Huber-based Unscented Kalman Filters with the q-gradient

This study presents the Huber-based unscented Kalman filters with the q-gradient (HUKF-Q). As an extension of the classical gradient vector based on the concept of Jackson's derivative, the q-gradient can be utilised to improve the optimisation performance of the Huber method, significantly. Combining the Huber method based on the q-gradient into state estimation based on the unscented transformation, generates the novel HUKF-Q. The Cramer-Rao lower bound is introduced as a performance measure metric. Compared with the conventional HUKF, the proposed HUKF-Q can achieve better filtering accuracy and robustness. In addition, the impact of the tuning parameter q on the filtering performance is discussed by simulations. Simulations on the two examples of univariate non-stationary growth model and bearings only tracking model, confirm the superior performance of the proposed HUKF-Q.