We consider the problem of approximating an unknown function from experimental data, while at same time its derivatives. Solving this is useful, for instance, in context nonlinear system identification, obtaining models that are more accurate and reliable than traditional ones based on plain approximation. Indeed, identified by accounting derivatives can provide improved performance several end...

We present a unifying view of discrete-time operator models used in the context of finite word length linear signal processing. Comparisons are made between the recently presented gamma operator model, and the delta and rho operator models for performing nonlinear system identification and prediction using neural networks. A new model based on an adaptive bilinear transformation which generaliz...

This paper is devoted to the blind identification problem of a special class of nonlinear systems, namely, Volterra models, using a real-coded genetic algorithm (RCGA). The model input is assumed to be a stationary Gaussian sequence or an independent identically distributed (i.i.d.) process. The order of the Volterra series is assumed to be known. The fitness function is defined as the differen...

Combining a note by Rissanen and an idea of enumerative coding we obtain a new implementation of the Ziv-Lempel incremental parsing algorithm for coding and decoding discrete data sequences. Index Terms -Ziv-Lempel algorithm, enumerative coding.

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalized orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and ...

This paper presents a procedure for time variant nonlinear system identification based on distribution theory. Some of the system parameters change in time according to unknown laws. These laws are expressed as finite degree time polynomials whose parameters are included in the set of parameters to be identified. Mainly it is an extension of the procedure developed in (Marin et al., 2005). Cons...

Providing flexibility and user-interpretability in nonlinear system identification can be achieved by means of block-oriented methods. One of such block-oriented system structures is the parallel WienerHammerstein system, which is a sum of Wiener-Hammerstein branches, consisting of static nonlinearities sandwiched between linear dynamical blocks. Parallel Wiener-Hammerstein models have more des...

Abstract: A new exact method of measuring the Volterra kernels of finite order discrete nonlinear systems is presented. The kernels are rearranged in terms of multivariate crossproducts in the vector form. The one-, two-, . . . , and `-dimensional kernel vectors are determined using a deterministic multilevel sequence with ` distinct levels at the input of the system. It is shown that the defin...

Block-oriented models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approx...