H2/H∞ filtering theory and an aerospace application

In many filtering problems of practical interest, some of the noise signals satisfy the assumptions of H2 (Kalman-Bucy) filtering, while others can be more accurately modelled as signals with bounded variance (hence more amenable to an H∞ filtering approach). These problems may be addressed by considering a mixed H2/H∞ filtering problem. In this paper we present a novel theory which solves the mixed problem exactly and in a computationally efficient way. The applicability of the theory is illustrated by designing a filter to estimate the states of an aircraft flying through a downburst.