This paper describes the design, analysis and testing of a navigation system based on combined GPS and laser-scanner measurements. Using carrier phase differential GPS, centimeter-level positioning of autonomous ground vehicles (AGVs) is achievable. However, GPS signals are easily attenuated or blocked, so their use is generally restricted to open-sky areas. In response, in this work we augment GPS with two-dimensional laser-scanner measurements. The latter are available when GPS is not, and provide in addition, a means for obstacle detection. Laser measurements are processed using a Simultaneous Localization And Mapping (SLAM) procedure. Vehicle and landmark position estimation is performed simultaneously using an extended Kalman filter; we address the data association problem, which establishes correspondences between consecutive sets of measurements and a continuously updated map of landmarks. The resulting laser-based SLAM solution is carefully analyzed by identifying and isolating the individual effects of the joint angular and ranging measurements, the combination of measurements from multiple landmarks, the correlation between vehicle and landmark position estimates, and the uncertainty on the vehicle's heading angle. A detailed covariance analysis is then carried out in order to quantify the sensitivity of the vehicle's position estimate error to the vehicle's velocity, the landmark geometry, and the laser's range limit. Further sensitivity analyses are structured around two scenarios: first, a 'forest scenario' where the vehicle roves across a GPS-unavailable area using tree trunks as landmarks in order to maintain a precise position estimate; second, an 'urban canyon' scenario describing how we can make use of GPS signals that alone are too few to generate a position fix, by utilizing additional laser measurements to buildings' edges. Finally, experimental results using a prototype AGV are presented to validate the navigation system performance.