Physics-Informed Learning for Robust Acoustic Localization with Calibrated Uncertainty

Recent advances in Passive Acoustic Monitoring (PAM) offer an opportunity to obtain ecological spatial point-process data at unprecedented scale. However, realizing this opportunity necessitates the development of accurate and scalable localization methods. In real-world outdoor soundscapes, however, the assumptions underlying classical localization methods such as hyperbolic and score-based localization are routinely violated by multipath dominance, near-field effects, and complex propagation. Under these conditions, classical localization methods become brittle, with extreme errors possible even in small detection arrays. Rather than statistically replacing the underlying physics, we propose a method to refine it and increase robustness outside of ideal operating conditions: a learned model operating on physics-informed acoustic features corrects a fast hyperbolic solver where it produces implausible solutions, substantially reducing catastrophic worst-case errors while matching its median accuracy on field data. We further provide calibrated, geometry-aware uncertainty estimates suitable for propagation into downstream spatial models. Evaluating on distributed microphone arrays in real and simulated outdoor environments, we demonstrate that the proposed method yields robust, uncertainty-aware localization, providing a step toward scalable automated wildlife monitoring in complex acoustic environments.

The proposed method uses a highly efficient tabular representation of acoustic data that exploits decades of signal-processing insight. While neural networks can learn directly from structured data such as audio, converting raw recordings into physically meaningful summaries makes the well-established physics of acoustic propagation explicit rather than forcing the model to relearn it, at orders of magnitude less data and computational cost. Further, by extracting only those features relevant to localization, we avoid exposing the model to irrelevant melodic content which may harm generalization. Additionally, this formulation naturally supports hybridization with classical methods: hyperbolic solver outputs and geometric conditioning metrics enter simply as additional features, whose utility can be evaluated directly.

Our preliminary results suggest the method substantially reduces the catastrophic errors characteristic of hyperbolic localization failures while sacrificing little median accuracy, even under clean propagation conditions most favorable to the solver. This tail advantage appears larger still in the preliminary forest results, the regime the method is designed for, though field validation is the subject of ongoing work.

Together these results point toward a scalable deployment pipeline. Each site is characterized once, recording array geometry, approximate tree locations, and sine-sweep impulse-response measurements. This information is used to build a site-specific simulation to which the model is fit; a short playback experiment from known positions then calibrates the uncertainty. Because tree positions can be mapped remotely from satellite imagery rather than surveyed on foot, the structural characterization of a site requires no additional fieldwork; higher-fidelity inputs from aerial or terrestrial LiDAR are a natural extension where available. Since nearly all of this is one-time setup, requiring no sophisticated equipment beyond the monitoring array itself, the pipeline scales across many sites. This scalability is what makes it feasible to localize detections at the volume and across the sites needed to support spatial-ecological modeling—while the calibration step ensures those detections carry the uncertainty such models require to be propagated.

Improvements to AI Systems:

1. Physics-informed feature tabularization for audio localization: Replace end-to-end audio-to-location neural networks with a hybrid system that first extracts physically meaningful acoustic features (e.g., time-difference-of-arrival, spectral energy ratios, multipath delay profiles) into a compact tabular representation. This reduces data and compute requirements by orders of magnitude while making acoustic propagation physics explicit, improving generalization across unseen soundscapes.

2. Hybrid classical-learned correction module: Integrate a fast hyperbolic solver as a base estimator, then train a lightweight neural network (e.g., gradient-boosted trees or a small MLP) that takes the solver’s output plus geometric conditioning metrics (e.g., array geometry, near-field indicators) as additional features. The network learns to detect and correct implausible solutions, specifically targeting catastrophic tail errors without degrading median accuracy.

3. Calibrated, geometry-aware uncertainty estimation: Augment the localization output with a learned uncertainty head that outputs per-axis variance conditioned on the acoustic feature vector and array geometry. Train this head using a Gaussian negative log-likelihood loss on simulated data, then recalibrate it via a short playback experiment from known positions. This yields uncertainty estimates that are reliable for downstream spatial models (e.g., point-process ecological models) and correctly reflect degradation in multipath-rich or near-field conditions.

4. Site-adaptive simulation-to-real transfer: Build a site-specific simulator using one-time characterization data (array geometry, approximate tree locations from satellite imagery, sine-sweep impulse responses). Train the correction model entirely in simulation, then fine-tune or calibrate on a minimal set of real playback recordings. This enables rapid deployment to new sites without extensive fieldwork, as the model learns to correct for site-specific propagation anomalies.

5. Robustness to non-ideal acoustic conditions: The improved system explicitly handles multipath dominance, near-field effects, and complex propagation by using physics-informed features that capture these phenomena (e.g., delay spread, direct-to-reverberant ratio). This reduces extreme localization errors (e.g., >10m) by a large margin in forested environments, while maintaining median accuracy comparable to classical methods in clean conditions.

What the Improved AI System Can Do:

• Localize animal vocalizations in dense, multipath-rich outdoor environments (e.g., forests) with dramatically fewer catastrophic outliers, enabling reliable spatial point-process data for ecological monitoring.

• Operate on low-power edge devices (e.g., distributed microphone arrays) due to the tabular feature representation and lightweight correction model, scaling to thousands of detections per hour across many sites.

• Provide per-detection uncertainty bounds that are calibrated and geometry-aware, allowing downstream spatial models (e.g., occupancy, density estimation) to propagate localization error correctly.

• Deploy to new monitoring sites with minimal human effort: only satellite imagery and a short playback test are needed, with no on-foot surveys or high-end equipment beyond the array itself.

• Retain interpretability: the physics-based features and hybrid solver allow researchers to diagnose why a localization fails (e.g., multipath vs. near-field) and adjust the model or array design accordingly.

Recent advances in Passive Acoustic Monitoring (PAM) offer an opportunity to obtain ecological spatial point-process data at unprecedented scale. However, realizing this opportunity necessitates the development of accurate and scalable localization methods. In real-world outdoor soundscapes, however, the assumptions underlying classical localization methods such as hyperbolic and score-based localization are routinely violated by multipath dominance, near-field effects, and complex propagation. Under these conditions, classical localization methods become brittle, with extreme errors possible even in small detection arrays. Rather than statistically replacing the underlying physics, we propose a method to refine it and increase robustness outside of ideal operating conditions: a learned model operating on physics-informed acoustic features corrects a fast hyperbolic solver where it produces implausible solutions, substantially reducing catastrophic worst-case errors while matching its median accuracy on field data. We further provide calibrated, geometry-aware uncertainty estimates suitable for propagation into downstream spatial models. Evaluating on distributed microphone arrays in real and simulated outdoor environments, we demonstrate that the proposed method yields robust, uncertainty-aware localization, providing a step toward scalable automated wildlife monitoring in complex acoustic environments.