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This paper addresses the sensorless speed and position control of induction motors using high-frequency injection at zero and low frequencies. A novel algorithm is presented which allows the rejection of saturation and nonlinear inverter effects without the need for an offline precommissioning process. The method is based on a set of synchronous filters to identify the disturbance waveforms and a memory algorithm that refines the quality of the disturbance waveforms as the motor's operational history is increased. The algorithm is entirely sensorless. Experimental results show sensorless low-frequency operation with and without the memory algorithm.