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We address the problem of robust state estimation of a class of discrete-timenonlinear systems with positive-slope nonlinearities when the sensors arecorrupted by (potentially unbounded) attack signals and bounded measurementnoise. We propose an observer-based estimator, using a bank of circle-criterionobservers, which provides a robust estimate of the system state in spite ofsensor attacks and measurement noise. We first consider the attack-free casewhere there is measurement noise and we provide a design method for a robustcircle-criterion observer. Then, we consider the case when a sufficiently smallsubset of sensors are subject to attacks and all sensors are affected bymeasurement noise. We use our robust circle-criterion observer as the mainingredient in building an estimator that provides robust state estimation inthis case. Finally, we propose an algorithm for isolating attacked sensors inthe case of bounded measurement noise. We test this algorithm throughsimulations.

A Robust Circle-criterion Observer-based Estimator for Discrete-time Nonlinear Systems in the Presence of Sensor Attacks and Measurement Noise