Source-linked AI summary
Source localization in an ocean waveguide using supervised machine learning
Haiqiang Niu, Emma Reeves, Peter Gerstoft
TL;DR
The paper addresses ocean source-range localization when matched-field processing is limited by mismatch between modeled and measured fields. It trains FNN, SVM, and RF models on normalized sample covariance matrices, treating localization as classification or regression. Classification methods perform better than regression and matched-field processing, with all three achieving best MAPE values of 2–3%.
Problem
Ocean source localization is difficult because matched-field processing depends on accurately modeling complicated and unstable environments.
Method
The paper trains FNN, SVM, and RF models using normalized sample covariance matrices from acoustic observations for classification and regression.
Results
Classification methods perform better than regression and MFP, with FNN, SVM, and RF all achieving best MAPE values of 2–3%.
Takeaways & Limitations
Noise09 experimental data demonstrates the validity of the machine learning algorithms for underwater source localization.
Abstract
from arXiv · showhide
Source localization in ocean acoustics is posed as a machine learning problem in which data-driven methods learn source ranges directly from observed acoustic data. The pressure received by a vertical linear array is preprocessed by constructing a normalized sample covariance matrix (SCM) and used as the input. Three machine learning methods (feed-forward neural networks (FNN), support vector machines (SVM) and random forests (RF)) are investigated in this paper, with focus on the FNN. The range estimation problem is solved both as a classification problem and as a regression problem by these three machine learning algorithms. The results of range estimation for the Noise09 experiment are compared for FNN, SVM, RF and conventional matched-field processing and demonstrate the potential of machine learning for underwater source localization..
I. INTRODUCTION
The paper motivates supervised machine learning for ocean source-range localization as an alternative to model-sensitive matched-field processing. It uses normalized sample covariance matrices from acoustic observations and compares FNN, SVM, and RF in classification and regression settings.
- Machine learning can learn features and nonlinear relationships directly from acoustic data without requiring sound propagation modeling, including for unknown environments.
- Matched-field processing is sensitive to mismatch between model-generated replica fields and measurements in complicated, unstable ocean environments.
- The paper investigates feed-forward neural networks, support vector machines, and random forests for source-range localization.
- Acoustic observations are used to train the models instead of model-generated fields, distinguishing this approach from several previous localization and inversion studies.
- Normalized sample covariance matrices containing amplitude and phase information are used as input features after preprocessing.
- Source localization is formulated as either classification or regression, with this work emphasizing classification alongside the regression approach used in previous studies.
B. Source range mapping
The source-range mapping converts continuous ranges into classification targets or retains them as continuous regression targets. For FNN classification, target vectors and softmax outputs represent probabilities over discrete range bins.
- Source range mapping: In classification, source ranges are discretized into K equal-width bins, and each input vector receives the corresponding true range-class label.
- Source range mapping: For FNN classification, each range class is mapped to a 1 × K binary target vector representing the expected output probability distribution.
- Feed-forward neural networks: The FNN produces a softmax distribution whose maximum identifies the predicted range class.
- Source range mapping: In regression, all three models use a continuous range variable as the target output.
- Feed-forward neural networks: The FNN uses a three-layer architecture with input variables, a hidden layer, and an output layer formed through weighted transformations and activation functions.
- Feed-forward neural networks: Training compares predicted and target probability distributions using KL divergence, which is equivalent here to minimizing cross entropy.
D. Support Vector Machine
SVM separates source-range classes with a maximum-margin hyperplane, extending to nonseparable, nonlinear, multiclass, and regression settings through slack variables and kernels.
- SVM divides input data into classes using a hyperplane that maximally separates them.For two classes, the hyperplane is w^T x + b = 0, with labels determined by the sign of the classifier output.
- The separating hyperplane is optimized by maximizing the margin to the closest points, called support vectors.The margin is the distance from the hyperplane to the nearest points on its boundary.
- Slack variables permit some misclassification when training classes overlap, while C controls the trade-off between slack penalties and margin.The relaxed constraints use ξ_n ≥ 0, and C > 0 sets the penalty balance.
- A feature-space transformation and Gaussian RBF kernel extend SVM to nonlinear relationships.The kernel is kφ(x_n, x_m) = φ(x_n)^T φ(x_m), with γ controlling the kernel shape.
- Support vector regression adapts SVM to continuous source-range prediction by minimizing an ε-sensitive error function.Points outside the ε region are the support vectors, and r_n denotes the true source range.
