Analytical Exploration of Spatial Audio Cues: A Differentiable Multi-Sphere Scattering Model

TL;DR

This paper introduces a differentiable, analytical model for underwater sound scattering from layered spheres, improving spatial localization and tracking by integrating physics-based modeling with machine learning.

Contribution

It presents a novel, closed-form, differentiable scattering model inspired by underwater animal anatomy, enabling enhanced localization and tracking in complex acoustic environments.

Findings

Improved convergence in localization under noisy conditions.

Accurate moving-source tracking using EKF with analytical Jacobians.

Potential for advanced scattering-based microphone array designs.

Abstract

A primary challenge in developing synthetic spatial hearing systems, particularly underwater, is accurately modeling sound scattering. Biological organisms achieve 3D spatial hearing by exploiting sound scattering off their bodies to generate location-dependent interaural level and time differences (ITD/ILD). While Head-Related Transfer Function (HRTF) models based on rigid scattering suffice for terrestrial humans, they fail in underwater environments due to the near-impedance match between water and soft tissue. Motivated by the acoustic anatomy of underwater animals, we introduce a novel, analytically derived, closed-form forward model for scattering from a semi-transparent sphere containing two rigid spherical scatterers. This model accurately maps source direction, frequency, and material properties to the pressure field, capturing the complex physics of layered, penetrable structures. Critically, our model is implemented in a fully differentiable setting, enabling its integration with a machine learning algorithm to optimize a cost function for active localization. We demonstrate enhanced convergence for localization under noise using a physics-informed frequency weighting scheme, and present accurate moving-source tracking via an Extended Kalman Filter (EKF) with analytically computed Jacobians. Our work suggests that differentiable models of scattering from layered rigid and transparent geometries offer a promising new foundation for microphone arrays that leverage scattering-based spatial cues over conventional beamforming, applicable to both terrestrial and underwater applications. Our model will be made open source.