As unmanned aerial vehicles are used in more environments, flexible navigation strategies are required to ensure safe and reliable operation. Operation in the presence of degraded or denied GPS signal is critical in many environments, particularly indoors, in urban canyons, and hostile areas. Two techniques, laser-based simultaneous localization and mapping (SLAM) and monocular visual SLAM, in conjunction with inertial navigation, have attracted considerable attention in the research community. This paper presents an integrated navigation system combining both visual SLAM and laser SLAM with an EKF-based inertial navigation system. The monocular visual SLAM system has fully correlated vehicle and feature states. The laser SLAM system is based on a Monte Carlo scan-to-map matching, and leverages the visual data to reduce ambiguities in the pose matching. The system is validated in full 6 degree of freedom simulation, and in flight test. A key feature of the work is that the system is validated with a controller in the navigation loop.