An adaptive unscented Kalman filtering approach using selective scaling

Classical Kalman filters require the exact knowledge of process noise and measurement noise covariance matrices. Different versions of Adaptive Kalman filters are used in situations where the noise covariance matrices are partially or fully unknown. In the discrete time case, one option is to use innovation-based adaptation laws to update the covariance matrices using measured data in a finite length observation window. This paper presents an augmented version of adaptive Kalman filters where additional state variables are used to estimate parameter values and/or unknown inputs. The behavior of the augmented state variables is modeled as random walk. The convergence properties of such adaptive filters may be poor, especially when the parameter values or the unknown inputs undergo a step-like change. To improve convergence, the paper suggests a selective scaling method so that uncertainty is scaled up for state variables which are not measured or belong to the set of augmented states if a specific scaling condition is satisfied. The method is applied for adaptive unscented Kalman filters that estimate parameters or unknown friction forces of a mechanical system as part of the augmented state vector. Simulation results for such applications are presented to show the effectiveness of the method.