Homography estimation between multiple aerial images can provide relative pose estimation for collaborative autonomous exploration and monitoring. The usage on a robotic system requires a fast and robust homography estimation algorithm. In this study, we propose an unsupervised learning algorithm that trains a Deep Convolutional Neural Network to estimate planar homographies. We compare the proposed algorithm to traditional feature-based and direct methods, as well as a corresponding supervised learning algorithm. Our empirical results demonstrate that compared to traditional approaches, the unsupervised algorithm achieves faster inference speed, while maintaining comparable or better accuracy and robustness to illumination variation. In addition, on both a synthetic dataset and representative real-world aerial dataset, our unsupervised method has superior adaptability and performance compared to the supervised deep learning method.