Crosstalk among telephone lines in the same or neighboring bundles is a major impairment in current xDSL systems. This paper proposes a novel idea of an impartial third party that identifies the crosstalk coupling functions among the twisted pairs in these xDSL systems. The crosstalk identification technique includes the following four major procedures: 1) the transmitted and received signals from each DSL modem for a predefined time period are collected and sent to the third party; 2) the signals are resampled according to the clock rate of the receiver of interest; 3) the signals' timing differences are estimated by cross correlation; and 4) the crosstalk coupling functions are estimated using the least-squares method. The performance of the cross correlation and least-squares methods is analyzed to determine the amount of data needed for identification. Simulation results show that the proposed methods can identify the crosstalk functions accurately and are consistent with theoretical analysis. These identified crosstalk functions can be used to significantly improve the data rate (e.g., multiuser detection) and to facilitate provisioning, maintenance, and diagnosis of the xDSL systems. Index Terms---Cross correlation, crosstalk, digital subscriber line (DSL), identification, resampling, third party, Wishart function. I.

In this paper the design of sensing systems for the measurement of multiple physical quantities related to a dynamical system is considered. A multivariate sensor comprises several simple transducers, each measuring a scalar quantity that comes from the combination of the components of the quantity to be measured. From the collection of measurements of single transducers at di#erent times, the desired information is extracted by analog or digital processing. Besides the choice of technological characteristics of the transducers to be employed, the designer of multivariate sensors is usually allowed some freedom in choosing the number of transducers, their arrangement in the system, and the time scheduling of their measurements. These choices are the subject of optimal policies in the design phase, whose goal is to maximize some performance #or minimize some cost# criterion. We survey some of the existing approaches to optimal design of multivariate sensors, according to t...

Abstract—Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Cramér–Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions. Index Terms—Frequency estimation, linear prediction, monic constraint, real sinusoids, unit-norm constraint, weighted least squares. I.

This paper addresses the problem of maximum likelihood parameter estimation in linear models affected by gaussian noise, whose mean and covariance matrix are uncertain. The proposed estimate maximizes a lower bound on the worst-case (with respect to the uncertainty) likelihood of the measured sample, and is computed solving a semidefinite optimization problem (SDP). The problem of linear robust estimation is also studied in the paper, and the the statistical and optimality properties of the resulting linear estimator are discussed.

Abstract: The objective of this contribution is input design for accurate identification of non-minimum phase zeros in linear systems. Recently, several variance results regarding estimation of non-minimum phase zeros have been presented. Based on these results, we will show how to design the input that has the least energy content required to keep the variance of an estimated zero below a certain limit. Both analytical and numerical results are presented. A striking fact of the analytical results is that the variance of an estimated zero is independent of the model order when the optimal input is applied. We will also quantify the benefits of using the optimal design compared to using a white input signal or a square-wave. Robustness issues will also be covered in this presentation. The optimal design depends on the location of the true unknown zero and is therefore infeasible. This is typically circumvented by replacing the true zero by an estimate. The sensitivity of the solution to this estimate is investigated. Copyright c○2005 IFAC

We present results concerning the parameter estimates obtained by prediction error methods in the case of input signals that are insufficiently rich. Such input signals are typical of industrial measurements where occasional stepwise reference changes occur. As is intuitively obvious, the data located around the input signal discontinuities carry most of the useful information. Using singular value decomposition techniques, we show that in noise undermodeling situations, the remaining data may introduce large bias on the model parameters with a possible increase of their total mean square error. A data selection criterion is then proposed to discard such poorly informative data so as to increase the accuracy of the transfer function estimate. Keywords : identification, persistence of excitation, parameter estimation, singular value decomposition. 1 Introduction The aim of this paper is to analyse in detail the accuracy of the least squares (LS) prediction error method [3] for estimat...

Abstract: It is commonly believed that solutions to optimal input design problems for identification of dynamical systems often are sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range (−π,π]) as number of estimated parameters. With such an input it is not possible to check whether the true system is of higher order or not since then the input is not persistently exciting enough. In this contribution we argue that the optimal solution is often not unique and that there are alternatives to sinusoidal inputs which are more robust. For simplicity, we restrict attention to finite impulse-response models. For such a model of order n, it is only the n first auto-correlation coefficients of the input which determine the accuracy of the parameter estimate. Thus, the remaining coefficients can be used to make the solution more robust. For the problem of estimating some scalar system quantity J with a prescribed accuracy using minimum input energy, there is, under certain assumptions, an input spectrum that is optimal regardless of the model order. Furthermore, we show that using this input allows J to be estimated consistently even when the model order is lower than the true system order. Copyright c○2006 IFAC

We consider the situation where the parameters # of a linear regression model have to be estimated from observations corrupted by an additive noise with unknown distribution f .

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for systems that exhibit both continuous dynamics and discrete mode changes. Estimating the hybrid discrete-continuous state of these systems is important for control and fault detection. Existing solutions for hybrid estimation approximate the belief state by maintaining a subset of the possible discrete mode sequences. This approximation can cause the estimator to lose track of the true mode sequence when the effects of discrete mode changes are subtle. In this paper we present a method for active hybrid estimation, where control inputs can be designed to discriminate between possible mode sequences. By probing the system for the purposes of estimation, such a sequence of control inputs can greatly reduce the probability of losing the true mode sequence compared to a nominal control sequence. Furthermore, by using a constrained finite horizon optimization formulation, we are able to guarantee that a given control task is achieved, while optimally detecting the hybrid state. In order to achieve this, we present three main contributions. First, we develop a method by which a sequence of control inputs is designed in order to discriminate optimally between a finite number of linear dynamic system models. These control inputs minimize a novel, tractable upper bound on the probability of model selection error. Second, we extend this approach to develop an active estimation method for Jump Markov Linear Systems by relating the probability of model selection error to the probability of losing the true mode sequence. Finally, we make this method tractable using a principled pruning technique. Simulation results show that the new method applied to an aircraft fault detection problem significantly decreases the probability of a hybrid estimator losing the true mode sequence. I.