The geometric unscented Kalman filter (GUF) is an effective method for state estimation due to its advantages of high precision, reasonable efficiency, and good stability. In order to further improve the filtering performance of GUF, multiple rotation matrices are first designed by optimizing the rotation angles of their corresponding sampling points with maximum likelihood estimation, leading to a novel sampling strategy, namely, rotating geometric unscented sampling (RGUS). Then, applying RGUS to the GUF framework generates a rotating geometric unscented Kalman filter (RGUF). Since observable measurements are generally corrupted by non-Gaussian noise, RGUF may suffer from performance degradation due to the used minimum mean square error (MMSE) criterion. To improve the robustness of RGUF against non-Gaussian noises, we propose a novel maximum correntropy rotating geometric unscented Kalman filter (MCRGUF) using the maximum correntropy criterion (MCC). Finally, a Cramér–Rao lower bound (CRLB) of MCRGUF is introduced as a performance indicator. Simulations on three examples validate the high filtering accuracy and strong robustness of MCRGUF in the presence of non-Gaussian noise.