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Gradient based robust deconvolution

In the present paper, we propose an approach to the problem of deconvolution in presence of model uncertainty based on the polynomial representation of linear discrete-time system. The basic idea consists in introducing the gradient of the estimation error with respect to the model uncertainty into a Minimum Variance (MV) criterion. The new criterion is a weighted sum of the MV and the variance of the gradient of the estimation error. The development is given for model uncertainties described in a polynomial or in a parametric form. The inverse filter is obtained by means of spectral factorization and a Diophantine equation.