Navigating toy drones through uncharted GPS-denied indoor spaces poses significant difficulties due to their reliance on GPS for location determination. In such circumstances, the necessity for achieving proper navigation is a primary concern. In response to this formidable challenge, we introduce a real-time autonomous indoor exploration system tailored for drones equipped with a monocular \emph{RGB} camera. Our system utilizes \emph{ORB-SLAM3}, a state-of-the-art vision feature-based SLAM, to handle both the localization of toy drones and the mapping of unmapped indoor terrains. Aside from the practicability of \emph{ORB-SLAM3}, the generated maps are represented as sparse point clouds, making them prone to the presence of outlier data. To address this challenge, we propose an outlier removal algorithm with provable guarantees. Furthermore, our system incorporates a novel exit detection algorithm, ensuring continuous exploration by the toy drone throughout the unfamiliar indoor environment. We also transform the sparse point to ensure proper path planning using existing path planners. To validate the efficacy and efficiency of our proposed system, we conducted offline and real-time experiments on the autonomous exploration of indoor spaces. The results from these endeavors demonstrate the effectiveness of our methods.