Passive Acoustic Mapping Essentials

• Passive acoustic mapping is a set of methodologies that reconstructs acoustic source distributions from unactuated signals using models like time-of-flight and multipath propagation.
• Techniques such as beamforming, model-based regularization, and deep learning enable high-resolution mapping while addressing challenges like noise and environmental heterogeneity.
• Applications in marine ecology, medical ultrasound, and non-line-of-sight imaging demonstrate PAM's practical significance and pave the way for robust, real-time performance.

Passive acoustic mapping (PAM) is a set of methodologies that reconstruct the spatial distribution of acoustic sources from passively received signals, without emission of controlled probing pulses. Developed for a broad spectrum of scientific and technological applications—including marine mammal ecology, medical ultrasound therapy, underwater surveillance, and non-line-of-sight (NLoS) imaging—PAM leverages diverse signal processing, statistical inference, and physical modeling techniques to map the location, intensity, or abundance of acoustic emitters or scatterers in complex environments.

1. Principles and Forward Models of Passive Acoustic Mapping

Fundamentally, PAM seeks to invert the physical process by which distributed acoustic sources produce observed signals at one or more receiver arrays. In most use cases, this involves modeling the propagation of noise, calls, or other emissions from unknown locations to a (possibly moving) set of hydrophones or microphones, accounting for multipath, attenuation, noise, and variable environmental properties.

Linear Time-of-Flight Model

A canonical forward model in medical and cavitation imaging is a discretized spatiotemporal convolution with propagation delays. For a 2D imaging domain discretized into pixels (x, z) and time samples tₖ, the vectorized measurement y relates to the unknown source cube 𝓧 by

$y = A\,x + \eta,$

where A is a block-sparse matrix encoding the integer sample delays δ_{m,n} due to propagation from voxel n to sensor m, and η is additive Gaussian noise. Each sensor’s signal is modeled as a sum over delayed contributions from all source voxels (Gelvez-Barrera et al., 25 Nov 2025).

Statistical Source Models

Alternative settings, such as ecological abundance estimation, employ inhomogeneous spatial Poisson point processes (e.g., log-Gaussian Cox processes) for latent animal locations, with PAM data (received calls, energy detections) forming a thinned realization of the true source field (Schliep et al., 2023). Detection probabilities model propagation loss, ambient noise statistics, and source-level variability (Petersma et al., 2022). The forward observation process for each hydrophone k is the integral

$$\Lambda_{\rm PAM,k} = \int_\mathcal{D} c\,\lambda(s)\,p_{\rm PAM,k}(s)\,ds,$$

where c is the call rate, λ(s) the spatial source intensity, and p_PAM,k(s) the detection probability at hydrophone k from position s.

Ray and Multipath Models

In shallow water or structured indoor/outdoor environments, PAM may require explicit modeling of multipath propagation (direct, surface-, bottom-reflected, and diffracted paths), as in the 3-ray model for underwater localization (Weiss et al., 2021), or non-line-of-sight around corners (Boger-Lombard et al., 2022). Analytical or precomputed ray tracing yields path-dependent time delays and amplitudes.

2. Inverse Problems, Beamforming, and Estimation Methods

Inverting the physical model to yield spatial maps or track sources demands regularization and statistical inference.

Beamforming Algorithms

Delay-and-sum (TEA) beamformers produce spatial maps by coherently summing time-delayed signals according to expected arrival times. While computationally efficient, they show poor resolution, especially axially, and limited artifact suppression. Data-adaptive beamformers (RCB, EISRCB, DAX) minimize off-axis interference by adjusting per-pixel weights, offering improved energy localization at high computational cost, often requiring per-pixel covariance inversion (Zeng et al., 3 Dec 2024, Zeng et al., 3 Dec 2024).

Model-Based Regularization

For ill-posed inverse problems (e.g., mapping cavitation activity), penalized least-squares reconstructions are solved: $$\hat x = \arg\min_x\,\frac{1}{2}\|A x - y\|_2^2 + \lambda \|x\|_1 + \gamma \|x\|_{TV} + \mu R_D(x),$$ using l₁, total-variation, or denoiser-based (BM4D) regularization. These promote sparse, spatially or temporally coherent solutions, and are solved by FISTA or ADMM (Gelvez-Barrera et al., 25 Nov 2025).

Statistical Inference and Bayesian Filtering

In ecology and surveillance, hierarchical Bayesian models integrate over latent states (abundance/intensity fields, source locations, or tracks) using MCMC or particle filtering. Joint likelihoods account for conditional independence of multimodal data sources, with Metropolis-within-Gibbs or factor-graph sum-product algorithms updating posterior distributions (Schliep et al., 2023, Zhang et al., 2022, Meyer et al., 2021).

GAN-Based and Fast Deep Learning Approaches

Recent advances have implemented deep GAN beamformers, conditioning on transducer geometry, to learn the inversion from RF data to high-quality PAM images with computational cost orders of magnitude lower than conventional or adaptive beamformers (Zeng et al., 3 Dec 2024).

