This paper considers an iterative algorithm for the identification of structured nonlinear systems. The systems considered consist of the interconnection of a MIMO linear systems and a MIMO nonlinear system. The considered interconnection structure can represent as particular cases Hammerstein, Wiener or Lur’e systems. A key feature of the proposed method is that the nonlinear subsystem may be ...

We show a result that can be viewed as a generalization of Bussgang’s classic theorem about static nonlinearities with Gaussian inputs. This new result is used to characterize the best linear approximation of a nonlinear finite impulse response (NFIR) system with a Gaussian input. The best linear approximation is here defined as the causal LTI system that minimizes the expected squared predicti...

Abstract. Application of least squares and instrumental variables to recovering parameters of nonlinear complex dynamic block-oriented systems is examined. For a system with the Hammerstein-Wiener structure the instrumental variable algorithm is designed and compared with the least squares algorithm for estimating system parameters. The advantages of the proposed instrumental variable estimator...

This paper describes a benchmark for nonlinear system identi cation. A Wiener-Hammerstein system is selected as test object. In such a structure there is no direct access to the static nonlinearity starting from the measured input/output, because it is sandwiched between two unknown dynamic systems. The signal-to-noise ratio of the measurements is quite high, which puts the focus of the benchma...

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the input nonlinearity is allowed to be a memory operator of backlash type and both input and output nonlinearities are polynomial and may be noninvertible. The linear subsystem may be parametric or not, continuousor discrete-time. A two-stage identification method is develop...

In this paper, we consider a new method for modeling and equalizing of nonlinear wireless channel. The Volterra structure equalizer has high computation burden and slow convergence rate due to its large number of coefficients and the pre-distortion method is very difficult to realize in actual wireless communication systems. Here, we take another scheme instead of those above. First assume the ...

Abstract. This paper presents the synthesis and analysis of the enhanced predictive fuzzy Hammerstein model of the water tank system. Fuzzy Hammerstein model was compared with three other fuzzy models: the first was synthesized using Mamdani type rule base, the second – Takagi-Sugeno type rule base and the third – composed of Mamdani and Takagi-Sugeno rule bases. The synthesized model is invert...

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, its hyperparameterestimation procedure suffers from numerous covariance-matrix inversions of prohibitively O(N) operations. In this paper, we propose using the quasi-Newton BFGS O(N)-operation formula to update recursively the inverse of covariance matrix at every itera...