Showing papers by "Ali H. Sayed published in 2001"
TL;DR: It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance.
Abstract: Develops a framework for state-space estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than deregularization. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (time- and measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with /spl Hscr//sub /spl infin// guaranteed-cost, and set-valued state estimation filters are provided.
393 citations
TL;DR: While the discussion focuses primarily on scalar-valued rational spectra, extensions to nonrational and vector-valued spectra are briefly noted.
Abstract: Spectral factorization is a crucial step in the solution of linear quadratic estimation and control problems. It is no wonder that a variety of methods has been developed over the years for the computation of canonical spectral factors. This paper provides a survey of several of these methods with special emphasis on clarifying the connections that exist among them. While the discussion focuses primarily on scalar-valued rational spectra, extensions to nonrational and vector-valued spectra are briefly noted. Copyright c 2001 John Wiley & Sons, Ltd.
285 citations
TL;DR: A unified approach to the steady-state and tracking analyses of adaptive algorithms that bypasses many of these difficulties and relies on a fundamental error variance relation.
Abstract: Most adaptive filters are inherently nonlinear and time-variant systems. The nonlinearities in the update equations tend to lead to difficulties in the study of their steady-state performance as a limiting case of their transient performance. This paper develops a unified approach to the steady-state and tracking analyses of adaptive algorithms that bypasses many of these difficulties. The approach is based on the study of the energy flow through each iteration of an adaptive filter, and it relies on a fundamental error variance relation.
267 citations
TL;DR: This paper performs stability and steady-state analysis of adaptive filters with error nonlinearities under weaker conditions than what is usually encountered in the literature, and without imposing any restriction on the color or statistics of the input.
Abstract: This paper develops a unified approach to the analysis and design of adaptive filters with error nonlinearities. In particular, the paper performs stability and steady-state analysis of this class of filters under weaker conditions than what is usually encountered in the literature, and without imposing any restriction on the color or statistics of the input. The analysis results are subsequently used to derive an expression for the optimum nonlinearity, which turns out to be a function of the probability density function of the estimation error. Some common nonlinearities are shown to be approximations to the optimum nonlinearity. The framework pursued here is based on energy conservation arguments.
101 citations
TL;DR: This paper formulates and solves a robust criterion for least-squares designs in the presence of uncertain data that incorporates simultaneously both regularization and weighting and applies to a large class of uncertainties.
Abstract: This paper formulates and solves a robust criterion for least-squares designs in the presence of uncertain data. Compared with earlier studies, the proposed criterion incorporates simultaneously both regularization and weighting and applies to a large class of uncertainties. The solution method is based on reducing a vector optimization problem to an equivalent scalar minimization problem of a provably unimodal cost function, thus achieving considerable reduction in computational complexity.
90 citations
TL;DR: This work develops an adaptive sigma-delta modulator that is based on adapting the quantizers step-size using estimates of the quantizer input rather than the modulator input, and it is shown to be independent of the input signal strength.
Abstract: This work develops an adaptive sigma-delta modulator that is based on adapting the quantizer step-size using estimates of the quantizer input rather than the modulator input. The adaptive modulator with a first-order noise shaping filter is shown to be bounded-input bounded-output stable. Moreover, an analytical expression for the signal-to-noise ratio is derived, and it is shown to be independent of the input signal strength. Simulation results confirm the signal-to-noise ratio performance and indicate considerable improvement in the dynamic range of the modulator compared to earlier structures.
43 citations
TL;DR: A computable condition for checking if the problem is degenerate as well as an efficient algorithm to find the global solution with minimum Euclidean norm are presented.
Abstract: We consider the following problem: $\min_{x \in {\cal R}^n} \min_{\|E\| \le \eta} \|(A+E)x-b\|$, where $A$ is an $m \times n$ real matrix and $b$ is an $n$-dimensional real column vector when it has multiple global minima. This problem is an errors-in-variables problem, which has an important relation to total least squares with bounded uncertainty. A computable condition for checking if the problem is degenerate as well as an efficient algorithm to find the global solution with minimum Euclidean norm are presented.
24 citations
07 May 2001
TL;DR: This work derives conditions on the step-size for stability, and provides closed form expressions for the steady-state performance of leaky adaptive algorithms that employ a general scalar or matrix data nonlinearity.
