AbstractIn many industrial applications, physical equipment for measuring may suffer from transient malfunctions, which can cause data outliers. This article addresses the problem of guaranteed set‐membership estimation of uncertain linear systems subject to outliers in measurements. To solve this problem, a robust set‐membership estimator is designed using the forward‐backward contraction procedure and a zonotopic filter. The setting up of these techniques offers two main advantages. On the one hand, outliers can be identified and discarded, which helps to resume the guaranteed property and avoid deadlock situations. On the other hand, the proposed method uses set‐inversion to fuse the available historical data, so as to attenuate the effect of uncertainties. Numerical examples are provided to show the efficiency of the proposed estimator.