Range estimation in a weakly range-dependent waveguide in the South China Sea using single hydrophone and multi-task trained deep neural network

In this paper, an underwater source range estimation method using a multi-task trained deep neural network is proposed. Unlike existing machine learning frameworks, in this case, the physical quantities utilized for the training and testing are not identical. The training data parameter is the phase of the complex sound pressure, which is independent of the source and receiver depth and can be generated easily by an acoustic propagation model with only a few environmental parameters, decreasing computational costs significantly. The testing data parameter is the realistically-measured complex sound pressure. Instead of simply using the range as the only supervision signal, two other parameters - the phase mode and the bottom sound speed - are applied as auxiliary labels during the training process, embedding additional information about the sound field into the deep model. The projection between the sound field features and the range extracted from the training data by the deep model is applied to range estimation task on testing data. The effectiveness of the proposed approach is verified for a weakly range-dependent waveguide in the South China Sea by localizing several upsweep signals within a frequency band of 20-200 Hz. Testing results illustrate that the proposed method outperforms the classical matched impulse response approach and deep-learning-based single-label trained models, with the mean absolute percentage error (MAPE) decreasing by 24.63% and 59.46%, respectively. The mechanism of promotion is explained by comparing visualized hidden features of the neural network using t-distributed stochastic neighbor embedding (t-SNE) between the single-task and multi-task approach, showing that the latter helps to construct a more reasonable data manifold in high-dimensional space and thus ensures better performance of the deep model. We also fine-tune the network with a few realistic samples and further improve the performance by up to 25.34% against the baseline.