Set-Membership filtering with incomplete observations

Abstract This study addresses the set-membership estimation problem for a class of discrete time-varying systems with incomplete observations. A set-membership filter is developed and a recursive algorithm is proposed to calculate the state estimate ellipsoid which contains the true value. To solve the problem that the conventional set-membership filter cannot guarantee the stability when applied to discrete time-varying systems with incomplete observations, a quantitative analysis method about incomplete observations is developed and a tight bound of the estimation error is found based on interval analysis and some bounded noise assumptions. In terms of bounded assumptions, the relationship between the bound of estimated error and the data dropout rate is obtained. If the data dropout rate is less than a maximal value, the set-membership filter is asymptotically stable. The proposed filter is applied to a two-state example to demonstrate the effectiveness of theoretical results.

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