Showing papers by "Ali H. Sayed published in 1997"
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TL;DR: This work exploits the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm that are applicable to a system identification problem and the tracking of a chirped sinusoid in additive noise.
Abstract: We exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms of the extended RLS algorithm are considered: one pertaining to a system identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise. For both of these applications, experiments are presented that demonstrate the tracking superiority of the extended RLS algorithms compared with the standard RLS and least-mean-squares (LMS) algorithms.
281 citations
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TL;DR: A computationally efficient order-recursive algorithm is derived that achieves the approximating a long FIR filter by a reduced-parameter stable pole-zero filter with high accuracy and is applied to reduce the implementation complexity of the decision feedback equalizer's long FIR feedforward and feedback filters encountered in high-speed data transmission on digital subscriber loops.
Abstract: The problem of approximating a long FIR filter by a reduced-parameter stable pole-zero filter is addressed. We derive a computationally efficient order-recursive algorithm that achieves this task with high accuracy. Our main emphasis is on applying this algorithm to reduce the implementation complexity of the decision feedback equalizer's long FIR feedforward and feedback filters encountered in high-speed data transmission on digital subscriber loops.
39 citations
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TL;DR: A new parameter estimation problem in the presence of bounded data uncertainties is formulated and the solution guarantees that the effect of the uncertainties will never be unnecessarily overestimated beyond what is reasonably assumed by the a priori bounds.
Abstract: We formulate and solve a new parameter estimation problem in the presence of bounded data uncertainties. The new method is suitable when a priori bounds on the uncertain data are available; its solution guarantees that the effect of the uncertainties will never be unnecessarily overestimated beyond what is reasonably assumed by the a priori bounds.
34 citations
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TL;DR: A feedback structure for the design of l2-stable algorithms for nonlinear adaptive filtering and identification, and establishes explicit connections between classical schemes in IIR modeling and more recent results in H∞ theory are proposed.
20 citations
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TL;DR: Bounds are established on the step-size parameters in order to guarantee that the resulting algorithms will behave as robust filters and that an intrinsic feedback structure can be associated with the training schemes.
Abstract: This paper provides a time-domain feedback analysis of the perceptron learning algorithm and of training schemes for dynamic networks with output feedback. It studies the robustness performance of the algorithms in the presence of uncertainties that might be due to noisy perturbations in the reference signals or due to modeling mismatch. In particular, bounds are established on the step-size parameters in order to guarantee that the resulting algorithms will behave as robust filters. The paper also establishes that an intrinsic feedback structure can be associated with the training schemes. The feedback configuration is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The stability of the feedback structure is then analyzed via the small gain theorem, and choices for the step-size parameter in order to guarantee faster convergence are deduced by using the mean-value theorem. Simulation results are included to demonstrate the findings.
16 citations
01 Oct 1997
9 citations
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04 Jun 1997TL;DR: In this paper, the problem of worst-case parameter estimation in the presence of bounded uncertainties in a linear regression model has been formulated and solved in Chandrasekaran et al. (1997).
Abstract: Deals with the problem of worst-case parameter estimation in the presence of bounded uncertainties in a linear regression model. The problem has been formulated and solved in Chandrasekaran et al. (1997). It distinguishes itself from other estimation schemes, such as total-least-squares and H/sub /spl infin//, methods, in that it explicitly incorporates an a-priori bound on the size of the uncertainties. The closed-form solution in the above mentioned articles, however, requires the computation of the SVD of the data matrix and the determination of the unique positive root of a nonlinear equation. This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation. Simulation results are included to demonstrate the good performance of the recursive scheme.
9 citations
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04 Jun 1997TL;DR: In this paper, the authors formulate and solve a new parameter estimation problem in the presence of bounded model uncertainties, and their solution guarantees that the effect of the uncertainties will never be unnecessarily over-estimated beyond what is reasonably assumed by the a priori bounds.
Abstract: We formulate and solve a new parameter estimation problem in the presence of bounded model uncertainties. The new method is suitable when a priori bounds on the uncertain data are available, and its solution guarantees that the effect of the uncertainties will never be unnecessarily over-estimated beyond what is reasonably assumed by the a priori bounds. This is in contrast to other methods, such as total least-squares and robust estimation that do not incorporate explicit bounds on the size of the uncertainties. A geometric interpretation of the solution of the new problem is provided, along with a closed form expression for it. We also consider the case in which only selected columns of the coefficient matrix are subject to perturbations.
8 citations
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04 Jun 1997
TL;DR: In this article, a parameter estimation problem in the presence of bounded data uncertainties is formulated as a minimization problem and admits a closed form solution in terms of the unique positive root of a secular equation.
Abstract: We pose and solve a parameter estimation problem in the presence of bounded data uncertainties. The new formulation involves a minimization problem and admits a closed form solution in terms of the unique positive root of a secular equation. It also has interesting connections with errors-in-variables and H/sub /spl infin// methods.
3 citations
01 Jan 1997
3 citations
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TL;DR: This correspondence presents a choice for the parameters that is motivated by a maximum-entropy formulation, and further motivates the introduction of the so-called generalized reflection coefficients which are, in general, different from the better known Schur coefficients.
Abstract: The study of matrices with a displacement structure is mainly concerned with recursions for the so-called generator matrices. The recursion usually involves free parameters, which can be chosen in several ways so as to simplify the resulting algorithm. In this correspondence we present a choice for the parameters that is motivated by a maximum-entropy formulation, This choice further motivates the introduction of the so-called generalized reflection coefficients which are, in general, different from the better known Schur coefficients.
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21 Apr 1997TL;DR: This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation.
Abstract: This paper deals with the important problem of parameter estimation in the presence of bounded data uncertainties. Its recent closed-form solution leads to more meaningful results than alternative methods (e.g., total least-squares and robust estimation), when a priori bounds about the uncertainties are available. The derivation requires the computation of the SVD of the data matrix and the determination of the unique positive root of a nonlinear equation. This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation. Simulation results are included to demonstrate the good performance of the recursive scheme.
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01 Jan 1997TL;DR: The modified Schur algorithm proposed in this work essentially achieves the bound for a large class of structured matrices that satisfy R-FRF T = GJG T, where J is a signature matrix, F is a stable lower-triangular matrix, and G is a generator matrix.
Abstract: We show how to stabilize the generalized Schur algorithm for the Cholesky factorization of positive-definite structured matrices R that satisfy R-FRF T = GJG T , where J is a signature matrix, F is a stable lower-triangular matrix, and G is a generator matrix. We use a perturbation analysis to indicate the best accuracy that can be expected from any finite precision algorithm that uses the generator matrix as the input data. We then show that the modified Schur algorithm proposed in this work essentially achieves this bound for a large class of structured matrices.