A robust algorithm for sound source localization in shallow sea based on a 2D Fourier transform of source motion interference patterns is developed. A spectrogram in time-frequency coordinates obtained after a Fourier transform contains localized areas of spectral density intensity of constructively interfering modes and a distributed area of noise spectral density. Signal spectral density is localized in an area whose linear sizes are determined by the lowest frequency and spatial scales of field variability. The peak input signal-to-noise ratio is estimated for a single receiver when robust detection is ensured and estimates of speed and initial distance to the receiver are close to the actual values. The high robustness of the algorithm is based on the coherent summation of mode amplitudes occurring at different times. Experimental results demonstrating the effectiveness of the algorithm are presented. For higher than peak signal-to-noise ratios, random estimates of the parameters are close to their statistically average values.