Regularized Nonparametric Volterra Kernel Estimation

One way to describe the nonlinear behavior of a process is by use of the nonparametric Volterra series representation. The major advantage lies in the fact that the problem of choosing the appropriate nonlinear model structure is bypassed. Unfortunately it comes at the cost that the number of parameters to be estimated increases fast for increasing memory of the several impulse responses. This results in a very large variance for the estimated parameters leading to a poor description of the system dynamics, unless very long data records are available. In this work, we present a method to estimate efficiently finite Volterra kernels without the need of long records, based on the regularization methods that have been developed for the one-dimensional (1-D) impulse responses for linear time invariant (LTI) systems.