HRTF magnitude modeling using a non-regularized least-squares fit of spherical harmonics coefficients on incomplete data

Head-related transfer functions (HRTFs) represent the acoustic transfer function from a sound source at a given location to the ear drums of a human. They are typically measured from discrete source positions at a constant distance. Spherical harmonics decompositions have been shown to provide a flexible representation of HRTFs. Practical constraints often prevent the retrieval of measurement data from certain directions, a circumstance that complicates the decomposition of the measured data into spherical harmonics. A least-squares fit of coefficients is a potential approach to determining the coefficients of incomplete data. However, a straightforward non-regularized fit tends to give unrealistic estimates for the region were no measurement data is available. Recently, a regularized least-squares fit was proposed, which yields well-behaved results for the unknown region at the expense of reducing the accuracy of the data representation in the known region. In this paper, we propose using a lower-order non-regularized least-squares fit to achieve a well-behaved estimation of the unknown data. This data then allows for a high-order non-regularized least-squares fit over the entire sphere. We compare the properties of all three approaches applied to modeling the magnitudes of the HRTFs measured from a manikin. The proposed approach reduces the normalized mean-square error by approximately 7 dB in the known region and 11 dB in the unknown region compared to the regularized fit.