Efficient Methods for Identification of Volterra Filters
Nowak, Robert David
Van Veen, Barry D.
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.