In this theoretical investigation, we consider the problem of estimating the state of a moving object, whose motion is described by a set of state equations. The observation equation is a nonlinear map between the position state variables of the object and the position on the plane of a camera(s). This mapping depends on variables such as: camera position and orientation, lens position, zoom action. Given a known time variation of these quantities, the observation equation is a known, nonlinear function. The variance of the measurement error is also a function of the state and the camera variables, hence time-varying for a given time profile of the camera variables. In that case, the state can be estimated with an extended Kalman filter. The observation can be optimised by solving the following problem: given an expected state trajectory, find the time history of camera variables that will minimize some function of the covariance of the state estimation error. A receding horizon method is used.
K. Benameur, P.R. Bélanger