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A nonlocally weighted soft-constrained natural gradient iterative method is introduced for robust blind separation in reverberant environment. The nonlocal weighting of the iterations promotes stability and convergence of the algorithm for long demixing filters. The scaling degree of freedom is controlled by soft-constraints built into the auxiliary difference equations. The small divisor problem of iterations in silence durations of speech is resolved. Computations on synthetic speech mixtures based on measured binaural room impulse responses show that the algorithm achieves higher signal-to-inteference ratio improvement than existing method (natural gradient time domain algorithm) in an office size room with reverberation time over 0.5 second.

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