The simultaneous localization and mapping (SLAM) problem has been investigated by many researchers, and solutions frequently rely on sensor based approaches, such as very accurate range/bearing sensors (mmw radar, laser rangefinders, imaging sonar) which measure the position of landmarks in the environment relative to the robot and complex kinematic vehicle models or inertial naviation systems which measure the motion of the robot through the environment. Some solutions also require that the robot can measure orientation by some accurate and external means, reducing pose estimation to position estimation. These solutions tend to rely on a Kalman Filter or Extended Kalman Filter to recursively estimate both the map and robot pose in one global, absolute coordinate system. In the proposed research, I will address the SLAM problem for an autonomous mobile robot in an unstructured environment using landmark bearing measurements and dead reckoning as its only means of sensing. I will investigate the use of a representation of the environment which parameterizes relationships between landmarks rather than their position in a global, absolute coordinate frame. These relationships are invariant to the position from which landmarks are observed, decoupling the uncertainties in landmark positions and robot position. This decoupling has implications on the way in which sensor fusion is done and the uncertainty in the environment map and robot position estimates which result. The aim of this research is to provide a more general framework for SLAM applicable over a wider range of scenarios, and to provide a solution to the SLAM problem that is efficient, scalable, and robust to sensing and modeling errors.