Research on augmentation and supplement systems for navigation systems has become a significant aspect in comprehensive positioning, navigation and timing (PNT) studies. The BeiDou-3 navigation satellite system (BDS-3) has constructed a dynamic inter-satellite network to gain more observation data than ground monitoring stations. Low Earth orbit (LEO) satellites have advantages in their kinematic velocity and information carrying rate and can be used as satellite-based monitoring stations for navigation satellites to make up for the distribution limitation of ground monitoring stations. This study constructs multi-source observation links with satellite-to-ground, inter-satellite and satellite-based observation data, proposes an orbit synchronization method for navigation satellites and LEO satellites and verifies the influence thereof on orbit accuracy with different observation data. The experimental results under conditions of real and simulated observation data showed the following: (1) With the support of satellite-based observation links, the orbit accuracy of the BDS-3 MEO satellites could be improved significantly, with a 78% improvement with the simulation data and a 76% improvement with the real data. When the navigation satellites leave the monitoring area of the ground monitoring stations, the accuracy reduction tendency of the orbit prediction could also be slowed down with the support of the LEO satellites and the accuracy could be maintained within centimeters. (2) Comparing the orbit accuracy with the support of the satellite-to-ground observation links, the orbit accuracy of the MEO satellites could be improved by 65.5%, 73.7% and 79.4% with the support of the 6, 12 and 60 LEO satellites, respectively. When the observation geometry and the covering multiplicity meet the basic requirement of orbit determination, the improvements to the orbit accuracy decrease with the growth of LEO satellite numbers. (3) The accuracy of orbit determination with the support of the LEO satellites or the inter-satellite links was at the centimeter level for both, verifying that inter-satellite links and satellite-based links can be used as each other’s backups for navigation satellites. (4) The accuracy of orbit determination with the multi-source observation links was also at the centimeter level, which was not better than the results with the support of the satellite-to-ground and inter-satellite links or the satellite-to-ground and satellite-based links.