Doppler Shift-Compensated FMCW Algorithm for Centimeter-Level Acoustic Single-Anchor Positioning of Moving Targets in Narrow Spaces

Abstract

This article proposes a novel Doppler shift-compensated frequency-modulated continuous wave (DSC-FMCW) algorithm for achieving high-precision time-of-arrival (TOA) estimation of moving targets based on acoustics. In this algorithm, the stationary speaker transmits a mixed signal with upchirp and downchirp components, received by the moving microphone. Measurements are then compensated using the DSC-FMCW method. We then apply this algorithm to achieve 2-D positioning of moving targets in narrow spaces, using only one external speaker. In this method, a mirror-image speaker concept is introduced, where the primary reflection from the opposite wall is treated as coming from the mirror-image speaker, while reflections from the floor and ceiling are excluded as multipath signals. Additionally, considering the inability to synchronize the microphone and speaker, we leverage the characteristics of narrow spaces and the Doppler effect to achieve precise clock synchronization by estimating the absolute distance from a reference position to the speaker. Experiments show that the DSC-FMCW algorithm outperforms existing methods, achieving high accuracy in both open and multipath-affected scenarios at a target speed of 1.5 m/s, with mean errors of 0.0219 and 0.0418 m, respectively. Additionally, experiments in a $1.735\times 6.5$ m corridor demonstrate an average error of 0.0446 m and a 95th percentile error of 0.0872 m. The proposed algorithm shows strong accuracy and robustness.