The distributed state estimation is a novel and effective solution for achieving unified state estimation results of the whole power system. This paper proposes a new distributed state estimation algorithm， which is based on decomposition-coordination of the non-constrained optimization problem. By dividing the KKT（Karush-Kuhn-Tucker） condition equations of the state estimation of the whole power grid， two subsets of the KKT condition equations are obtained for both the regional power grids and the coordination sides. With given states of the boundary buses， the state estimation of the regional power grids can be worked out individually by solving the corresponding KKT condition equations. Then， if the demand to errors of coordination equation is satisfied， the overall state estimation is converged. Therefore， solving the overall state estimation is equal to solving the coordination equation with the constraint as that all regional state estimations are converged with the given states of the boundary buses. Moreover， to simplify the data exchange interfaces， the JFNG（Jacobian-free Newton-GMRES（generalized minimal residual）） and inverse Broyden quasi-Newton methods are utilized to solve the coordination equation， which makes the proposed algorithm being compatible with the legacy computing resources. Test results of the IEEE 14-bus system， IEEE 39-bus system and the North China 1 165-bus system show that the proposed algorithm can obtain the exactly same results as the centralized ones as well as converge fast and robustly， which enables it to be applied in the wide area networks.