A distributed recursive state estimation algorithm is proposed for spatially interconnected systems. Necessary and sufficient conditions for the convergence of the algorithm are obtained. This suggested distributed estimator is comprised of a series of sub-estimators so that states of the local subsystem can be estimated only by utilizing outputs of the local subsystem and its adjacent ones. Compared with the lumped Kalman filter, the derived distributed algorithm reduces sharply computational complexity and communicating burden, in the case of sacrificing a small amount of estimation accuracy.