Inspired by human perception, novel research into the sub-domain of robotic perception, known as extended object tracking, is presented. This research is motivated by the practical challenges of deploying robot driven cars (aka robocars, self-driving cars, autonomous road vehicles, etc.) into the existing transportation infrastructure alongside human-controlled vehicles. In this vein, arbitrary, uncooperative extended objects maneuvering in close proximity to the ego vehicle are considered, without a priori knowledge of the environment (e.g. road structure, traffic laws, etc.) or the objects to be tracked (e.g. controls, intent, shape, size, type, etc.). The novel approaches presented here are primarily aimed at improving the precision and accuracy of extended object tracking by mitigating the inherent information loss associated with interpreting sensor data returned from arbitrary extended objects. Specifically, a rigorous probabilistic occlusion model is derived for identifying and fusing negative information inherently present in sensor data; information that is heavily leveraged by humans, but largely ignored by robots. Further, a rigorous estimation framework is proposed for estimating the detailed shape of extended objects jointly with their kinematics; detailed object shape estimates enable explicit sensor models, which, in turn, engender improved tracking precision. Additionally, a hierarchical tracking framework is proposed for dynamically allocating computational resources in proportion to an objects continuously changing relevance to the ego robot task, as defined by novel probabilistic object relevancy metrics. As a result, at any given time, objects considered to be of central importance to the ego robot task are tracked with relatively complex, high-precision methods, while objects deemed merely peripheral to the ego robot task are tracked with relatively low complexity, low precision methods; a direct analog to the human concepts of attention and focus in allocating finite cognitive resources. The proposed work is evaluated via simulation and experiments involving Cornell University's autonomous Chevy Tahoe, Skynet, demonstrating that non-traditional sensor models are necessary for high precision tracking of arbitrary extended objects, and that humans are worth emulating en route to this goal.