Interval Kalman Filtering - Aerospace and Electronic Systems, IEEE Transactions on

0018-9251/97/$10.00 @ 1997 IEEE Robust estimation, or robust filtering, for uncertain linear systems has been investigated under different conditions in the last two decades (see, for instance, [8, 91 and the references therein). In particular, robust Kalman filtering with respect to uncertain linear systems is still an active research topic that attracts increasing interest, on which several approaches have been proposed: using H,-criteria 14, 12, 14, 16, 171, set-valued estimations [5, 6, 111, and interval systems analysis [7, 13, 15, 181. It is well known that optimal estimates are given by a conditional expectation of the unknown random variable (or random vector), under the condition that the data to be used were given [2]. The standard Kalman filtering scheme was derived directly from this statistical criterion, and is hence optimal in the sense that it exactly (not approximately) satisfies the criterion, and so provides a precise linear, unbiased and minimum-error-variance estimate at each recursive step throughout the filtering process. However, to the best of our knowledge, the aforementioned approaches to robust filtering essentially suggest approximate estimations, such as the best solution in the worst case, and do not provide theoretically optimal estimations (in the statistical sense of conditional expectation) for each linear system existing within the uncertain bounds. Besides, these approaches have more or less lost the fundamental characteristic of the standard Kalman filter (SKF) that satisfies the familiar statistical conditions and criteria.