Globally exponentially convergent observer for vision-based range estimation

A nonlinear observer is presented to estimate the distance from a moving camera to a feature point on a static object (i.e., range identification), where full velocity and linear acceleration feedback of the calibrated camera is assumed. The presented observer is globally exponentially stable and thus, identifies the range exponentially fast provided some observability condition is satisfied. A sufficient condition on the observer gain is derived to prove the stability using a Lyapunov-based analysis. The contribution of this work is the development of a global exponential range observer that as a result, enables the observer to encompass a larger set of camera motions.