Improving Kalman Filtering by Input Selection for Non-uniformly Observable State-Affine Systems
Résumé
In this paper, a problem of persistent input design for the application of a Kalman-like observer to a class of systems which are not uniformly observable is considered. The class of systems is that of state-affine ones, for which Kalman filtering theory can be applied as soon as the input is defined as a function of time. In fact, it is first highlighted how an appropriate choice of the system input can improve the performance of the Kalman filter in this case. It is then emphasized how this input selection amounts to a control problem, which can be solved by an appropriate optimization approach. This input design is finally illustrated with some simulation results on an application example.