This paper proposes new sensor fault detection algorithms for linear discrete-time systems with bounded perturbations and bounded measurement noise. This fault detection technique is based on a zonotopic set-membership estimation method. The first proposed fault detection algorithm allows to detect the presence of a fault. A second algorithm leading to guaranteed state estimation in the presence of sensor faults is developed, sometimes leading to conservative results. Thereafter, the last proposed algorithm allows to reduce the conservativeness while offering an estimation of the state closer to the real state of the faulty system. An illustrative example is analyzed to show the performance of the proposed algorithms.