Application of Kalman filters with a loop delay in synchronization

Discrete-time Kalman filters under a loop-delay constraint suffer performance loss and cease to be optimal. In this letter, modified Kalman filters are proposed to compensate for loop delay. The proposed filter performance is similar to a Kalman predictor. The results are applied to synchronizer loop-filter, design. Closed form expressions for both the update gain and the performance values are derived for first- and second-order disturbance models.