Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text overlap with arXiv:1303.671

Adaptive kernel canonical correlation analysis algorithms for nonparametric identification of Wiener and Hammerstein systems

This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem.We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memor

Identification of hammerstein-wiener systems including backlash input nonlinearities

Postprint (published version