The sliding sigmoid filter

Traditional state estimation methods often become unreliable in the presence of measurement anomalies, abrupt disturbances, and nonlinear dynamics. Such conditions are ubiquitous in high-stakes operational settings, including air traffic surveillance, autonomous systems, and advanced manufacturing. These challenges expose an enduring methodological gap: the inability to ensure both strong robustness to uncertainty and stable, continuous correction behaviour. This paper aims to address these limitations by developing estimation methods that maintain stability while adapting intelligently to uncertainty. To this end, we introduce the Sliding Sigmoid Filter (SSF), a novel estimator that combines sliding-mode robustness with a continuous sigmoid-based gain function, and further extend it to the Adaptive Sliding Sigmoid Filter (ASSF), which adjusts its gain online using recent innovation statistics for fault detection and adaptive correction. Using linear and nonlinear simulation benchmarks together with a full experimental pipeline involving physics-informed neural network parameter identification and SSF-based state estimation for a magnetorheological damper, we evaluate the performance of the proposed filters against classical methods. The results show that SSF and ASSF significantly reduce estimation error, attenuate outliers more smoothly than threshold-based approaches, and provide faster recovery under measurement faults. Overall, the findings demonstrate that the proposed filters offer a practical and theoretically grounded alternative for robust state estimation in uncertain and fault-prone environments.