White-box Differentiable Model of Perceived Localisation

Auditory models are useful tools for estimating perceptual attributes of a sound field. Integrating such auditory models in the optimisation of immersive sound systems is a promising strategy when listeners’ perception is central to the application. To that end, differentiability is key to allowing the perceptual model to be included in gradient-based optimisation loops. Existing differentiable models, however, are black-box deep-learning based, which limits their interpretability. In this paper, we propose an analytical white-box differentiable model of auditory localisation based on an existing non-differential model. Our evaluations show that the model produces outputs that are highly correlated with the outputs of the non-differential model and data collected in subjective listening tests. The proposed model also enables optimisation of amplitude panning laws in a stereophonic spatial sound field rendering through gradient descent. This study therefore demonstrates, more generally, the feasibility of designing and optimising immersive sound systems using white-box differentiable models of auditory perception.