Abstract: We study leaky adaptive algorithms that employ a general scalar or matrix data nonlinearity. We perform mean-square analysis of this class of algorithms without imposing restrictions on the distribution of the input signal. In particular, we derive conditions on the step-size for stability, and provide closed form expressions for the steady-state performance.
24 citations
TL;DR: It is shown, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures, and that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models.
Abstract: The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models. One of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses.
24 citations
15 Nov 2001
TL;DR: This paper presents a tracking methodology based on a robust state-space estimation algorithm, which attempts to control the influence of uncertain environment conditions on the system's performance by adapting the tracking model to compensate for the uncertainties inherent in the data.
Abstract: Key to the design of human-machine gesture interface applications is the ability of the machine to quickly and efficiently identify and track the hand movements of its user. In a wearable computer system equipped with head-mounted cameras, this task is extremely difficult due to the uncertain camera motion caused by the user's head movement, the user standing still then randomly walking, and the user's hand or pointing finger abruptly changing directions at variable speeds. This paper presents a tracking methodology based on a robust state-space estimation algorithm, which attempts to control the influence of uncertain environment conditions on the system's performance by adapting the tracking model to compensate for the uncertainties inherent in the data. Our system tracks a user's pointing gesture from a single head mounted camera, to allow the user to encircle an object of interest, thereby coarsely segmenting the object. The snapshot of the object is then passed to a recognition engine for identification, and retrieval of any pre-stored information regarding the object. A comparison of our robust tracker against a plain Kalman tracker showed a 15% improvement in the estimated position error, and exhibited a faster response time.
23 citations
07 May 2001
TL;DR: An adaptive delta modulator that has improved SNR performance and robustness in tracking highly varying signals and is BIBO stable is proposed and studied.
Abstract: We propose and study an adaptive delta modulator that has improved SNR performance and robustness in tracking highly varying signals. The step-size adaptation used in this modulator is based on information about the absolute value of the quantizer input. The modulator is shown to be free of zero-input limit cycles and is BIBO stable.
11 Jun 2001
TL;DR: A technique for detecting and providing an estimate of the number of overlapping fading multipath components is developed, vital for accurate resolution of overlapping multipath component resolution as well as avoiding unnecessary computations and errors in single-path propagation cases.
Abstract: The Federal Communications Commission (FCC) mandate for locating the position of wireless 911 callers is fueling research in the area of mobile-positioning technologies. Overlapping multipath propagation is one of the main sources of mobile-positioning errors, especially in fast channel fading situations. In this paper we develop a technique for detecting and providing an estimate of the number of overlapping fading multipath components. Such information is vital for accurate resolution of overlapping multipath components as well as avoiding unnecessary computations and errors in single-path propagation cases. The proposed technique exploits the fact that multipath components fade independently as well as the pulse shape symmetry. The paper also presents supporting simulation results.
07 May 2001
TL;DR: This paper develops a framework for the mean-square analysis of adaptive filters with general data and error nonlinearities and provides closed form expressions for the steady-state performance and necessary and sufficient conditions for stability.
Abstract: This paper develops a framework for the mean-square analysis of adaptive filters with general data and error nonlinearities. The approach relies on energy conservation arguments and is carried out without restrictions on the probability distribution of the input sequence. In particular, for adaptive filters with diagonal matrix nonlinearities, we provide closed form expressions for the steady-state performance and necessary and sufficient conditions for stability. We carry out a similar study for long adaptive filters that employ error nonlinearities relying on a weaker form of the independence assumption. We provide expressions for the steady-state error and bounds on the step-size for stability by exploiting the Cramer-Rao bound of the underlying estimation process.
TL;DR: This paper develops several lattice structures for RLS-Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattICE filters, and normalized lattice filter structures.
Abstract: This paper develops several lattice structures for RLS-Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattice filters, and normalized lattice filters. All structures are efficient in that their computational cost is proportional to the number of taps, albeit some structures require more multiplications or divisions than others. The performance of all filters, however, can differ under practical considerations, such as finite-precision effects and regularization. Simulations are included to illustrate these facts.
06 May 2001
TL;DR: This paper studies adaptive Laguerre networks, where shift structure no longer holds, and shows that fast fixed-order updates are still possible.
