Bounded-error constrained state estimation in presence of sporadic measurements

Abstract

This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for linear discrete-time models with additive unknown disturbances vectors, bounded by known possibly degenerate zonotopes and polytopes, corrupting respectively, the state difference equation and the sporadic measurement vectors, which are expressed as linear inequality and equality constraints on the state vector. New algorithms are designed considering the unprecedented fact that, due to equality constraints, the shape matrix of the ellipsoid characterizing all possible values of the state vector is non invertible. The two main size minimizing criterions (volume and sum of squared axes lengths) are examined in the time update step and also in the observation updating, in addition to a third one, minimizing some error norm and ensuring the input-to-state stability of the estimation error.