Unmanned Aerial Vehicles (UAVs) rely on satellite systems for stable positioning. However, due to limited satellite coverage or communication disruptions, UAVs may lose signals for positioning. In such situations, vision-based techniques can serve as an alternative, ensuring the self-positioning capability of UAVs. However, most of the existing datasets are developed for the geo-localization task of the objects captured by UAVs, rather than UAV self-positioning. Furthermore, the existing UAV datasets apply discrete sampling to synthetic data, such as Google Maps, neglecting the crucial aspects of dense sampling and the uncertainties commonly experienced in practical scenarios. To address these issues, this paper presents a new dataset, DenseUAV, that is the first publicly available dataset tailored for the UAV self-positioning task. DenseUAV adopts dense sampling on UAV images obtained in low-altitude urban areas. In total, over 27K UAV- and satellite-view images of 14 university campuses are collected and annotated. In terms of methodology, we first verify the superiority of Transformers over CNNs for the proposed task. Then we incorporate metric learning into representation learning to enhance the model's discriminative capacity and to reduce the modality discrepancy. Besides, to facilitate joint learning from both the satellite and UAV views, we introduce a mutually supervised learning approach. Last, we enhance the Recall@K metric and introduce a new measurement, SDM@K, to evaluate both the retrieval and localization performance for the proposed task. As a result, the proposed baseline method achieves a remarkable Recall@1 score of 83.01% and an SDM@1 score of 86.50% on DenseUAV. The dataset and code have been made publicly available on https://github.com/Dmmm1997/DenseUAV.