Convergence of the Distributed SG Algorithm Under Cooperative Excitation Condition

Abstract: In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The proposed distributed SG algorithm combines the consensus strategy of the estimation of neighbors with the diffusion of regression vectors. A cooperative excitation condition is introduced, under which the convergence of the distributed SG algorithm can be obtained without relying on the independency and stationarity assumptions of regression vectors which are commonly used in existing literature. Furthermore, the convergence rate of the algorithm can be established. Finally, we show that all sensors can cooperate to fulfill the estimation task even though any individual sensor can not by a simulation example.