Modeling head-related transfer functions via spatial-temporal Gaussian process

We propose a novel application of a family of non-parametric statistical models to estimate head-related transfer functions (HRTFs) using spatial-temporal Gaussian processes (GPs). In this approach, we model the head-related impulse response (HRIR) utilizing non-parametric regression via a GP. The challenge posed by this problem involves accurate modeling of the spatial correlation structure jointly with the temporal correlation structure at each spatial location for the HRIR. We solve this problem by constructing a joint spatial-temporal kernel characterizing the GP regression model. To perform inference, we estimate the hyper-parameters of the GP regression kernel via maximum signal-to-deviation-ratio estimation on the basis of a real experimental setup in which we collected observations of the HRIR using two head-and-torso simulators (HATSs): KEMAR and B&K. We also perform cross validation of the model by training on the KEMAR system and assessing the generalization of our model and its out-of-sample predictive power for HRIRs at any locations that we predict by the model assessed on the B&K system. The corresponding HRTFs are obtained as the Fourier transform of the HRIRs. In the experiments, we show that our method is robust against variation in the azimuth interval needed to perform high-accuracy interpolation and has the expressive power to handle the individual characteristics of each HATS.