Advantages of sensorless drives include higher reliability, simpler hardware, lower maintenance, and lower initial cost. Considering the progress of semiconductors, increasing the processing speed of processors, and the advancement of control systems, removing the sensor from the drives is not out of reach. Among synchronous motors, permanent magnet synchronous motors (PMSMs) are used in various industries due to their high power density, high reliability, high efficiency, good controllability, and wide speed range. For sensorless drives of PMSMs, at low and zero speeds, the nonlinearity of inverters and variation of motor parameters, and at higher speeds, the bandwidth of the estimators are the main challenges of control system design. So far, various methods have been proposed for sensorless control of this motor. In this research, sensorless control of PMSM using rotor flux field orientation control is considered as the basis of the control method. To estimate the position/speed of this motor, from two important categories of estimation, "signal injection" and "model-based" methods, the second is focused on. Estimation of rotor position and speed using the motor model using the "Adaptive Reference Model", "Sliding Mode Observer" and "Expanded Kalman Filter" methods is reviewed. The Kalman filter method is simulated and implemented and is considered as a benchmark for comparison with the proposed methods. In the first proposed method, a Simplified EKF is examined, simulated, and implemented. By simplifying the model and assigning this approximation to the filter, a method to reduce its computational burden is proposed. In order to optimally control the motor and eliminate the maximum sensitivities of the estimator-based control system, a second method is proposed in which the back-electromotive force signals are used and with the appropriate filter, the estimation process is performed. This method has significant advantages compared to similar methods. Also in this research, the general concept and advantages and disadvantages of the most important methods of position and speed estimation in vector control of a permanent magnet synchronous motor are investigated. Simulation, implementation, and verification of the correct operation of the basic and proposed methods have been done. Simulink MATLAB used for simulation and TMS320F28335 is used to practically drive the motor. The results of these practical implementations and the response of the proposed systems to the control commands in the presence of environmental and model perturbations, confirm the accuracy and efficiency of the proposed methods for their widespread use. Keywords: Controllability, Permanent Magnet Synchronous Motor, Sensorless Control, Model Reference Adaptive System, Sliding Mode Observer, Extended Kalman Filter.