In this paper, we discuss optimal synchronization of local clocks using Global Positioning System (GPS) one-pulseper- second (1PPS) timing signals. To eliminate sawtooth errors that are peculiar to the 1PPS signals and optimally steer the clock errors each M seconds, we propose the use of a ramp-predictive finite-impulse-response (FIR) filter that is known to be optimal for clock models on large averaging horizons. A low-pass filter is used to smooth the hold filter output between the optimally predicted points. A GPS-locked crystal clock has been investigated in detail in terms of the time interval error, Allan deviation, and precision time protocol (PTP) variance. A high-efficiency implementation of the proposed synchronization algorithm is experimentally demonstrated.