Traditional satellite orbit determination methods primarily rely on post-processing on the ground, which results in significant time delays and fails to meet the real-time requirements of autonomous on-board tasks. To address this issue, this paper proposes an autonomous real-time orbit determination algorithm based on the extended Kalman filter (EKF). The algorithm integrates quality control of observational data, dynamic orbit integration, and parameter estimation techniques to achieve real-time orbit determination for low-Earth orbit (LEO) satellites. The accuracy of the algorithm was assessed by comparing the real-time and predicted orbits with the ground-based post-processed precise reference orbits. Results show that, after accumulating 72 hours of observational data, the three-dimensional position error of real-time orbit determination was 15.18 cm, and the three-dimensional position error of orbit prediction within 2 hours was better than 18.75 cm, meeting the requirements for autonomous mission planning. Moreover, validated on an embedded platform, the algorithm has a single calculation cycle of less than 35 seconds and a memory footprint of less than 4 MB, complying with the onboard resource requirements. This study not only provides a theoretical and technical foundation for the design of autonomous navigation systems for medium and high Earth orbit satellites but also holds engineering value for enhancing the real-time response capabilities of satellites in orbit.