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Head-related transfer functions (HRTFs) describe the filtering of the incoming sound by the torso, head, and pinna. As a consequence of the propagation path from the source to the ear, each HRTF contains a direction-dependent, broadband time-of-arrival (TOA). TOAs are usually estimated independently for each direction from HRTFs, a method prone to artifacts and limited by the spatial sampling. In this study, a continuous-direction TOA model combined with an outlier-removal algorithm is proposed. The model is based on a simplified geometric representation of the listener, and his/her arbitrary position within the HRTF measurement. The outlier-removal procedure uses the extreme studentized deviation test to remove implausible TOAs. The model was evaluated for numerically calculated HRTFs of sphere, torso, and pinna under various conditions. The accuracy of estimated parameters was within the resolution given by the sampling rate. Applied to acoustically measured HRTFs of 172 listeners, the estimated parameters were consistent with realistic listener geometry. The outlier removal further improved the goodness-of-fit, particularly for some problematic fits. The comparison with a simpler model that fixed the listener position to the center of the measurement geometry showed a clear advantage of listener position as an additional free model parameter.

Modeling the direction-continuous time-of-arrival in head-related transfer functions