The classical sigma-point Kalman filter (SPKF) is widely used in a spacecraft state estimation area with the Gaussian white noise hypothesis. The actual sensor noise is often disturbed by outliers in the harsh space environment, and the SPKF algorithm will reduce the filtering accuracy or even diverge. In this study, to enhance the robustness under non-Gaussian noise condition, the outlier-robust SPKF algorithm based on a centered error entropy (CEE) criterion is derived. Unscented Kalman filter (UKF) is typical of SPKF; combining the deterministic sampling criterion with the centered error entropy criterion, a robust centered error entropy UKF (CEEUKF) algorithm is proposed. The CEEUKF uses the unscented transformation (UT) method to perform time update step and then uses the robust regression model and CEE criterion to reconstruct the measurement update step. The effectiveness of the proposed CEEUKF is verified by a spacecraft attitude determination system.