Efficient Methods for Identification of Volterra Filter Models

Robert D. Nowak and Barry D. Van Veen
Department of Electrical and Computer Engineering
University of Wisconsin-Madison, WI 53706 USA

R. Nowak supported by Rockwell International Doctoral Fellowship 
Program.   B. Van Veen supported in part by the National Science Foundation 
under Award MIP-895 8559 and the Army Research Office under Grant
DAAH04-93-G-0208.

Abstract --

A major drawback of the truncated Volterra series or ``Volterra filter'' for
system identification is the large number of parameters required by the 
standard filter structure.  The corresponding estimation problem requires 
the solution of a large system of simultaneous linear equations. Two methods 
for simplifying the estimation problem are discussed in this paper.

First, a Kronecker product structure for the Volterra filter is reviewed.
In this approach the inverse of the large correlation matrix is expressed as
a Kronecker product of small matrices.

Second, a parallel decomposition of the Volterra filter based on uncorrelated,
symmetric inputs is introduced.  Here the Volterra filter is decomposed into 
a parallel combination of smaller orthogonal ``sub-filters''.  It is shown 
that each sub-filter is  much smaller than the full Volterra filter and hence 
the parallel decomposition offers many advantages for estimating the Volterra
kernels.   Simulations illustrate application of the parallel structure with 
random and pseudorandom excitations.  Input conditions that guarantee the 
existence of a unique estimate are also reviewed.