Synchronization is a challenging problem for wireless nodes, especially for applications demanding good synchronization accuracy over wide areas. In that case, the GPS is a valuable solution as the nodes can independently synchronize to UTC. However, the energy consumption of a GPS receiver (over 100 mW when switched on) is not sustainable on a wireless node. Therefore, in this work, we developed a synchronization scheme based on periodic extinctions of the GPS receiver. The goal is to study the GPS power switching effect on the synchronization accuracy.To do so, a node with dedicated timestamping hardware was designed. Two clock models were compared to predict the node time when the GPS is off and the impact of a Kalman filter, to remove the GPS noise, was evaluated. From experimental data, we show that the choice of the clock model depends on the accuracy needed and that the Kalman filter improves the estimation of the clock frequency for both models. In our design, the GPS can be off from 60% up to 95% of the time for mean synchronization errors of 20 ns to 420 ns, respectively. This work demonstrates that GPS power switching is an efficient solution to reduce energy costs while maintaining a high synchronization accuracy.