This paper proposes a new scaleless position estimation method. From the industrial perspective, the Hall sensor has several advantages: tiny size, light weight, extremely lowcost, and insensitivity to environmental contamination and external disturbance. Compared to the square wave Hall sensor, the linear Hall sensor provides more detailed information along the position. However, for combining more than two linear Hall sensors, the sensor offset, the difference in scale, and the unwanted phase shift between them and the harmonics would decrease the validity and reliability of sensor measurement. The fast Fourier transform and the fixed point iteration method are applied to compensate for those issues without any low-pass filter or additional signal conditioning. The effectiveness of the proposed scheme is verified through a prototype permanent magnet linear synchronous motor system.