In practice, many autonomous vehicle developers put a tremendous amount of time and efforts in tuning and calibrating the path tracking controllers in order to achieve robust tracking performance and smooth steering actions over a wide range of vehicle speed and road curvature changes. This design process becomes tiresome when the target vehicle changes frequently. In this study, a model-based Linear Quadratic Gaussian (LQG) Control with adaptive Q-matrix is proposed to efficiently and systematically design the path tracking controller for any given target vehicle while effectively handling the noise and error problems arise from the localization and path planning algorithms. The regulator, in turn, is automatically designed, without additional efforts for tuning at various speeds. The performance of the proposed algorithm is validated based on KAIST autonomous vehicle. The experimental results show that the proposed LQG with adaptive Q-matrix has tracking performance in both low (15kph) and high (45kph) speed driving conditions better than those of other conventional tracking methods like the Stanley and Pure-pursuit methods.