Energy–based approach for sound source distance measurement in reverberant rooms

This study addresses the challenge of estimating sound source distance in reverberant environments by evaluating the energy relationship between direct sound and reflected sound. This relationship is widely regarded as more robust for distance estimation than indicators based on time differences of arrival, especially under strong reverberation. However, many existing estimation methods still lack sufficient robustness. For instance, even a small coherence estimation error of about 1%–5% can lead to deviations of 5–15 dB in the derived energy ratio. In addition, when the source angle departs from 90° and the distance exceeds 3 meters, estimation errors of approximately 0.5–1 m may occur. To mitigate such instability, a geometrically constrained DRR estimation transformation is proposed from complex plane received mix signal coherence perturbation analysis. Based on the classic direct–diffuse decomposition model, the time-delay-induced coherence perturbation is analyzed, and reverberant noise distorts the coherence trajectory into a dynamically perturbation circle is revealed. On this basis, this paper adopts a near estimation method, whose pattern is perpendicular to the line formed by direct and diffuse coherence points. The transformed estimator is then applied to mid– and long–range distance estimation in both anechoic chambers and real classrooms. Experiments were conducted across multiple directions, distances, SNR conditions, and reverberant environments in two scenarios. The results demonstrate that the proposed estimator and transformation mechanism achieve distance estimates 0.2–0.5 m closer to the true value compared with other energy ratio based methods and time difference based approaches.