Abstract <p>The problem of estimating the distance to a sound source in an underwater waveguide from sound field measurements using a vertical receiving array is considered. In recent years, methods for solving this problem using an artificial neural network, to the input of which a sample correlation matrix of the recorded field is applied, have been developed. The inevitable inaccuracy of the mathematical model of environment makes it possible to train the network on only short paths using the so-called synthetic data, i.e., data of theoretical calculation. This paper considers an alternative approach, where input data are set by the distribution of recorded field intensity in the depth–arrival angle plane. This distribution, constructed using the coherent state method borrowed from the quantum theory, is less sensitive to the environment model inaccuracies than the initial field recorded by the array and the correlation matrix of the field. It is shown by numerical simulation that the use of the aforementioned distribution may expand the range of distances for which the network can be trained on synthetic data.</p>