Multi-target azimuth estimation using a single acoustic vector sensor via a mixture of wrapped Cauchy distributions

A single acoustic vector sensor (AVS) enables collocated measurements of acoustic pressure and three orthogonal particle velocity components, providing unambiguous azimuth estimation. However, azimuth estimation methods adapted from array signal processing to a single AVS often suffer from limited robustness and angular resolution. Conventional active sound intensity approaches are likewise challenged in multi-target scenarios and require prior knowledge of the signal-to-noise ratio. To address these limitations, this study preserves the frequency-domain processing framework of the complex sound intensity method and introduces a mixture of wrapped Cauchy distribution (MWC) to characterize the statistical distribution of sound intensity-derived direction angles. The expectation–maximization algorithm clusters frequency-dependent azimuth estimates within a specified frequency band, enabling multi-target azimuth estimation without prior SNR knowledge. To assess algorithmic performance, the influence of multi-target signal coherence and energy ratios on azimuth estimation based on the complex sound intensity method is analytically derived and examined. Three simulations are included: MWC goodness-of-fit under different conditions, comparison with existing methods, and assessment of multi-target tracking. Finally, experimental data acquired in the South China Sea are used to validate the proposed method, demonstrating its capability to accurately estimate the azimuths of multiple targets.