Diagonal Kernel Point Estimation of"Equation missing" th-Order Discrete Volterra-Wiener Systems

Abstract

The estimation of diagonal elements of a Wiener model kernel is a well-known problem. The new operators and notations proposed here aim at the implementation of efficient and accurate nonparametric algorithms for the identification of diagonal points. The formulas presented here allow a direct implementation of Wiener kernel identification up to the nth order. Their efficiency is demonstrated by simulations conducted on discrete Volterra systems up to fifth order.

Improving the approximation ability of Volterra series identified with a cross-correlation method

“…Four Volterra series were identified with the classic algorithm (10), using the standard deviationsσ x in the set {0.2, 0.4, 0.8, 1.6}. One series (V 3 NEW ) was estimated with the proposed algorithm (14) using eachσ x in the same set for each different order kernel. Figure 6 shows the RRMSE between the Volterra series and the test system, calculated accordingly to (13) and obtained with a different input sequence with respect to that used for the identification.…”

“…In [14], authors proposed a formula for an efficient implementation of the Lee-Schetzen method for the estimation of Wiener series of any order. The formula simplifies to the classic Lee-Schetzen one if nondiagonal terms of the Wiener kernel are identified.…”

“…Effective solutions that overcome this problem have been proposed in literature, for series up to the third order in [5], and for a generic order in [14], where a comparison between the two methods can also be found. Using cumulants instead of input moments in [7], Koukoulas at alii proposed a proof of the nthorder case valid also for non-i.i.d.…”

“…This work proposes a change in Lee-Schetzen's method, taking the formulas presented in [14] as the reference for the method, with the aim to improve the approximation capabilities of Volterra series versus errors due to input non-idealities and model truncation. In particular, the proposed method will ensure a lower error for a wider range of input variances and will make it easier to identify high-order kernels.…”

Multivariance nonlinear system identification using Wiener basis functions and perfect sequences

“…Furthermore, the central moments of a Gaussian input soon depart from ideal values as the moment order increases unless millions of values are used [4]. Some improvements of the first implementations of the crosscorrelation method (e.g., Lee-Schetzen [1]) were provided in [4], [5] to reduce the input non-ideality and errors due to model order truncation that affect the kernels diagonal points [4].…”