Range Estimation of a Moving Target Using Ultrasound Differential Zadoff–Chu Codes

High-accuracy range estimation is essential in modern applications and technologies. However, it is challenging to estimate the continuous-range of a moving target, especially under Doppler effects. This article 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 over its performance when using regular Zadoff-Chu (ZC) sequences. We propose a reduced-complexity ranging algorithm using DZC sequences and show that it outperforms the regular ZC ML-based range estimation. We evaluate the proposed system in a typical indoor environment using a low-cost ultrasound hardware. Under a low signal-to-noise ratio (-10 dB SNR), more than 90% of the range estimates have less than a 1.6-mm error, with a movement range from 0.2 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) of less than 0.76 mm in a high SNR scenario (10 dB), and an RMSE less than 0.85 mm in a low SNR scenario (-10 dB). For a larger movement range from 1.8 to 4.2 m with a maximum velocity of 1.91 m/s, the proposed system provides range estimates with an RMSE less than 7.70 mm at 10 dB SNR.