and the mean-square error (MSE) of each
agent's estimate vanishes to zero at the same rate of the MSE of the optimal
estimator at an almighty central node; fifth, and most importantly, when
compared with a state-of-art consensus+innovation (CI) algorithm, it yields
estimates with outstandingly lower mean-square errors, for the same number of
communications -- for example, in a sparsely connected network model with 50
agents, we find through numerical simulations that the reduction can be
dramatic, reaching several orders of magnitude.