Stability of distributed LMS under cooperative stochastic excitation

Distributed estimation algorithms can estimate a dynamic process of interest by a set of estimators cooperatively, when any individual estimator cannot. The paper considers this kind of problems and focuses on a class of distributed least mean-square(LMS) algorithms in discrete time. Stability analysis will be provided under a weakest possible cooperative stochastic excitation condition. We remark that the stringent conditions such as independency and stationarity that have been used in almost all the existing literatures are no longer used in this paper. In addition, a simulation result comparing with the non-cooperative LMS algorithm will be provided to show the advantage of the distributed LMS algorithm studied in the paper.