- Multiclass SVM uses K(K − 1)/2 pairwise models in a one-versus-one scheme, assigning labels by the most frequent class decisions.The same SVM framework is adapted to K source-range classes through all pairwise class combinations.
E. Random forests
Random forests make decision-tree range estimation more robust by averaging trees trained on random bootstrap subsets, with regression assigning regional means and using squared error.
- Random forests: Random forests reduce decision-tree overfitting by fitting multiple trees to bootstrap samples and aggregating their predictions.Each bootstrap subset is sampled with replacement, and classification uses the most frequent class across trees.
- Decision trees: A decision tree recursively partitions D-dimensional inputs into regions using cutoffs along selected dimensions.A cutoff c assigns samples to left or right regions according to the value of x_ni.
- Decision trees: Each tree branch minimizes a cost function based on region sizes and an impurity function.For classification, the impurity function is the Gini index and each region receives its most common class label.
- Decision trees: In this paper, iterative partitioning defines M regions according to the minimum number of points allowed in each region.The illustrated tree has M = 3 regions with cutoff values 1.9 and 4.6.
- Random forests: For RF regression, each region predicts the mean true value of its points and uses mean squared error as the impurity function.Here, r_n denotes the source range at sample n.
F. Performance metric
The paper evaluates range predictions with mean absolute percentage error (MAPE), which captures both error magnitude and the frequency of correct estimates.
- MAPE measures average absolute percentage deviation between predicted and ground-truth ranges over N samples.R_pi is the predicted range and R_gi is the ground-truth range.
- MAPE is preferred because it accounts for error magnitude and the frequency of correct range estimates.The paper notes that MAPE is asymmetric but adequate for the small output range considered.
G. Source localization algorithm
The localization pipeline converts recorded pressure signals into SCM-based inputs, trains supervised models on labeled data, and predicts unlabeled source ranges evaluated by MAPE.
- Recorded pressure signals are Fourier transformed, and Ns snapshots are used to form the SCM input x.This preprocessing produces the model input used for source-range localization.
- Preprocessed data are divided into training and test sets, with training labels prepared for the selected machine-learning algorithms.The test data remain available for subsequent prediction.
- Training inputs X = [x1 ··· xN] and corresponding labels are used to fit the machine-learning models.The labels serve as the desired outputs during supervised training.
- Trained model parameters predict source ranges for unlabeled test data, and the outputs are mapped back to range.Prediction error is reported using mean absolute percentage error.
III. SIMULATIONS
Simulations examine FNN-based source-range localization using simulated Noise09 acoustic data and a vertical array. The study varies source range and SNR while comparing machine-learning behavior.
- Simulation setup: The simulation examines FNN performance on data generated with environmental parameters modeled on the Noise09 experiment.Only the FNN classifier is examined in this section, although later discussion covers SVM and RF.
- Environmental model: The modeled source is 5 m deep in a 152 m waveguide, with a 24 m sediment layer and fluid halfspace bottom.The sediment and bottom are assigned specified sound speeds, densities, and attenuation coefficients.
- Array configuration: The vertical array contains 16 receivers spanning 128–143 m depth with 1 m inter-sensor spacing.
- Data generation: The source moves away from the receiver at 2 m/s across ranges from 0.1 to 2.86 km sampled every 2 m.Different SNR realizations are produced by adding complex Gaussian noise to the simulated complex pressure signals.
- Data generation: SNR is defined at the most distant range bin because the source moves while its level is assumed constant.
- Input signals: The 16-element array’s received signals are used to form the simulation inputs, with pressure and noise variance defining the SNR-related quantities.
B. Input preprocessing and learning parameters
The section describes SCM-based preprocessing, neural-network settings, and simulated and experimental evaluation conditions. Results show strong dependence on SNR and evidence of low-SNR overfitting.
- Input preprocessing: Each 16-element array SCM is formed by averaging 10 successive snapshots, with nine snapshots overlapped.
- Input preprocessing: The simulation uses 272-dimensional inputs from 1380 range samples spanning 0.1–2.86 km, while test samples use 20 m range spacing.
- Learning parameters: The FNN uses 128 hidden neurons, dropout keep probability 0.5, initial Adam learning rate 0.01, and at most 1000 iterations.
