Observer design for range and orientation identification

A reduced-order globally convergent observer to estimate the depth of an object projected on the image plane of a camera is presented, assuming that the object is planar or has a planar surface and the orientation of the plane is known. A locally convergent observer can be obtained when the plane unit normal is unknown, and the latter is estimated together with the depth of the object. The observer exploits the image moments of the object as measured features. The estimation is achieved by rendering attractive and invariant a manifold in the extended state space of the system and the observer. The problem is reduced to the solution of a system of partial differential equations. The solution of the partial differential equations can become a difficult task, hence it is shown that this issue can be resolved by adding to the observer an output filter and a dynamic scaling parameter.