Nowadays, with the drive towards smart power distribution grids and the improvements in monitoring and communications infrastructure, distribution system state estimation has been receiving significant research interest. The state vector of the grid is composed of those electrical quantities which are costly or inaccessible to measure such as the voltage phasor at buses.etwork topology and transmitted measurements are needed in each state estimation process. In this thesis, by reducing themeasurementdata volume before transmission, in addition to decreasing the required bandwidth, problems such as lack of storage space, interference and delay would be resolved. Compressive sensing and separation of major singular values have been suggested to reduce the amount of power injection measurement s, with both online and offline views. Then, all power injection values are reconstructed from compressed measurements fed as inputs to the weighted least square algorithm and a backward-forward method to estimate states . Moreover , a technique has been proposed estimating states from compressed data directly without applying the compressive sensing reconstruction procedure. Therefore, less storage space would be needed while the sparse space of measurementdoes not need to be known. Since the impact of the measurements on the state estimation, discontinuing data transmission would be decreased the accuracy of the estimation results. By proposing an approximate calculation of required quantities based on past measurements and using a nonlinear Kalman filter, the disadvantage of discontinuous data from meters over a long period of time would be reduced. The unknown switching operations cause topological changes and unreliable estimation results. To solve the aforementioned issue, a criterion independent of measurements has been proposed identifying the changing of a switch status. Therefore, this criterion can also be used in the state estimation based on compressed data without using reconstruction process . The simulation results demonstrate that the proposed estimation method can detect switch status while estimating the stat e vector with high accuracy, especially when a part of the grid is islanded. Key Words: Smart distribution grid, Compressive sensing , State estimation , nonlinear Kalman filter, Topology identification .