The JSEA (joint source-environment adaptation) method of Kari, Vishnu, and Singer (IEEE Journal of Oceanic Engineering, 2026) adapts a pre-trained CNN-based underwater acoustic ranging model to an environmentally mismatched test environment without target labels or access to training data: test samples are partitioned by a peakwise-uncertainty indicator into a certain set S\mathcal{S} and an uncertain set, and pseudo-labels for uncertain samples are selected by matching received signal power to a local average over certain samples within a range window δ, with the partition governed by a peak-significance factor Q. The authors explicitly leave open the minimum number of certain samples required for successful operation of JSEA and provide only empirical defaults (Q = 10, δ = 500 m) with qualitative guidelines. This problem asks for a characterization — analytical or empirical — of the conditions on the certain set (cardinality, range distribution, and pseudo-label correctness) and on Q, δ, SNR, quantization, and mismatch type/magnitude under which JSEA's power-based pseudo-label selection and subsequent adaptation are reliable, clarifying how the coupled choice of Q and δ affects that reliability.

Background

Underwater acoustic (UWA) source ranging is the task of estimating the distance between an acoustic source and a receiver array from recorded signals. Classical matched field processing (MFP) compares the recorded array data against predictions of a numerical waveguide propagation model for candidate source positions; more recently, deep-learning models have been trained to perform the same estimation. In the benchmark line of work by Chen and Schmidt (JASA, 2021), a convolutional neural network (CNN) is trained on synthetic data generated by the KRAKEN normal-mode propagation model for the SWellEx-96 experiment environment (a well-known at-sea dataset recorded on a vertical linear array, VLA, off San Diego); the network input is the spatial covariance matrix (SCM), the matrix of cross-spectra between array elements at a single frequency, and the output is a probability mass function (PMF) over discretized source ranges.

Such data-driven models degrade under environmental mismatch (called domain shift in machine learning): differences between the training and test environment such as water depth, bathymetric shape, seabed sediment type, or sound-speed profile. Because underwater devices are often low-power and decentralized, retraining with original training data or labeled target data is frequently impractical. Test-time adaptation (TTA), also called source-free domain adaptation, instead updates a pre-trained model at inference time using only unlabeled test data. A representative TTA method is SHOT (source hypothesis transfer), which freezes the classifier head and retrains the feature extractor using pseudo-labels and an information-maximization objective.

Kari, Vishnu, and Singer (IEEE Journal of Oceanic Engineering, 2026; arXiv:2503.23258) propose JSEA (joint source-environment adaptation). They first observe that model uncertainty grows with mismatch: a mutual-information-based uncertainty computed via MC-dropout (averaging the predictive PMFs over stochastic dropout realizations of the network) increases with depth or sound-speed mismatch, and a much cheaper surrogate — peakwise uncertainty (PU) — flags any test sample whose output PMF contains more than one significant peak, where a peak is significant if it is either unique or exceeds the next-largest peak by a factor Q ≥ 1. Samples with PU = 0 form the certain set S\mathcal{S}; the remainder form Sc\mathcal{S}^c. JSEA then exploits a physical prior that the usual power normalization of the SCM discards: the received signal power ψ\psi fluctuates around a decreasing trend ψ0(d)\psi_0(d) as a function of range d. Under an independence assumption, the posterior over range factorizes as p(d∣C)∝p(d∣C~)p(d∣ψ)p(d|C) \propto p(d|\tilde{C})p(d|\psi), where C~\tilde{C} is the power-normalized SCM. For each uncertain sample i with candidate peak ranges P(y^i)P(\hat{y}_i), JSEA selects the pseudo-label

d^i=arg⁡min⁡d∈P(y^i)(ψi−1∣Sδ(d)∣∑j∈Sδ(d)ψj)2,\hat{d}_i = \arg\min_{d \in P(\hat{y}_i)} \left( \psi_i - \frac{1}{|\mathcal{S}_\delta(d)|} \sum_{j \in \mathcal{S}_\delta(d)} \psi_j \right)^2,

where Sδ(d)={j∈S:∣d−d^j∣≤δ}\mathcal{S}_\delta(d) = \{ j \in \mathcal{S} : |d - \hat{d}_j| \le \delta \} is the set of certain samples within range δ of candidate d. These pseudo-labels are used to adapt the model. On SWellEx-96 real data and on synthetic data with controlled water-depth, bathymetric, and sediment mismatch, the classification variant (JSEA-c) substantially reduces the ranging mean absolute error (MAE) relative to the unadapted CNN, especially at low signal-to-noise ratio (SNR).

