## 1 Introduction  
The sensorless techniques for different types of electric machines are still improving, especially in the automotive industry. PMSMs are highly demanded in such applications for their high power density factor, high dynamic features, robustness, and high efficiency. Due to cost reduction, which is a critical factor, especially in the automotive industry, researchers are forced to find new solutions for not only electrical drive but also the battery management system, power electronics, machine design, or software modifications of different control strategies. In particular, sensorless strategies are still very popular and attractive, because they offer the elimination of mechanical speed or position sensors coupled with the rotor shaft. This eliminates potential troubles coming mainly from the mechanical connection but also coming with vibration or temperature instability. A damaged sensor or one with inappropriate functionality would completely disable further motor operation in a sensored motor drive. Therefore, a proper sensorless algorithm could improve the minimization of the final cost, and furthermore, this solution decreases drive volume or maintenance cost. However, sensorless control could also offer a specified level of redundancy in case of a sudden mechanical sensor failure, which could be even more attractive, especially in the automotive industry but not only in this field. In general, sensorless vector control is one of the alternatives for operating PMSM without a mechanical sensor. The second alternative is a simpler scalar control, which also offers some benefits. Vector control provides separate torque and flux control in AC machines. Such a control strategy is similar to separately excited DC machines, in which a mechanical commutator maintains such effect. Field-oriented control (FOC) is a common form of vector control. This control strategy is primarily used for applications requiring high dynamic performance, such as servo systems. In FOC, the control reference frame is oriented on the flux vector. Therefore, the position of the flux vector has to be identified to ensure precise and reliable speed or position control. The most accurate way to determine its position is through the mechanical sensor. The other way to distinguish the location of the flux vector is estimating its position by employing a sensorless algorithm. In this case, the requirement of a mechanical sensor is eliminated. The sensorless algorithms could be divided into two basic groups: model-based (back-EMF-based) and non-model based methods (well known as saliency-based methods). The model-based methods, as the name says, include an exact mathematical model consisting of differential equations. The main idea is to estimate the back-EMF from stator voltages and currents and then use this information to estimate rotor position and speed. These methods provide a satisfactory control performance in medium- and high-speed regions, and many algorithms have been proposed. These include an extended Kalman filter (EKF) [1; 2; 3], a model reference adaptive system (MRAS) [4], a Luenberger observer [5], and a sliding mode observer (SMO) [6; 7; 8; 9; 10; 11]. There are also other methods such as a least-order observer [12] and a disturbance observer [13]. These two employ an extended EMF term and can be applied for interior PMSM (IPMSM), where the rotor position information is contained not only in the flux or the EMF but also in the inductances due to their saliency. In [14; 15], authors used a special asymptotic state observer with PLL. A different approach is proposed in [16], where an adaptive observer has been used. As was mentioned above, the main drawback of model-based estimators is in low-speed regions, where they are not applicable for well-known reasons (mostly for an unfavorable signal-to-noise ratio of the voltage measurement). Different start-up algorithms have to be applied to overcome this problem [17; 18; 19].