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The advancement in embedded systems and positional accuracy with base station GPS modules created opportunity to develop high performance autonomous ground vehicles. However, the development of vehicle model and making accurate state estimations play vital role in reducing the cross track error. The present research focus on developing Linear Quadratic Gaussian (LQG) with Kalman estimator for autonomous ground vehicle to track various routes, that are made with the series of waypoints. The model developed in the LQG controller is a kinematic bicycle model, which mimics 1/5th scale truck. Further, the cubic spline fit has been used to connect the waypoints and generate the continuous desired/target path. The testing and implementation has been done at APS labs, MTU on the mentioned vehicle to study the performance of controller. Python has been used for simulations, controller coding and interfacing the sensors with controller.