Autonomous navigation of drones using computer vision has achieved promising performance. Nano-sized drones based on edge computing platforms are lightweight, flexible, and cheap, thus suitable for exploring narrow spaces. However, due to their extremely limited computing power and storage, vision algorithms designed for high-performance GPU platforms cannot be used for nano drones. To address this issue this paper presents a lightweight CNN depth estimation network deployed on nano drones for obstacle avoidance. Inspired by Knowledge Distillation (KD), a Channel-Aware Distillation Transformer (CADiT) is proposed to facilitate the small network to learn knowledge from a larger network. The proposed method is validated on the KITTI dataset and tested on a nano drone Crazyflie, with an ultra-low power microprocessor GAP8.