Estimating second-order Volterra system parameters from noisy measurements based on an LMS variant or an errors-in-variables method

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.

► The estimated parameters of a second-order Volterra system from noisy measurements are biased.
► We present an LMS variant to estimate the parameters when the input-noise variance is available.
► We suggest an EIV method using the Frisch scheme to estimate both the parameters and the variances.
► We compare our modified unbiased LMS method with the LMS algorithm.
► We compare our EIV approach with other methods.