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

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

Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling

Accepted for publication in the Proceedings of the European Signal Processing Conference (EUSIPCO) 2015.International audienceThe computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB

State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

System Identification Based on Errors-In-Variables System Models

We study the identification problem for errors-in-variables (EIV) systems. Such an EIV model assumes that the measurement data at both input and output of the system involve corrupting noises. The least square (LS) algorithm has been widely used in this area. However, it results in biased estimates for the EIV-based system identification. In contrast, the total least squares (TLS) algorithm is unbiased, which is now well-known, and has been effective for estimating the system parameters in the EIV system identification. In this dissertation, we first show that the TLS algorithm computes the approximate maximum likelihood estimate (MLE) of the system parameters and that the approximation error converges to zero asymptotically as the number of measurement data approaches infinity. Then we propose a graph subspace approach (GSA) to tackle the same EIV-based system identification problem and derive a new estimation algorithm that is more general than the TLS algorithm. Several numerical examples are worked out to illustrate our proposed estimation algorithm for the EIV-based system identification. We also study the problem of the EIV system identification without assuming equal noise variances at the system input and output. Firstly, we review the Frisch scheme, which is a well-known method for estimating the noise variances. Then we propose a new method which is GSA in combination with the Frisch scheme (GSA-Frisch) algorithm via estimating the ratio of the noise variances and the system parameters iteratively. Finally, a new identification algorithm is proposed to estimate the system parameters based on the subspace interpretation without estimating noise variances or the ratio. This new algorithm is unbiased, and achieves the consistency of the parameter estimates. Moreover, it is low in complexity. The performance of the identification algorithm is examined by several numerical examples, and compared to the N4SID algorithm that has the Matlab codes available in Matlab toolboxes, and also to the GSA-Frisch algorithm