Distance estimation in the spherical harmonic domain using the spherical wave model

•Proposal of novel spherical harmonic domain distance estimator.•Based on recurrence relations of spherical Hankel functions.•Frequency averaging to increase robustness.•Comparison of spherical harmonic domain distance estimators.•Experimental determination of applicable distance estimation range. Compact spherical microphone arrays are often used to record 3D sound scenes and are well suited to estimate the directions of sound sources. However, estimating the distance of a sound source is a challenging task due to the small dimensions of compact microphone arrays. In this work, different spherical harmonic domain distance estimation methods that utilize the spherical wave propagation model are investigated. Two existing methods are discussed and a new distance estimation method is proposed, which utilizes recurrence relations of spherical Hankel functions. The proposed estimator is related to the ratio between the real and imaginary components of the intensity vector for first-order spherical harmonic domain signals. In addition, a frequency averaging method is proposed and investigated for broadband distance estimation. Finally, the existing and proposed methods are evaluated using simulated anechoic and reverberant scenarios, as well as spherical microphone array recordings in outdoor and indoor environments.