Autonomous rendezvous and docking is an important research area within the new exploration missions called forth by NASA. Relative navigation requires special sensors and algorithms to provide the necessary information. It may be possible to use reflected GPS signals as a source of ``free'' relative navigation measurements. Thus requiring no additional hardware except added algorithmic complexity. This thesis examines the use of an extended Kalman filter with reflected GPS measurements as a form of bi-static radar. It compares two different types of dynamic models, an absolute orbit model versus Hill's equations. The scenarios were implemented in Matlab using Satellite Toolkit to generate a high fidelity truth model. The thesis also examines visibility of reflected signals in a typical Hubble rendezvous scenario. This is done by approximating the Hubble as a cylinder, and using geometric optics to predict the reflective pattern.