This paper reports the results of our efforts to synchronize two 6 GHz oscillators to sub-picosecond precision using an ultra-precise phase detector and Kalman filter. Kalman filters have been incorporated into clock steering algorithms since the mid-1980s. However, they have not been used as frequently for the synchronization of high-frequency oscillators. We utilized a proportional-integral-differential (PID) controller with and without a Kalman filter. Our results show that the Kalman filter reduced timing jitter at long time scales, reduced timing jitter due to vibration and other frequency shocks, and enabled the system to synchronize more quickly after being shocked than when the PID loop was run by itself.