A robust accuracy improvement method for blind identification using higher order statistics

The accuracy improvement of parameter estimates using higher order statistics (HOS) of the input process is treated. It is shown that the robust distribution minimizing the Fisher information under moment constraints is of the exponential type, which covers moment sequences of sub-Gaussian distributions only. To enable accuracy-improvement for the class of heavy-tailed, super-Gaussian distributions, the Gaussian scale-mixtures as modeling distributions are introduced. It is shown that the additional knowledge about moments results in improved parameter estimates and that the scale-mixture found by the moment method is the most robust one among the class of Gaussian scale-mixtures. The prediction error algorithm with the newly introduced moment based norm has been verified in simulation runs with both a priori known moments of the input process and moments estimated from the residual.