The mechanism, however, works only if the certain set is sufficient in size, range coverage, and correctness. The paper requires δ to be small enough that distinct candidate peaks have distinct neighborhoods (Sδ(d1)≠Sδ(d2)\mathcal{S}_\delta(d_1) \ne \mathcal{S}_\delta(d_2) for d1≠d2d_1 \ne d_2) yet large enough that every candidate peak has a nonempty neighborhood (Sδ(d)≠∅\mathcal{S}_\delta(d) \ne \varnothing), and it fixes Q = 10 and δ = 500 m empirically. The authors state that determining the minimum number of certain samples required for successful operation of JSEA is left for future research, and no general theory for choosing Q and δ under arbitrary mismatch conditions exists. This is the open core: a reliability and sample-complexity characterization of the certain-set mechanism that JSEA depends on.

Problem Statement

Characterize the minimum certain-sample requirement for reliable operation of JSEA. Concretely: for a pre-trained classification-based ranging model applied to a test set from an environment mismatched with the training environment (in water depth, bathymetric shape, sediment type, or sound-speed profile) at given SNRs, establish conditions — in terms of the cardinality of the certain set S\mathcal{S}, the distribution of its members' ranges over the search interval and around the candidate peaks P(y^i)P(\hat{y}_i) of uncertain samples, the fraction of certain samples that are correctly classified, the neighborhood radius δ, the peak-significance factor Q, the range-quantization bin size B (the source paper discretizes source range into bins of size B, using B = 100 m), and the type and magnitude of the mismatch — under which the power-based pseudo-label selection d^i=arg⁡min⁡d∈P(y^i)(ψi−ψ^0(d))2\hat{d}_i = \arg\min_{d \in P(\hat{y}_i)} (\psi_i - \hat{\psi}_0(d))^2, where ψ^0(d)\hat{\psi}_0(d) is the local average of the received powers of certain samples within δ of candidate d (Eq. 17 of the source paper), returns the true range class with a stated high probability, supporting successful operation of JSEA's subsequent adaptation. The characterization may be analytical (sufficient, ideally necessary, conditions with proofs) or empirical (a systematic, reproducible measurement of the success/failure boundary across the source paper's synthetic KRAKEN/SWellEx-96 mismatch scenarios and the real SWellEx-96 S5 data). It should respect the paper's qualitative necessary conditions on δ (peak separation and nonempty neighborhoods) and should clarify the coupled trade-off between Q and δ that the paper's empirical defaults Q = 10 and δ = 500 m currently fix.

References

  1. Dariush Kari, Hari Vishnu, Andrew C. Singer, 'Joint Source-Environment Adaptation of Data-Driven Underwater Acoustic Source Ranging Based on Model Uncertainty', IEEE Journal of Oceanic Engineering 51(2):1534-1549 (2026), DOI 10.1109/JOE.2025.3638518, https://doi.org/10.1109/JOE.2025.3638518; preprint arXiv:2503.23258, https://arxiv.org/abs/2503.23258
  2. Dariush Kari, Andrew C. Singer, 'Joint Source-Environment Adaptation for Deep Learning-Based Underwater Acoustic Source Ranging', 2024 58th Asilomar Conference on Signals, Systems, and Computers, DOI 10.1109/ieeeconf60004.2024.10942791, https://doi.org/10.1109/ieeeconf60004.2024.10942791
  3. Dariush Kari, Yongjie Zhuang, Andrew C. Singer, 'Mismatch-Robust Underwater Acoustic Localization Using A Differentiable Modular Forward Model', 2025 59th Annual Conference on Information Sciences and Systems (CISS), DOI 10.1109/CISS64860.2025.10944684; preprint arXiv:2503.23260, https://arxiv.org/abs/2503.23260
  4. Rui Chen, Henrik Schmidt, 'Model-based convolutional neural network approach to underwater source-range estimation', Journal of the Acoustical Society of America 149(1):405-420 (2021), DOI 10.1121/10.0003329, https://doi.org/10.1121/10.0003329
  5. Jian Liang, Dapeng Hu, Jiashi Feng, 'Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation', ICML 2020, arXiv:2002.08546, https://arxiv.org/abs/2002.08546
  6. Quoc Thinh Vo, Joe Woods, Priontu Chowdhury, David K. Han, 'Adaptive Control Attention Network for Underwater Acoustic Localization and Domain Adaptation', arXiv:2506.17409 (2025), https://arxiv.org/abs/2506.17409