  This paper investigates the state estimation problem for a class of complex
networks, in which the dynamics of each node is subject to Gaussian noise,
system uncertainties and nonlinearities. Based on a regularized least-squares
approach, the estimation problem is reformulated as an optimization problem,
solving for a solution in a distributed way by utilizing a decoupling
technique. Then, based on this solution, a class of estimators is designed to
handle the system dynamics and constraints. A novel feature of this design lies
in the unified modeling of uncertainties and nonlinearities, the decoupling of
nodes, and the construction of recursive approximate covariance matrices for
the optimization problem. Furthermore, the feasibility of the proposed
estimators and the boundedness of the mean-square errors are ensured under a
developed criterion, which is easier to check than some typical estimation
strategies including the linear matrix inequalities-based and the
variance-constrained ones. Finally, the effectiveness of the theoretical
results is verified by a numerical simulation.
