Derivation and adaptive enhancement of the sliding sigmoid filter

The Sliding Sigmoid Filter (SSF) is a type of predictor-corrector estimator that integrates sliding mode control concepts into the state estimation process. Unlike traditional Kalman filters, which rely on linear corrections, the SSF, similar to its predecessor the Sliding Innovation Filter (SIF), adjusts the system’s gain based on the magnitude of the innovation. However, the SSF employs the Sigmoid function to implement an update of the state. By modifying the correction step to account for non-linearities smoothly, the SSF enhances estimation accuracy, making it particularly useful in dynamic environments where the system model or sensor data may be prone to errors or fluctuations. This paper derives the recursive equations utilized in the SSF and makes advances in these equations with the implementation of an optimization approach to provide zero-knowledge covariance optimization.