TENSOR PRODUCT BASIS APPROXIMATIONS FOR VOLTERRA FILTERS

This paper studies approximations for a class of nonlinear filters kno wn as Volterra filters, Although the Volterra filter provides a relati vely simple and general representation for nonlinear filtering, it is often highly overparameterized, Due to the large number of parameters, the utility of the Volterra filter is limited. The overparameterizati on problem is addressed in this paper using a tensor product basis app roximation (TPBA), In many cases, a Volterra filter may be well approx imated using the TPBA with far fewer parameters. Hence, the TPBA offer s considerable advantages over the original Volterra filter in terms o f both implementation and estimation complexity, Furthermore, the TPBA provides useful insight into the filter response. This paper studies the crucial issue of choosing the approximation basis, Several methods for designing an appropriate approximation basis and error bounds on the resulting mean-square output approximation error are derived. Cert ain methods are shown to be nearly optimal.