Unmanned aerial vehicles (UAVs) have been used in a wide range of applications and become an increasingly important radar target. To better model radar data and to tackle the curse of dimensionality, a three-step classification framework is proposed for UAV detection. First we propose to utilize the greedy subspace clustering to handle potential outliers and the complex sample distribution of radar data. Parameters of the resulting multi-Gaussian model, especially the covariance matrices, could not be reliably estimated due to insufficient training samples and the high dimensionality. Thus, in the second step, a multi-Gaussian subspace reliability analysis is proposed to handle the unreliable feature dimensions of these covariance matrices. To address the challenges of classifying samples using the complex multi-Gaussian model and to fuse the distances of a sample to different clusters at different dimensionalities, a subspace-fusion scheme is proposed in the third step. The proposed approach is validated on a large benchmark dataset, which significantly outperforms the state-of-the-art approaches.