  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.
