The unmanned aerial vehicles (UAVs) will play an important role in the future urban transportation systems. This requires designing robust localization schemes especially for non-cooperative UAVs that do not share any information about their movements. This paper designs a multimodal UAV localization framework which utilizes camera, LiDAR and radar sensing modalities. The underlying data processing and the subsequent inference of the UAV location are distributed among the sensing nodes and the edge server attached to the base station. The proposed UAV localization framework addresses three key challenges. First, the sensing nodes have limited computing and communication resources, and they contain only single modality sensors. Second, the multimodal data differ greatly in the sampling rates, time alignment and the encodings. Third, the changes in the environment and the hardware failures cause the modal data to degrade, or to be completely missing. The proposed localization framework utilizes several data processing modules including a information-bottleneck (IB)-based compression module that extracts the most relevant features from each modality, a time-encoding alignment module that provides the unified representation in a shared latent space, a multimodal fusion module that accounts for the degraded and missing data, and a Mamba-based regression module that predicts the present UAV location. The experiments involving a real-world dataset demonstrate that the proposed framework accurately and reliably obtains the UAV location while outperforming other existing frameworks.