Smart grid technologies have significantly enhanced robustness and efficiency of the traditional power grid networks by exploiting technical advances in sensing, measurement, and two-way communications between the suppliers and customers. The state estimation plays a major function in building such real-time models of power grid networks. For the smart grid state estimation, one of the essential objectives is to help detect and identify the topological error efficiently. In this paper, we propose the quickest estimation scheme to determine the network topology as quickly as possible with the given accuracy constraints from the dispersive environment. A Markov chain-based analytical model is also constructed to systematically analyze the proposed scheme for the online estimation. With the analytical model, we are able to configure the system parameters for the guaranteed performance in terms of the false-alarm rate (FAR) and missed detection ratio under a detection delay constraint. The accuracy of the analytical model and detection with performance guarantee are also discussed. The performance is evaluated through both analytical and numerical simulations with the MATPOWER 4.0 package. It is shown that the proposed scheme achieves the minimum average stopping time but retains the comparable estimation accuracy and FAR.