With satellite platforms gazing at a target territory, the captured satellite videos exhibit local misalignment and local intensity variation on some stationary objects that can be mistakenly extracted as moving objects and increase false alarm rates. Typical approaches for mitigating the effect of moving cameras in moving object detection (MOD) follow domain transformation technique, where the misalignment between consecutive frames is restricted to the image planar. However, such technique cannot properly handle satellite videos, as the local misalignment on them is caused by the varying projections from the 3D objects on the Earth's surface to 2D image planar. In order to suppress the effect of moving satellite platform in MOD, we propose a Moving-Confidence-Assisted Matrix Decomposition (MCMD) model, where foreground regularization is designed to promote real moving objects and ignore system movements with the assistance of a moving-confidence score estimated from dense optical flows. For solving the convex optimization problem in MCMD, both batch processing and online solutions are developed in this study, by adopting the alternating direction method and the stochastic optimization strategy, respectively. Experimental results on the videos captured by SkySat and Jilin-1 show that MCMD outperforms the state-of-the-art techniques with improved precision by suppressing effect of nonstationary satellite platforms.