Simultaneous Estimation of Euclidean Distances to a Stationary Object's Features and the Euclidean Trajectory of a Monocular Camera

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Data-based, exponentially converging observers are developed for a monocular camera to estimate the Euclidean distance (and hence accurately scaled coordinates) to features on a stationary object and to estimate the Euclidean trajectory taken by the camera while tracking the object, without requiring the typical positive depth constraint. A Lyapunov-based stability analysis shows that the developed observers are exponentially converging without requiring persistence of excitation through the use of a data-based learning method. An experimental study is presented, which compares the developed Euclidean distance observer to previous observers demonstrating the effectiveness of this result.