Stubborn and Dead-Zone Redesign for Nonlinear Observers and Filters

We propose a redesign paradigm for stable estimators by introducing a saturation or a dead-zone nonlinearity with adaptive thresholds on the output injection term. Such nonlinearities allow improving the sensitivity to measurement noise in different scenarios (impulsive disturbances or persistent noise such as sensor bias), while preserving the asymptotic convergence properties of the original observer. These redesigns apply to a broad class of state estimators, including linear observers, observers for input-affine systems, observers for Lipschitz systems, observers based on the circle criterion, high-gain observers, standard and extended Kalman filters. Simulation results confirm the effectiveness of both the stubborn and dead-zone redesigns.