This thesis examines the design and implementation of the navigation solution for an autonomous ground vehicle suited with global position system (GPS) receivers, an inertial measurement unit (IMU), and wheel speed sensors (WSS) using the framework of Kalman filtering (KF). To demonstrate the flexibility of the KF several methods are explored and implemented such as constraints, multi-rate data, and cascading filters to augment the measurement matrix of a main filter. GPS and IMU navigation are discussed, along with common errors and disadvantages of each type of navigation system. It is shown that the coupling of sensors, constraints, and self-alignment techniques provide an accurate solution to the navigation problem for an autonomous vehicle. Filter divergence is discussed during times when the states are unobservable. Post processed data is analyzed to demonstrate performance under several test cases, such as GPS outage, and the effect that the initial calibration and alignment has on the accuracy of the solution.