State estimation within a guaranteed interval

This paper presents a state estimator for systems linear in an unknown parameter. The estimate is given via a weighted mean of both an under- and an over-estimate provided by an interval observer. The weighting factor is computed in real-time from the difference between the output measurements and the interval bounds. The convergence of the estimate is first shown for a class of LTI systems. The generalization to a class of nonlinear systems is then presented. Both cases are illustrated with numerical simulations.