A navigation system useful for providing speed and heading and other navigational data to a drive system of a moving body, e.g., a vehicle body or a mobile robot, to navigate through a space. The navigation system integrates an inertial navigation system, e.g., a unit or system based on an inertial measurement unit (IMU). with a vision-based navigation system unit or system such that the inertial navigation system can provide real time navigation data and the vision-based navigation can provide periodic, but more accurate, navigation data that is used to correct the inertial navigation system's output. The navigation system was designed with the goal in mind of providing low effort integration of inertial and video data. The methods and devices used in the new navigation system address problems associated with high accuracy dead reckoning systems (such as a typical vision-based navigation system) and enhance performance with low cost IMUs.