FADE: Fast and Asymptotically Efficient Distributed Estimator for Dynamic Networks

Consider a set of agents that wish to estimate a vector of parameters. For this estimation goal, each agent can measure (in additive Gaussian noise) linear combinations of the unknown vector of parameters and can broadcast information to a few other neighbors. To coordinate the agents, we propose a distributed algorithm called FADE (fast and asymptotically efficient distributed estimator). FADE enjoys five attractive features: first, it is simple to derive; second, it withstands dynamic networks; third, it is strongly consistent with each agent's estimate converging (almost surely) to the true vector of parameters; fourth, it is both asymptotically unbiased and efficient with each agent's estimate becoming unbiased and the mean square error (MSE) of each agent's estimate vanishing to zero at the same rate of the MSE of the optimal centralized estimator; and finally, when compared with the popular consensus+innovation algorithm, it yields estimates with MSEs that, for some networks, can be orders of magnitude smaller.