Contents I. Introduction
It is well known that state estimation of dynamic systems with both process and measurement noise inputs is a very important and challenging problem in engineering applications [1], [19]. The celebrated Kalman filtering (also called filtering) [12], [27] has found many applications in aerospace [20], economics [16] etc., which minimizes the norm of the filtering error transfer function under the assumption that the noise processes have known power spectral densities. In many practical situations, however, we may not be able to have exactly known information on the spectral densities of the noise processes. In such cases, an alternative is to reformulate the estimation problem in an filtering framework, which has been well addressed for different systems through different techniques during the past decade (see, for instance, [6], [8], [10], [15], [28], and the references therein). It is noted that although filtering offers much better robustness in performance than filtering, filtering may be very conservative and may lead to a large intolerable estimation error variance when the system is driven by white noise signals. Therefore, to capture the benefits of both pure and filters, the mixed filtering problem, which simultaneously takes into account the presence of two kinds of exogenous signals (that is, the energy-bounded disturbance input and the stochastic disturbance input with known statistics), was introduced in [3]. An important application of the mixed filtering in aerospace can be found in [21].
