Decentralized parameter estimation by consensus based stochastic approximation

In this paper an algorithm for decentralized estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. A rigorous analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of local measurements and communication faults. In the case of non-vanishing gains in the stochastic approximation algorithms, an upper bound of the mean-square estimation error matrix is defined as a solution of a Lyapunov-like matrix equation, while in the case of asymptotically vanishing gains the mean-square convergence is proved. It is also demonstrated how the consensus strategy can contribute to the reduction of measurement noise influence.