Optimizing Kalman optimal observer for state affine systems by input selection

In this paper, a new algorithm to build an optimal input for state reconstruction in the class of state-affine systems is proposed, in the sense that it enhances the performances of a Kalman-like observer, as well as it guarantees the system observability. The approach relies on the fact that for a state-affine system, as soon as the input is defined as a function of time, Kalman filtering theory can be applied. In fact, it is first highlighted how an appropriate choice of the system input can improve the Kalman filtering performance in this case. It is then emphasized how this input selection amounts to a control problem, which can be solved by an appropriate optimization algorithm. Finally, the algorithm is applied to a case of fault detection in a pipeline as an illustrative example, with some simulation results showing the observer performance improvement with the proposed input.