Blind estimation of row relative degree via constrained mutual information minimization

This paper studies a method for blind (input signals being unknown) estimation of the row relative degrees of a system non invertible at infinity. The proposed method uses a blind signal deconvolution scheme: A system, called demixer, is applied to the observed signals and is updated in order to minimize the mutual information. A key point is that the demixer is constrained to be biproper whereas the system is not invertible at infinity, consequently deconvolution is not achievable. But, the row relative degrees can be obtained in two steps: i) minimizing the mutual information at the output of the demixer. ii) using second order statistics of the obtained outputs. Although convergence has not yet been proved, extensive numerical simulation shows the effectiveness of this method.