Strong consistency of the distributed stochastic gradient algorithm

With the development of computer science and communication, the sensor networks are widely applied due to the advantages of flexibility, fault tolerance, and ease of deployment. In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the distributed 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. The cooperative excitation condition is introduced, under which the strong consistency can be established for the distributed SG algorithm, without relying on the independency and stationarity assumptions of regression vectors which are commonly used in existing literature.