Precise modelling, control and monitoring of machines improve the overall stability and operation of power systems. State estimation reduces the effect of noises and presents all hidden variables, which can be beneficial especially in non-linear control. In this study, first, a complete 16th-order state space model is developed for a grid-connected permanent magnet synchronous generator-based wind turbine (PMSG-WT). Due to non-linearity of the model, extended Kalman filtering is utilised for state estimation. A phasor measurement unit connected to permanent magnet synchronous generator bus is utilised to provide required electrical values for state estimation in a synchronous manner. In order to evaluate the accuracy of the proposed algorithm, four different cases are studied corroborating the robustness of the proposed algorithm in the presence of high noises or in the case of large disturbances. Some comparisons are also provided with another non-linear model proposed recently for PMSG-WT, which verifies the advantages of the proposed model. Such results are expected to improve stability of wind farms especially in the case of large disturbances, which can lead to enhancing the whole network stability.