- Simulation results: FNN MAPE across SNRs −10, −5, 0, and 5 dB is 20.6, 6.5, 0.2, and 0.0%, respectively.After 300 training steps, the output probability distribution for a 1.5 km, 5 dB signal resembles the target output.
- Simulation results: The FNN converges after about 300 optimization steps at all tested SNRs.
- Simulation results: At SNRs below 0 dB, training performance remains good while test predictions are poor, indicating overfitting; at 0 and 5 dB, both errors converge low.Increasing training-set size can reduce overfitting, although additional data may be unavailable because of experimental or computational constraints.
A. Input preprocessing and learning parameters
Experimental Noise09 localization uses SCM inputs from a 16-hydrophone array and evaluates single- versus multi-frequency classification across FNN, SVM, and RF. Multi-frequency inputs improve FNN predictions, while classifiers perform comparably overall.
- Input preprocessing: Experimental inputs are 16×16 SCMs averaged over 10 successive 1-s snapshots, with 1380 training samples and 120 samples per test set.The 0.1–3 km range is divided into 138 discrete points.
- Learning parameters: FNN hidden-layer width is 128 neurons for one frequency and 1024 neurons for 66 frequencies, with dropout keep probability 0.5.
- Frequency inputs: SCM inputs use 550 Hz, 950 Hz, or 66 frequencies from 300–950 Hz at 10 Hz increments; multi-frequency vectors concatenate single-frequency inputs.
- FNN frequency results: Multi-frequency FNN prediction error is 8% on Test-Data-1 and 6% on Test-Data-2, compared with single-frequency errors of 12% and 18% in the reported Test-Data-2 cases.Multi-frequency predictions perform well regardless of source range, whereas single-frequency predictions are generally better at close ranges.
- Classifier comparison: For classification, SVM reaches 2% MAPE on both test sets, RF reaches 3% and 2%, and FNN reaches 3% on both; their performance is described as comparable.
D. Source localization as a regression problem
Regression maps SCM inputs directly to continuous ranges but performs worse than classification, whereas Bartlett MFP is substantially less accurate than the machine-learning classifiers in the reported comparison.
- Regression formulation: In regression, the vectorized covariance matrix remains the input, while direct GPS ranges are continuous labels trained with least-squares objectives.
- FNN regression: Increasing FNN hidden layers reduces regression error by increasing model nonlinearity and the number of learnable parameters.
- Regressor comparison: SVM and RF regression lag FNN because additional layers cannot be added to increase their nonlinearity.
- Task comparison: FNN, SVM, and RF degrade significantly when range estimation is formulated as regression rather than classification.
- Matched-field comparison: Bartlett MFP’s minimum MAPE is 19% on Test-Data-1 and 30% on Test-Data-2, much larger than the machine-learning classifiers’ errors.Single-frequency Bartlett MFP fails to determine source positions, while broadband MFP remains affected by sidelobes.
- Resolution and snapshots: The three classifiers perform well across all tested range resolutions, while one-snapshot inputs degrade performance and more snapshots improve robustness.Averaging more snapshots can also introduce mismatch when the source or environment changes during averaging.
C. Number of hidden neurons and layers for FNN
FNN performance depends on hidden-neuron count and layer depth, while SVM and RF show distinct hyperparameter sensitivities and robustness. Across the evaluated methods, classification achieved 2–3% best MAPE, with limitations for more complex settings and multiple sources.
- C. Number of hidden neurons and layers for FNN: FNN reached minimum MAPE at 128 or 2048 hidden neurons for Test-Data-1 and 512 for Test-Data-2.The corresponding MAPE values were 7% and 4%, respectively.
- C. Number of hidden neurons and layers for FNN: Two hidden layers did not improve FNN classification performance.
- SVM was robust only within 10 < C < 10^3 and 10^-3 < γ < 10^-1, whereas FNN and RF were more robust to parameter choices.SVM degraded significantly outside its appropriate parameter interval.
- RF performed best with more than 500 trees and 20 to 50 minimum samples per leaf, without failing across the tested parameter choices.
- RF was fastest at 52 s, compared with 110 s for SVM and 140 s for FNN under the reported settings.The FNN setting used 1024 hidden neurons and 1000 training steps; RF used 500 trees and 50 minimum samples per leaf.
- The study considered one source, while multiple-source localization would require multiple binary classification and additional training data.More complicated geometries or ocean environments may require algorithms such as deep learning.
- Multi-frequency input produced more accurate FNN predictions than single-frequency input, although training and test data came from the same ship.