ESTIMATION OF PARSIMONIOUS DISCRETE VOLTERRA SERIES

摘要

The discrete Volterra series represents an important model for the representation, analysis and synthesis of nonlinear dynamical systems. A major problem with this approach to system identification is that the number of terms to be estimated grows combinatorially with memory length and polynomial degree often leading to redundancy, over-fitting and numerical difficulties. Many attempts have been made to recover only the salient terms in the expansion but none is, to our knowledge, optimal. In this paper we apply a simple, iterative approach derived from a majorization-minorization technique that delivers parsimony as a result of optimization and allows a trade-off between model accuracy and sparsity. While this is viable for problems of moderate size, a new algorithm is derived that requires no matrix inversion and is suited to larger scale systems. The method is demonstrated, successfully, on synthetic data.