Spread spectrum sound-based local positioning systems (SSSLPS) have demonstrated centimeter-level accuracy in static scenarios and even for moving ground robots. However, when either the transmitter or the receiver is in motion, a major challenge arises because the Doppler effect induces a frequency shift in the acoustic signals, which can significantly degrade ranging accuracy. This chapter investigates the influence of the Doppler effect on acoustic positioning systems and introduces Doppler shift compensation algorithms. It describes the underlying principles and signal processing procedures of these methods, and emphasizes their role in enabling reliable, high-accuracy acoustic positioning in dynamic, GPS-denied environments.