Multi-source information fusion (MSIF) leverages diverse data streams to enhance decision-making, situational awareness, and system resilience. Federated Learning (FL) enables MSIF while preserving privacy but suffers from client drift under high data heterogeneity, leading to performance degradation. Traditional mitigation strategies rely on reference-based gradient adjustments, which can be unstable in partial participation settings. To address this, we propose Gradient Centralized Federated Learning (GC-Fed), a reference-free gradient correction method inspired by Gradient Centralization (GC). We introduce Local GC and Global GC, applying GC during local training and global aggregation, respectively. Our hybrid GC-Fed approach selectively applies GC at the feature extraction layer locally and at the classifier layer globally, improving training stability and model performance. Theoretical analysis and empirical results demonstrate that GC-Fed mitigates client drift and achieves state-of-the-art accuracy gains of up to 20% in heterogeneous settings.