Non-orthogonal joint diagonalization algorithm preventable ill conditioned solutions for blind source separation

Abstract

The general joint diagonalization problem involves estimating the separating matrix only given mixing signals interrelated matrix set. For nonorthogonal joint diagonalization based on the weighted least-squares criterion, the algorithms may converge to trivial (zero) solution. Certainly, the trivial solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms. However, free of zero solution is not enough, especially for the blind signal separation (BSS). Actually, ill-conditioned diagonalizer even though nonzero makes the objective function unstable or even divergence in the process optimization. Therefore, it is necessary to prevent the iterative solutions from degenerating ill-conditioned forms. To solve this problem, a novel nonleast-squares criterion for non-orthogonal joint diagonalization is proposed. It is imposed constrainted terms on diagonalizers, which are induced form the mathematic define of the ill condition matrix. Finally, Computer simulations indicate that the new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible, meanwhile, degenerate solutions are avoided strictly.