In this paper, designing optimal linear controller for non-holonomic wheeled mobile robots based on Linear Quadratic Gaussian (LQG) controller is considered. Parameters of the governing kinematics equation of motion are derived based on system identification techniques by using real experimental data. The autoregressive moving average-exogenous input (ARMAX) models are taken into account. The least square (LS) algorithm is utilized to estimate the parameters of the model. Thereafter, optimal model order and the performance of the model are determined using several statistical analyses. Also, the recursive LS (RLS) with forgetting factor is employed to demonstrate the convergence of the model parameters. Verification of discrete linear model implies the possibility of using the linear controllers. Therefore, the optimal LQG controller for wheeled mobile robots is designed to track the reference trajectory. The Kalman observer is used to estimate un-measurable states of the robot. Furthermore, the optimal linear control together with system identification techniques yields simpler controller than nonlinear controllers. Designed controller and verified model are simulated using the MATLAB-Simulink software. Results show the effectiveness of the controller in tracking the desired reference trajectory.