The positioning accuracy determines the scope of the application of an unmanned aerial vehicle (UAV). In view of the existing UAV cooperative localization methods that normally require prior information and the assistance of external systems, such as the global positioning system (GPS), this study aims to adopt range radios to measure the time-of-arrival (TOA) information among UAVs and then perform clock synchronization and cooperative localization based on ranging measurements. We propose a framework to jointly estimate the clock error and relative distance, adjust the onboard clock, and perform relative positioning. To achieve autonomous clock synchronization and ranging, a practical approach based on peer-to-peer pseudorange measurements is proposed in this study. We modeled the synchronous two-way ranging (STWR) process using a discretetime state-space model, according to which a linear parameter estimation method and clock steering method are presented. Finally, a closed loop consisting of STWR, parameter estimation, and clock tuning is constructed to improve the ranging accuracy, which leads to improved localization accuracy. Simulation results show that the proposed approach outperforms existing methods and can achieve sub-nanosecond-level time synchronization and meter-level cooperative localization.