This method for the non-linear estimation of no more than two mixed signals from separate sources, the time/frequency representation of which shows an unknown non-zero proportion of zero components, using an array made up of P>2 antennas, when the directional vectors U and V of the sources emitting these signals are additionally known or estimated, includes the following steps: a) Calculating the successive discrete Fourier transforms of the signal received by the antennas and sampled to obtain a time-frequency P-vector grid of the signal; each element of the grid being referred to as a box and containing a complex vector X forming a measurement; b) For each box, calculating the conditional expectation estimator of the signal, or of the signals, from the measurement X and an a priori probability density for the signals that is a Gaussian mixture.