Performance analysis of Volterra kernel estimators with Gaussian inputs

The focus of this paper is on Volterra nonlinear system identification from input-output data. When the system is linear-quadratic and the input is Gaussian, closed-form expressions for the kernels were derived by Tick (1961) based on input-output cross-cumulants. However, there have been no known variance expressions for the kernel estimates. In this paper, we analyze the performance of the first- and second-order kernel estimates when the input is zero-mean white Gaussian, and the additive noise has unknown color and distribution. Closed-form variance expressions are presented and verified by simulations.