This paper describes a demodulation approach based on the least squares method for a saliency based position estimation in slowly sampled field-oriented control systems. The proposed approach focuses on the sensorless control of electrical drives in which the sample rate of the control task is chosen slower than both the maximum possible update rate of the phase voltages and the maximum possible sample rate of the phase current measurement by a multiple. Under those conditions it is possible to inject multiple-frequency carrier signals between two successive control sampling instances without affecting the control. Furthermore, a combined demodulation of these signals is enabled by exploiting the constant manipulated variables of the field-oriented control system during the injection sequence. With the proposed method the signal-to-noise-ratio (SNR) of the calculated rotor position as well as the acoustic noise produced by signal injections can be optimized. The approach is implemented in a field-oriented control for permanent magnet synchronous machines (PMSM) and is verified in experiments.