Some of the embodiments of the present disclosure provide a method for generating each of (i) a first signal and (ii) a second signal based at least in part on a position of a carriage, where the carriage is a component of a printing device, estimating (i) a major cycle duration associated with the first signal and (ii) a first minor cycle duration associated with the second signal, estimating a position of the carriage based at least in part on the estimated major cycle duration and the estimated first minor cycle duration, and generating a plurality of print synchronization pulses based at least in part on the estimated position of the carriage.