PMSM(permanent magnet synchronous motor) are widely used in industrial and home appliance because of their high torque to inertia ratio, superior power density, and high efficiency For the high control performance, accurate information of rotor position Is essential. In recent, sensorless algorithms are much studied due to high cost problem of position sensor and low reliability in harsh environment. In the proposed method, a differential linkage flux is used for the estimation of rotor position. The differential magnetic field flux is calculated by the voltage equations and measured phase current without any integration and differential calculus. Instead of linkage flux calculation with differential operation, a new mathematical differential method is introduced by a-$eta$ transformation. The proposed novel position sensorless speed control scheme is verified through experimental results.