An onboard robust and stable vision-inertial navigation system that makes an unmanned vehicle autonomous in its navigation capabilities in the absence of external navigation aids like a global positioning system (GPS). The system is robust to the sensor noise properties of the onboard vision and inertial sensors, as well as errors in initial estimates of the position and orientation of the vehicle. The system enables any unmanned vehicle to autonomously navigate an unfamiliar or unknown environment. The system is also stable and robust to uncertainties in the measurement noise and dynamics of the unmanned vehicle, and does not exhibit any instability when sensors are changed or when sensor noise properties change over time.