Showing papers by "Ali H. Sayed published in 1998"
TL;DR: In this paper, the authors formulate and solve a new parameter estimation problem in the presence of data uncertainties, which is suitable when a priori bounds on the uncertain data are available, and its solution leads to more meaningful results, especially when compared with other methods such as total least squares and robust estimation.
Abstract: We formulate and solve a new parameter estimation problem in the presence of data uncertainties. The new method is suitable when a priori bounds on the uncertain data are available, and its solution leads to more meaningful results, especially when compared with other methods such as total least-squares and robust estimation. Its superior performance is due to the fact that the new method guarantees that the effect of the uncertainties will never be unnecessarily over-estimated, beyond what is reasonably assumed by the a priori bounds. A geometric interpretation of the solution 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.
172 citations
TL;DR: This paper proposes two modifications of the filtered-x least mean squares algorithm with improved convergence behavior albeit at the same computational cost of 2M operations per time step as the original FxLMS update.
Abstract: This paper proposes two modifications of the filtered-x least mean squares (FxLMS) algorithm with improved convergence behavior albeit at the same computational cost of 2M operations per time step as the original FxLMS update The paper further introduces a generalized FxLMS recursion and establishes that the various algorithms are all of filtered-error form A choice of the stepsize parameter that guarantees faster convergence and conditions for robustness are also derived Several simulation results are included to illustrate the discussions
56 citations
TL;DR: In this paper, the authors describe estimation and control strategies for models with bounded data uncertainties, referred to them as BDU estimation and BDU control methods, which are based on constrained game-type formulations that allow the designer to explicitly incorporate into the problem statement a priori information about bounds on the sizes of the uncertainties.
48 citations
TL;DR: A stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitzer, and product of two Toe Plitz matrices) is derived.
Abstract: We derive a stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitz, and product of two Toeplitz matrices). The algorithm is based on a modified fast QR factorization of the coefficient matrix and relies on a stabilized version of the generalized Schur algorithm for matrices with displacement structure. All computations can be done in O(n2) operations, where n is the matrix dimension, and the algorithm is backward stable.
45 citations
01 Nov 1998
TL;DR: An estimation technique for problems that involve multiple sources of uncertainties or errors in the data that allows the designer to explicitly incorporate into the problem formulation bounds on the sizes of the uncertainties; thus leading to solutions that will not over-emphasize the effects of the uncertainty beyond what is assumed by the prior information.
Abstract: We develop an estimation technique for problems that involve multiple sources of uncertainties or errors in the data. The method allows the designer to explicitly incorporate into the problem formulation bounds on the sizes of the uncertainties; thus leading to solutions that will not over-emphasize the effects of the uncertainties beyond what is assumed by the prior information. Applications in array signal processing and image processing are considered.
7 citations
01 Nov 1998
TL;DR: It is shown that when the step-size is large, this approximation of the MSE can be misleading, contrary to what one would expect, given the excellent agreement one obtains between simulations and theory for small step-sizes and independent inputs.
Abstract: We treat the computation of the learning curves of the LMS algorithm by simulation (that is, the computation of the MSE as a function of the time instant). Since closed-form analytic expressions for learning curves are quite hard to obtain in most practical situations, one usually approximates learning curves by performing several repeated experiments and by averaging the resulting squared-error curves. We show, both by examples and analytically, that when the step-size is large, this approximation of the MSE can be misleading. This is contrary to what one would expect, given the excellent agreement one obtains between simulations and theory for small step-sizes and independent inputs, even using only as few as 10 experiments. The theoretical analysis explains both the good results obtained for small step-sizes, and the discrepancies that arise for large step-sizes.
3 citations
Proceedings Article•
01 Jan 1998
2 citations
01 Nov 1998
TL;DR: This paper develops frequency-domain adaptive structures that are based on the trigonometric transforms DCT and DST that are derived by first presenting a derivation for the classical DFT-based filter that allows us to pursue these extensions very immediately.
Abstract: Frequency-domain implementations improve the computational efficiency and the convergence rate of adaptive schemes. This paper develops frequency-domain adaptive structures that are based on the trigonometric transforms DCT and DST. The structures involve only real arithmetic and efficient algorithms exist for computing these transforms. The new filters are derived by first presenting a derivation for the classical DFT-based filter that allows us to pursue these extensions very immediately.