3. Applications Across Scientific Domains

PAM underpins numerous application areas:

• Medical Ultrasound: Mapping cavitation activity in therapeutic ultrasound for therapy guidance, using GAN-based, model-driven, or cross-correlated angular spectrum methods to achieve high spatiotemporal resolution (Zeng et al., 3 Dec 2024, Gelvez-Barrera et al., 25 Nov 2025, Zeng et al., 3 Dec 2024).
• Marine Ecology: Estimating marine mammal abundance and spatial distribution by fusing aerial and passive acoustic monitoring, using hierarchical models to correct for missed detections and spatial/temporal effort gaps (Schliep et al., 2023). Acoustic spatial capture-recapture models further enable robust density estimation even with false detections (Petersma et al., 2022).
• Robotics & SLAM: Bearing-only EKF- and FastSLAM-based PAM enables landmark mapping and robot self-localization when only passively acquired bearings or energy are available, with multi-hypothesis initialization for range ambiguity (Bradley et al., 19 Apr 2024).
• Underwater Surveillance: Tracking multiple submerged sources from sparse TDOA measurements via particle-flow factor-graph Bayesian frameworks, handling uncertainty in data association, and high-dimensional state spaces (Zhang et al., 2022).
• Non-Line-of-Sight Imaging: Correlating ambient noise signals to reconstruct Green’s functions and enable "NLoS" mapping of hidden targets, e.g., around corners in urban environments. This exploits the equivalence between passive temporal cross-correlations and impulse responses, using delay-and-sum backprojections to "image" hidden regions (Boger-Lombard et al., 2022).

4. Algorithmic Strategies and Computational Considerations

Different approaches vary dramatically in computational cost and scalability.

Methodology	Resolution/Accuracy	Computational Load
Time-Exposure Acoustics	Low (especially axially)	O(n_e n_t n_x n_z)
Data-Adaptive Beamformers	High (artifact suppression)	O(n_e³ n_x n_z), ~minutes/image
Angular Spectrum (AS-TAX)	Nearly as high as adaptive	O(n_x n_t log(n_x n_t)), ~ms/image (GPU)
GAN Deep Beamformer	As good as data-adaptive	~10 ms/image (GPU)
TD-LM-PAM (FISTA/ADMM)	State-of-the-art (axial<1mm)	Scales with #sensors·#pixels·#time

In ecology, MCMC with 20,000 iterations suffices to estimate whale density maps under 2–3 minutes per chain (Schliep et al., 2023), while SLAM approaches must maintain computational tractability in joint robot–landmark state spaces (Bradley et al., 19 Apr 2024). For multi-object 3D acoustic tracking, particle-flow importance sampling increases sample efficiency and reduces particle degeneracy (Zhang et al., 2022).

5. Robustness to Environmental Complexity, Multipath, and Uncertainty

Modern PAM techniques explicitly address challenging propagation environments. Multipath (surface/bottom reflections, diffraction, occlusion) is not simply a nuisance but exploited through multi-ray and multi-hypothesis models (Meyer et al., 2021, Weiss et al., 2021, Boger-Lombard et al., 2022). Semi-blind matched-field methods jointly estimate path gains and source waveforms, retaining near-optimal resolution but achieving robustness to environmental mismatch and sensor occlusions; such methods generalize well to real-world tank and field experiments (Weiss et al., 2021). Factor graph and particle filtering methods maintain consistent object identification and localization in the presence of missed detections and false positives (Zhang et al., 2022, Petersma et al., 2022).

6. Quantitative Performance and Trade-Offs

Quantitative evaluation demonstrates substantial gains from model- and learning-based PAM compared to classical beamforming. For cavitation mapping (Gelvez-Barrera et al., 25 Nov 2025, Zeng et al., 3 Dec 2024, Zeng et al., 3 Dec 2024):

• Axial FWHM can be reduced from 7–14 mm (DAS) to <1 mm (TD-LM-PAMSP) using only 20% of the data.
• ISNR improvements of 10–23 dB and energy spread area reductions of 18–66% compared to TEA.
• GAN-based methods match these improvements while achieving real-time performance.

In ecological mapping (Schliep et al., 2023), joint fusion of aerial and acoustic data reduces posterior SD of total abundance estimates from ~21 (aerial only) to 4.4 (fusion), while in tracking, particle-flow approaches lower track fragmentation and improve OSPA error even in heavily nonlinear, data-association-challenged environments (Zhang et al., 2022).

7. Limitations, Future Directions, and Open Questions

Despite rapid advances, several open challenges persist:

• Realistic modeling of environmental heterogeneity, time-varying noise, and sensor imperfections.
• Extension of PAM deep learning methods to arbitrary geometries, wide band operation, and real-time clinical/field use.
• Robustness to source-level heterogeneity and false positive suppression in low-SNR, sparse-data regimes (Petersma et al., 2022).
• Joint mapping and localization under non-Gaussian, non-stationary, and adversarial noise environments, and in NLoS scenarios requiring diffraction-aware solvers or learned geometrical priors (Boger-Lombard et al., 2022).
• Optimizing sensor placement using information-theoretic bounds such as the Cramér–Rao lower bound to maximize mapping accuracy in resource-constrained deployments (Weiss et al., 2021).

Overall, passive acoustic mapping continues to underpin methodological innovations across domains requiring non-invasive, high-resolution, spatially aware sensing, with converging threads from inverse problems, probabilistic graphical models, and modern deep learning architectures.