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Relative localization is an important ability for multiple robots to perform cooperative tasks in GPS-denied environments. This paper presents a novel autonomous positioning framework for monocular relative localization of multiple tiny flying robots. This approach does not require any groundtruth data from external systems or manual labeling. Instead, the proposed framework is able to label real-world images with 3D relative positions between robots based on another onboard relative estimation technology, using ultrawideband (UWB). After training in this self-supervised manner, the proposed deep neural network (DNN) can predict relative positions of peer robots by purely using a monocular camera. This deep learning-based visual relative localization is scalable, distributed, and autonomous. We also built an open-source and lightweight simulation pipeline by using Blender for 3D rendering, which allows synthetic image generation of other robots, and generalized training of the neural network. The proposed localization framework is tested on two real-world Crazyflie2 quadrotors by running the DNN on the onboard AIdeck (a tiny AI chip and monocular camera). All results demonstrate the effectiveness of the self-supervised multi-robot localization method. Video: https://youtu.be/7arkaIblPps