Permanent Magnet Synchronous Motors (PMSMs) have been replacing conventional DC motors in numerous automotive applications. One of which is Electrically Power Assisted Steering Systems (EPAS). PMSMs offer better performance and a longer lifetime while slightly increasing the system's cost and complexity. In a vector-controlled PMSM drive system, the rotor position sensor's resolution plays a vital role in the overall system performance. The better the resolution, the higher the cost. Although numerous sensor-less control algorithms currently exist, machine startup and operation with dynamically changing set-points and loads still impose a challenge for such an approach. For this reason, inexpensive Hall-Effect sensors have been recently used along with a proper position estimation algorithm to provide high-resolution rotor position. In this paper, an implementation of a vector-controlled drive system is applied to an EPAS using only low-resolution Hall-Effect sensors. Additionally, an improved rotor position estimation algorithm based on speed integration is developed to decrease estimation errors and torque ripples in the case of direction reversal. This is to cater to the dynamically changing commands encountered during the normal power assist operation. Comparisons of the proposed rotor position estimation system with the conventional technique are introduced. A complete representation of the proposed system is built using MATLAB/Simulink. An experimental setup is developed and built around a Motor-Driven Power Steering (MDPS) unit which is a column-assist type EPAS system made by Hyundai Mobis. The simulation and experimental results are presented to verify and evaluate the effectiveness of the proposed algorithm.