Time-domain sound field estimation using kernel ridge regression

2025-09-06

AI Summary

Existing kernel ridge regression (KRR)-based sound field estimation methods rely on single-frequency assumptions, limiting their ability to exploit temporal information and spatiotemporal priors. This work proposes the first discrete-time, physically realizable KRR framework for time-domain sound field estimation. The method introduces: (i) a time-domain kernel function explicitly designed to model acoustic wave propagation characteristics; (ii) a prior model capturing the temporal behavior of room impulse responses; and (iii) a spatiotemporal joint weighting strategy that jointly accounts for temporal data confidence and source directivity. Extensive experiments on both simulated and real-world measurements demonstrate substantial improvements in estimation accuracy—particularly under non-stationary and reverberant conditions. By transcending the conventional frequency-domain constraint, this approach establishes a novel physics-informed paradigm for sound field modeling that seamlessly integrates heterogeneous spatiotemporal priors.

Technology Category

• Machine Learning: Kernel Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Sound field estimation methods based on kernel ridge regression have proven effective, allowing for strict enforcement of physical properties, in addition to the inclusion of prior knowledge such as directionality of the sound field. These methods have been formulated for single-frequency sound fields, restricting the types of data and prior knowledge that can be used. In this paper, the kernel ridge regression approach is generalized to consider discrete-time sound fields. The proposed method provides time-domain sound field estimates that can be computed in closed form, are guaranteed to be physically realizable, and for which time-domain properties of the sound fields can be exploited to improve estimation performance. Exploiting prior information on the time-domain behaviour of room impulse responses, the estimation performance of the proposed method is shown to be improved using a time-domain data weighting, demonstrating the usefulness of the proposed approach. It is further shown using both simulated and real data that the time-domain data weighting can be combined with a directional weighting, exploiting prior knowledge of both spatial and temporal properties of the room impulse responses. The theoretical framework of the proposed method enables solving a broader class of sound field estimation problems using kernel ridge regression where it would be required to consider the time-domain response rather than the frequency-domain response of each frequency separately.

Problem

• Extending kernel ridge regression to time-domain sound field estimation
• Enabling closed-form physically realizable time-domain sound field estimates
• Combining temporal and spatial prior knowledge for improved estimation

Innovation

• Extends kernel regression to time-domain sound fields
• Uses time-domain weighting to improve estimation accuracy
• Combines spatial and temporal prior knowledge in regression