In this study, a new robust sensorless control of doubly-fed induction generator (DFIG) in the complex domain has been investigated. The proposed sensorless control is based on the extended complex Kalman filter (ECKF) and proportional–integral complex controller. The design of this sensorless control in the complex domain allowed a threefold objective: a decrease in the system's dimension by half, an optimisation in the implementation of the control strategy and a decrease of the CPU computational time. In fact, to obtain the latter, the dimension of the DFIG model involved in this control has been halved, which leads to a reduction in the control's schema. Moreover, all the matrices involved in the ECKF have smaller dimensions than those of the real extended Kalman filter and no matrix inversion is needed because the output of the system is a scalar variable. The proposed sensorless control has been tested experimentally for several operating points, namely: nominal operation, operation under asymmetrical voltage dip and parameter variations. Moreover, the observability of the complex state model has been analysed and the required conditions for the local weak observability have been defined. The experimental results confirm the theoretical study and show a good reliability and a high rotor speed estimation accuracy.