In recent years, analysis, estimation and control of distributed systems have gained considreble attention, because of advances in the fields of electronics, wireless communications, and mems technology for sensors implementation. Many research teams are formed around the world to model and analyze these systems. State estimation of distributed systems is important to identify and control their performance. A centralized state estimation algorithm, although possibly easy to design, is neither robust nor scalable. The large-scale systems are very high-dimensional, thus they require extensive computations to implement a centralized approach; and the span of the geographical region, over which a wide area system is deployed, poses a large communication burden to implement a centralized procedure. A computationally efficient implementation is to employ a distributed algorithm that relies only on local communication and low-order computation. Hence, design and analysis of distributed algorithms is vital for efficient and scalable operation of large-scale complex infrastructures. In this thesis, distributed state estimation algorithms for both linear and nonlinear wide area systems are proposed, and their convergence conditions are studied. In the proposed distributed state estimation methods, after the spatial decomposition of the broad system to overlap subsystems with the fewer dimensions, a recursive distributed algorithm for local state estimation is presented. It should be noted that in nonilinear systems, each subsystem after model linearization around previous estimation in each time step, estimates local state variables. At the end of each time step, estimates of each state variable to be shared between overlap subsystems by the weighted average algorithm. Estimation algorithms presented in this thesis, unlike previous similar cases, are completely decentralized and nowhere in the network, storage, communication, or computation of the global system dimensional vectors and matrices are needed. In separate theories and using the Lyapunov functional technique, sufficient conditions are presented to guarantee the exponentially boundedness in mean square and bounded with probability one of the estimation errors in both linear and nonlinear proposed estimation methods. A numerical example is provided to show effectiveness and applicability of proposed algorithm. Localization is a fundamental problem in sensor networks. Information about locations of sensors is the key to process the sensors' measurements accurately. Due to measurement noise, analytical methods are not effective enough. Finally in this thesis, as an application of wide area nonlinear systems, a localization algorithm based on distributed state estimation in the presence of noise will be presented. In the proposed algorithm, the minimum number of anchor nodes is calculated and one of the most important advantages of this approach is a drastic reduction of the number of anchors. Also, it will be proved that using m+1 anchor nodes in m-dimansional space the proposed localization method is convergence and the estimation error is exponentially bounded in mean square. Simulation results demonestrate the convergence of estimated coordinations to actual sensors locations. Keywords : Distributed state estimation, Large-scale systems, Spatial decomposition, Overlap subsystems, Sensor localization, Data fusion, Anchor node, Exponentially bounded in mean square.