This article describes a simple monocular navigation system for a mobile robot based on the map-and-replay technique. The presented method is robust and easy to implement and does not require sensor calibration or structured environment, and its computational complexity is independent of the environment size. The method can navigate a robot while sensing only one landmark at a time, making it more robust than other monocular approaches. The aforementioned properties of the method allow even low-cost robots to effectively act in large outdoor and indoor environments with natural landmarks only. The basic idea is to utilize a monocular vision to correct only the robot's heading, leaving distance measurements to the odometry. The heading correction itself can suppress the odometric error and prevent the overall position error from diverging. The influence of a map-based heading estimation and odometric errors on the overall position uncertainty is examined. A claim is stated that for closed polygonal trajectories, the position error of this type of navigation does not diverge. The claim is defended mathematically and experimentally. The method has been experimentally tested in a set of indoor and outdoor experiments, during which the average position errors have been lower than 0.3 m for paths more than 1 km long
