The joint object recognition and distance determination are considered by comparing the spectral pressure density of the noise signal observed at a certain object distance, with the samples of the spectral pressure density of the noise signals of the objects stored in the database. The solution of the problem is based on minimization of the measure of proximity between the detected signal and the samples stored in the database of signal spectra. The article analyzes the main known methods of distance estimation at the passive detection sonar, and carries out a comparative analysis of various proximity measures to solve recognition problems and estimate the distance of a detected marine object. The most characteristic measures reflecting the specifics of different types of distances were considered: similarities and distances for numerical data (Ruzhechka, Bray–Curtis, Canberra, Kulczinski), analogs of Euclidean distance (Euclidean distance, Manhattan distance, Penrose size distance, Penrose form distance, Lorentzian distance, Hellinger distance, Minkowski distance, Mahalanobis distance or statistical distance), correlation similarities and distances (correlation similarity, cosine similarity). Low efficiency of metrics of correlation and cosine and expediency of use for the problem decision such metrics, as analogues Euclidean distance, is shown. It is shown that the values of these metrics are the functions of the signal level of the object, which determines the need to compare the measured signal and the samples of the database of signal spectra for different noise levels. The perspective directions of further researches are defined.