PENALIZED LEAST-SQUARES ESTIMATION OF VOLTERRA FILTERS AND HIGHER-ORDER STATISTICS

Volterra filters (VF's) and higher order statistics (HOS) are importan t tools for nonlinear analysis, processing, and modeling, Despite thei r highly desirable properties, the transfer of VF's and HOS to real-wo rld signal processing problems has been hindered by the requirement of very large data records needed to obtain reliable estimates, The iden tification of VF's and the estimation of BOS both fall into the catego ry of ill-posed estimation problems. In this paper, we develop penaliz ed least squares (PLS) estimation methods for VF's and HOS. It is show n that PLS is a very effective way to incorporate prior information of the problem at hand without directly constraining the estimation proc edure, Hence, PLS produces much more reliable estimates, The main cont ributions of this paper are the development of appropriate penalizing functionals and cross-validation procedures for PLS based VF identific ation and HOS estimation.