Ground-based pseudolite systems have some limitations, such as low vertical accuracy, multipath effects and near-far problems. These problems are not significant in airborne-based pseudolite systems. However, the monitoring of pseudolite positions is required because of the mobility of the platforms on which the pseudolites are mounted, and this causes performance degradation. To address these pseudolite system limitations, we propose an airborne relay-based regional positioning system that consists of a master station, reference stations, airborne relays and a user. In the proposed system, navigation signals are generated from the reference stations located on the ground and are relayed via the airborne relays. Unlike in conventional airborne-based systems, the user in the proposed system sequentially estimates both the locations of airborne relays and his/her own position. Therefore, a delay due to monitoring does not occur, and the accuracy is not affected by the movement of airborne relays. We conducted several simulations to evaluate the performance of the proposed system. Based on the simulation results, we demonstrated that the proposed system guarantees a higher accuracy than airborne-based pseudolite systems, and it is feasible despite the existence of clock offsets among reference stations.