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After the type of object is identified, and it is associated as either a newly or previously observed object, it is useful to develop a mathematical model of where it may go next. The Kalman filter is an algorithm capable of being employed for this purpose. This thesis presents the design of a Kalman filter tuned for tracking objects commonly observed by autonomous vehicles and augmented to handle object motion exceeding its base design. The design results from an evaluation of relevant mathematical models of an object's motion, methods to quickly reduce the error of the filter's estimate, and methods to monitor the filter's performance to see if it is operating outside of normal bounds. Evaluation is performed through simulation and with real data from the KITTI autonomous vehicle benchmark. 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