Improving the Robustness of Stationary Kalman Filter via Parametric Design

This paper presents a novel design approach for a robust sub-optimal Kalman filter using parametric eigenstructure placement. Initially, a system without model uncertainty is considered, and a condition for the parametrically designed filter to be optimal is obtained. It is shown, under this condition, that there is a subset of the parametrically designed gain matrices which will also lead to Kalman filter. For the system with structured model uncertainty, a performance functional index is constructed in which the penalty terms to both the sensitivity and the non-optimality of the filter are included. A parametrically designed gain matrix is then evaluated via standard minimisation and the so-obtained filter is shown to be sub-optimal and more robust than Kalman filter.