  Approximate joint diagonalization of a set of matrices provides a powerful
framework for numerous statistical signal processing applications. For
non-unitary joint diagonalization (NUJD) based on the least-squares (LS)
criterion, outliers, also referred to as anomaly or discordant observations,
have a negative influence on the performance, since squaring the residuals
magnifies the effects of them. To solve this problem, we propose a novel cost
function that incorporates the soft decision-directed scheme into the
least-squares algorithm and develops an efficient algorithm. The influence of
the outliers is mitigated by applying decision-directed weights which are
associated with the residual error at each iterative step. Specifically, the
mixing matrix is estimated by a modified stationary point method, in which the
updating direction is determined based on the linear approximation to the
gradient function. Simulation results demonstrate that the proposed algorithm
outperforms conventional non-unitary diagonalization algorithms in terms of
both convergence performance and robustness to outliers.
