State estimation in presence of uncertain model error statistics based on filter stability. Application to an adaptive filter

Abstract

This paper proposes an optimal filtering approach for state estimation in the presence of uncertainties in model error statistics. The approach is developed based on the important filter property of stability, which ensures reliable performance in the presence of disturbances. The resulting algorithm is particularly efficient for adaptive filtering and is designed to optimize filter performance in the face of uncertainty. Numerical experiments are presented to illustrate and confirm the high performance of the proposed approach.