Hybrid multi-harmonic model for the prediction of interaural time differences in individual behind-the-ear hearing-aid-related transfer functions

Spatial sound perception in aided listeners partly relies on hearing-aid-related transfer functions (HARTFs), describing the directional acoustic paths between a sound source and the hearing-aid (HA) microphones. Compared to head-related transfer functions (HRTFs), the HARTFs of behind-the-ear HAs exhibit substantial differences in spectro-temporal characteristics and binaural cues such as interaural time differences (ITDs). Since assumptions on antipodal microphone placement on the equator of a three-concentric sphere are violated in such datasets, predicting the ITDs via Kuhn’s simple analytic harmonic model entails excessive errors. Although angular ear-canal offsets have been addressed in an extended Woodworth model, the prediction errors remain large if the frequency range does not comply with the model specifications. Tuned to the previously inaccurately modelled frequency range between 500 Hz and 1.5 kHz, we propose a hybrid multi-harmonic model to predict the ITDs in HRTFs and HARTFs for arbitrary directions in the horizontal plane with superior accuracy. The target model coefficients are derived from individual directional measurements of 30 adults, wearing two dual-microphone behind-the-ear HAs and two in-ear microphones. Model individualisation is facilitated by the availability of polynomial weights that are applied to subsets of individual anthropometric and HA features to estimate the target model coefficients. The model is published as part of the Auditory Modeling Toolbox (AMT, pausch2022) and supplemented with the individual features and directional datasets.