As distributed sensing technologies evolve, the collection of time series data is becoming increasingly decentralized, which introduces serious challenges for both model training and data privacy protection. In response to this trend, federated time series anomaly detection enables collaborative analysis across distributed sensing nodes without exposing raw data. However, federated anomaly detection experiences issues with unstable training and poor generalization due to client heterogeneity and the limited expressiveness of single-path detection methods. To address these challenges, this study proposes FedSW-TSAD, a federated time series anomaly detection method based on the Sobolev–Wasserstein GAN (SWGAN). It leverages the Sobolev–Wasserstein constraint to stabilize adversarial training and combines discriminative signals from both reconstruction and prediction modules, thereby improving robustness against diverse anomalies. In addition, FedSW-TSAD adopts a differential privacy mechanism with L2-norm-constrained noise injection, ensuring privacy in model updates under the federated setting. The experimental results determined using four real-world sensor datasets demonstrate that FedSW-TSAD outperforms existing methods by an average of 14.37% in the F1-score while also enhancing gradient privacy under the differential privacy mechanism. This highlights the practical value of FedSW-TSAD for privacy-preserving anomaly detection in sensor-based monitoring systems such as industrial IoT, remote diagnostics, and predictive maintenance.