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

2026-03-02

AI Summary

This work addresses the failure of conventional rigid-scattering-based head-related transfer function (HRTF) models in underwater acoustic environments, where the acoustic impedance of water closely matches that of soft biological tissues. To overcome this limitation, the authors propose the first differentiable, layered multi-sphere scattering analytical model tailored for underwater settings. The model analytically simulates the acoustic pressure field of a semi-transparent spherical structure containing two rigid scatterers, mapping source direction, frequency, and material properties to the resulting pressure distribution. By integrating physics-informed learning with a frequency-weighting strategy, the framework enables end-to-end optimization and incorporates an extended Kalman filter (EKF) for high-precision real-time tracking of moving sound sources. Experimental results demonstrate that the proposed method significantly improves convergence in source localization under noisy conditions, establishing a new paradigm for scattering-enhanced underwater microphone arrays.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Learning with Manifolds

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• spatial audio
• sound scattering
• underwater acoustics
• HRTF
• interaural cues

Innovation

• differentiable scattering model
• spatial audio cues
• multi-sphere acoustic scattering
• physics-informed localization
• underwater HRTF