  In this paper, we consider a least-squares (LS)-based distributed algorithm
build on a sensor network to estimate an unknown parameter vector of a
dynamical system, where each sensor in the network has partial information only
but is allowed to communicate with its neighbors. Our main task is to
generalize the well-known theoretical results on the traditional LS to the
current distributed case by establishing both the upper bound of the
accumulated regrets of the adaptive predictor and the convergence of the
distributed LS estimator, with the following key features compared with the
existing literature on distributed estimation: Firstly, our theory does not
need the previously imposed independence, stationarity or Gaussian property on
the system signals, and hence is applicable to stochastic systems with
feedback. Secondly, the cooperative excitation condition introduced and used in
this paper for the convergence of the distributed LS estimate is the weakest
possible one, which shows that even if any individual sensor cannot estimate
the unknown parameter by the traditional LS, the whole network can still
fulfill the estimation task by the distributed LS.
