Adaptive Square-Root Unscented Kalman Filter: Implementation of Exponential Forgetting Factor

This paper proposes a new form of adaptive square root unscented Kalman filter that implements an exponential forgetting factor to update the filter. It aims at estimating the states of nonlinear systems without a priori knowledge about the statistics of noises. The filter updates the estimation of covariances of noises with time, and the updated covariances are used to update the states of the system. The proposed approach is implemented to a servo-hydraulic system which states and measurements are affected by time varying noises with time-varying statistics. The obtained results along with the mean square errors of the estimation of states confirmed the performance and precision of the proposed filter.