  High accuracy range estimation is an essential tool required in many modern
applications and technologies. However, continuous range estimation of a moving
target is a challenging task, especially under Doppler effects. This paper
presents a novel signal design, which we name differential Zadoff-Chu (DZC).
Under Doppler effects, DZC sequences improve the performance of the maximum
likelihood (ML)-based range estimation compared to its performance when using
regular ZC sequences. Moreover, a reduced-complexity ranging algorithm is
proposed utilizing DZC sequences and is shown to outperform the regular ZC
ML-based range estimation. The proposed system is evaluated in a typical indoor
environment, using low-cost ultrasound hardware. Under a low signal to noise
ratio (-10 dB SNR), more than 90% of the range estimates are in less than 1.6
mm error, with a movement range from $0.2$ m to 2.2 m and a maximum velocity of
0.5 m/s. For the same movement range, the system provides range estimates with
a root mean square error (RMSE) less than 0.76 mm in a high SNR scenario (10
dB), and an MSE less than 0.85 mm in a low SNR scenario (-10 dB). For a larger
movement range from 1.8 m to 4.2 m with a maximum velocity of 1.91 m/s, the
proposed system provides range estimates with RMSE less than 7.70 mm at 10 dB
SNR.
