Abstract: The invention provides a method of sampling precision measurement signals to achieve an accurate measurement position at a particular measurement time, such that the measurement accuracy is unaffected by the velocity of motion. The method involves sampling each signal during a predetermined sampling period such that a signal from one sensor is sampled first, a signal from a second sensor sampled second, etc., and then the signals are sampled in reverse order such that the first signal sampled is sampled last. These sampled signals are averaged and produce a precision measurement at a time measured at one-half of the sampling time. In addition, this method can be applied to the use of separate scale tracks where each scale track is alternately sampled, or alternatively, where one scale track is sampled in the middle of the sampling period of another scale track.