A new gradient technique is introduced for linear independent component analysis (ICA) based on the Edgeworth expansion of mutual information, for which the algorithm operates sequentially using fixed-point iterations. In order to address the adverse effect of outliers, a robust version of the Edgeworth expansion is adopted, in terms of robust cumulants, and robust derivatives of the Hermite polynomials are used. Also, a new constrained version of ICA is introduced, based on goal programming of mutual information objectives, which is applied to the extraction of the antepartum fetal electrocardiogram from multielectrode cutaneous recordings on the mother's thorax and abdomen.