Ground-based pseudolite systems (GBPS) have recently rekindled interest. Which broadcasts GNSS-like signals and can be flexibly deployed in these locations based on positioning needs, avoiding the impacts of building obstruction and offering high accuracy positioning services without ionosphere interference. Providing accurate and robust time synchronization among nodes is one of the most challenging problems for designing and operating GBPS. The low time synchronization precision of GBPS is due to the lack of high accuracy oscillators and measurement noise. Time synchronization can be accomplished in a variety of ways. However, existing methods lack adaptive tuning capability, crystal oscillators are severely affected by complex and changing environmental factors such as temperature. When the time synchronization information of the reference station is lost or the environment changes, the time of the slave station will generate errors by using these methods and cause the positioning failure. A novel theoretic time synchronization algorithm, named Extreme Learning Machine Kalman Filter (ELMKF) is presented to synchronize the base stations in GBPS in this paper. The proposed method uses a pre-trained learning model to reduce the volatility of input variables and provides timely information, which improves the filter's accuracy and stability. In addition to the observational information, this new method can give predictive values to support the station’s synchronization with the system when the slave station has no line of sight (LOS) signal from the master station. The performance of the proposed method is examined for simulations that correspond to natural world restrictions, as well as a detailed comparison with the well-known adaptive Kalman Filter algorithm.