How positioning inaccuracies influence the spatial upsampling of sparse head-related transfer function sets

Determining full-spherical individual sets of head-related transfer functions (HRTFs) based on sparse measurements is a prerequisite for various applications in virtual acoustics. To obtain dense sets from sparse measurements, spatial upsampling of sparse HRTF sets in the spatially continuous spherical harmonics (SH) domain can be performed by an inverse SH transform. However, this involves artifacts caused by spatial aliasing and order truncation. In a previous publication we presented the SUpDEq method (Spatial Upsampling by Directional Equalization), which reduces these artifacts by a directional equalization prior to the SH transform. Generally, apart from the spatial resolution of the HRTF set, measurement inaccuracies, for example caused by displacements of the head during the measurement, can influence the spatial upsampling as well. By this direction-depending temporal and spectral deviations are added to the dataset, which in the process of spatial upsampling can cause artifacts comparable to spatial aliasing errors. To reduce the influence of the distance inaccuracies, we present a method for distance error compensation that performs an appropriate distance-shifting of the measured HRTFs. Determining the required values for the shift benefits from the directional equalization performed by SUpDEq and results in time-aligning the directionally equalized HRTFs. We analyze the influence of the angular and distance displacements on spectrum, on interaural cues and on modeled localization performance. While limited angular inaccuracies only have a low impact, already small random distance displacements cause strong impairments, which can be significantly reduced applying the proposed distance error compensation method.