Unmanned aerial vehicles (UAVs) are becoming more widely used in various industries, raising growing concerns about their safety and reliability. The flight data of UAVs can directly reflect their flight health status; however, the rarity of abnormal flight data and the spatiotemporal characteristics of these data represent a significant challenge for constructing accurate and reliable anomaly detectors. To address this, this study proposes an anomaly detection framework that fully considers the temporal correlations and distribution characteristics of flight data. This framework first combines a one-dimensional convolutional neural network (1DCNN) with an autoencoder (AE) to establish a feature extraction model. This model leverages the feature extraction capabilities of the 1DCNN and the reconstruction capabilities of the AE to thoroughly extract the spatiotemporal features from UAV flight data. Then, to address the challenge of adaptive anomaly detection thresholds, this research proposes a nonlinear model of support vector data description (SVDD) utilizing a 0/1 soft-margin loss, referred to as L0/1-SVDD. This model replaces the traditional hinge loss function in SVDD with a 0/1 loss function, with the goal of enhancing the accuracy and robustness of anomaly detection. Since the 0/1 loss function is a bounded, non-convex, and non-continuous function, this paper proposes the Bregman ADMM algorithm to solve the L0/1-SVDD. Finally, the difference between the reconstructed and the actual value is employed to train the L0/1-SVDD, resulting in a hypersphere classifier that is capable of detecting UAV anomaly data. The experimental results using real flight data show that, compared with methods such as AE, LSTM, and LSTM-AE, the proposed method exhibits superior performance across five evaluation metrics.