  The Volterra series is a powerful tool in modelling a broad range of
nonlinear dynamic systems. However, due to its nonparametric nature, the number
of parameters in the series increases rapidly with memory length and series
order, with the uncertainty in resulting model estimates increasing
accordingly. In this paper, we propose an identification method where the
Volterra kernels are estimated indirectly through orthonormal basis function
expansions, with regularization applied directly to the expansion coefficients
to reduce variance in the final model estimate and provide access to useful
models at previously unfeasible series orders. The higher dimensional kernel
expansions are regularized using a method that allows smoothness and decay to
be imposed on the entire hyper-surface. Numerical examples demonstrate improved
Volterra series estimation up to the 4th order using the regularized basis
function method.
