A method for the non-linear estimation, by calculation means, of 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, including 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 an estimation of the dual-source signal S = (s,c) T, s being the signal associated to the first source, and c being the signal associated to the second source, and (.) T being the transposed of (.), by an approximation of the conditional expectation estimator of the signal, or of the signals, the probability density of S being modeled as a Gaussian mixture centered and weighted by coefficients q 1, q 2, q 3, q 4 of the for possible situations in each case among, bothe sources present,: source 1 present and source 2 absent, source 1 absent and source 2 present, both sources absent, said approximation being S ^ = ∑ j = 1 k q j det Q j det Γ j exp X * MQ j M * X 2 σ 2 Q j M * X ∑ j = 1 4 q j det Q j det Γ j exp X * MQ j M * X 2 σ 2 where (.) * is the conjugated transpose of matrix (.); and where: Q 1 = 1 1 + σ 2 / σ 1 2 1 + σ 2 / σ 2 2 − U * V 2 1 − U * V − V * U 1 Q 2 = 1 / 1 + σ 2 / σ 1 2 0 0 0 Q 3 = 0 0 0 1 / 1 + σ 2 / σ 2 2 Q 4 = 0 0 0 0 and where det Q 1 det Γ 1, det Q 2 det Γ 2, det Q 3 det Γ 3, det Q 4 det Γ 4 are chosen respectively equal to: 1 − U * V 2 − 1 σ 4 / σ 1 2 σ 2 2, σ 2 / σ 1 2, σ 2 / σ 2 2, and 1; and where 2 σ 1 2, 2 σ 2 2 and respectively the power of the signal from source 1, the power of the signal from source 2, and where 2σ 2 is the power of the noise supposed Gaussian, spatially, frequentially and temporally white; and where M = ( U V). 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 an estimation of the dual-source signal S = (s,c) T, s being the signal associated to the first source, and c being the signal associated to the second source, and (.) T being the transposed of (.), by an approximation of the conditional expectation estimator of the signal, or of the signals, the probability density of S being modeled as a Gaussian mixture centered and weighted by coefficients q 1, q 2, q 3, q 4 of the for possible situations in each case among, bothe sources present,: source 1 present and source 2 absent, source 1 absent and source 2 present, both sources absent, said approximation being S ^ = ∑ j = 1 k q j det Q j det Γ j exp X * MQ j M * X 2 σ 2 Q j M * X ∑ j = 1 4 q j det Q j det Γ j exp X * MQ j M * X 2 σ 2 and where det Q 1 det Γ 1, det Q 2 det Γ 2, det Q 3 det Γ 3, det Q 4 det Γ 4 are chosen respectively equal to: 1 − U * V 2 − 1 σ 4 / σ 1 2 σ 2 2, σ 2 / σ 1 2, σ 2 / σ 2 2, and 1; and where 2 σ 1 2, 2 σ 2 2 and respectively the power of the signal from source 1, the power of the signal from source 2, and where 2σ 2 is the power of the noise supposed Gaussian, spatially, frequentially and temporally white; and where M = ( U V).