Summary: Considering the inaccurate characteristics of noise statistics and the characteristics of non-zero mean noise statistics in the filtering process, in this paper, the \({H_\infty}\) fuzzy adaptive cubature Kalman filtering is designed based on the cubature Kalman filtering and \({H_\infty}\) filtering theory. Thus, the filter accuracy and robustness of the system unmodeled dynamics are improved effectively. Considering that a priori statistics characteristics of the noise that has been known are necessary during the cubature Kalman filtering process, a fuzzy adaptive method is proposed for estimation of the system noise and measurement noise, so as to improve the stability of the filtering and the rapidity of convergence. The simulation results demonstrate that the \({H_\infty}\) fuzzy adaptive cubature Kalman filtering is able to effectively estimate the noise characteristics and is more robust under the system perturbations.