Abstract: Conventional derivations of fast fixed-order RLS filters rely on the shift structure that is characteristic of regressors in a tapped-delay line implementation. In this paper, we study adaptive Laguerre networks, where shift structure no longer holds. We show that fast fixed-order updates are still possible.
Patent•
13 Jul 2001TL;DR: In this article, an adaptive sigma-delta modulation and demodulation technique is proposed, where a quantizer step size is adapted based on estimates of an input signal to the quantizer, rather than on the estimates of the input signal itself to the modulator.
Abstract: An adaptive sigma-delta modulation and demodulation technique, wherein a quantizer step-size is adapted based on estimates of an input signal to the quantizer, rather than on estimates of an input signal to the modulator.
04 Dec 2001
TL;DR: In this article, the scaling parameter is chosen as the square root factor of the inverse of a positive-definite solution to certain matrix inequalities, motivated by the desire to generate an estimator dynamics with a stable closed-loop matrix whose maximum singular value is bounded by unity.
Abstract: The paper describes a procedure for improving the robustness margins of robust filters via parameter scaling. The scaling parameter is chosen as the square-root factor of the inverse of a positive-definite solution to certain matrix inequalities. This choice is motivated by the desire to generate an estimator dynamics with a stable closed-loop matrix whose maximum singular value is bounded by unity; a step that enhances the robustness of the filters.
01 Jan 2001
TL;DR: Models for motion uncertainties associated with a human hand are produced and applied to a robust state-space estimation algorithm used to track a user's pointing fingertip and a comparison is performed between the results from the robust tracker against a Kalman filter.
Abstract: This paper studies the application of robust state-space estimation with uncertain models to tracking problems in human-machine interfaces. The need for robust methods arises from the desire to control the influence of uncertain environmental conditions on system performance, such as the effect of abrupt variations in object speed and motion characteristics. This paper produces models for motion uncertainties associated with a human hand, and applies them to a robust state-space estimation algorithm used to track a user's pointing fingertip. Then a comparison is performed between the results from the robust tracker against a Kalman filter.
01 Jan 2001
TL;DR: An adaptive technique for resolving overlapping multipath components using a gradient-based adaptive filter with projections to incorporate a-priori channel information and improve the algorithm robustness against data ill-conditioning and high noise levels, which are common in wireless location applications.
Abstract: We develop an adaptive technique for resolving overlapping multipath components. The technique relies on replacing the least-squares operation needed for resolving overlapping components by a gradient-based adaptive filter with projections. The projections are designed to incorporate a-priori channel information and improve the algorithm robustness against data ill-conditioning and high noise levels, which are common in wireless location applications.
06 May 2001
TL;DR: An error variance analysis of the new adaptive sigma delta modulator and derive expression for the SNR shows that theSNR is independent of the input signal strength, which supports the simulation results.
Abstract: In a previous study, we proposed an adaptive sigma delta modulator with an improved dynamic range. The modulator adapts the step size of the quantizer from estimates of the quantizer input instead of the modulator input. In this study, we conduct an error variance analysis of the new modulator and derive expression for the SNR. The derived expression shows that the SNR is independent of the input signal strength, which supports the simulation results.
Proceedings Article•
01 Jan 2001TL;DR: In this paper, an adaptive sigma delta modulator with an improved dynamic range was proposed, where the modulator adapts the step size of the quantizer from estimates of quantizer input instead of modulator input.
Abstract: In a previous study, we proposed an adaptive sigma delta modulator with an improved dynamic range. The modulator adapts the step size of the quantizer from estimates of the quantizer input instead of the modulator input. In this study, we conduct an error variance analysis of the new modulator and derive expression for the SNR. The derived expression shows that the SNR is independent of the input signal strength, which supports the simulation results.
07 May 2001
TL;DR: It is shown, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures, and that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally-based models.
Abstract: The existing derivations of fast RLS adaptive filters are dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally-based models. One of the benefits of working with an orthonormal basis is that fewer parameters can be used to model long impulse responses.
06 May 2001
TL;DR: This paper develops lattice structures for RLS Laguerre adaptive filtering including error-feedback and array-based lattice versions that can differ under practical considerations, such as finite-precision effects and regularization.
Abstract: This paper develops lattice structures for RLS Laguerre adaptive filtering including error-feedback and array-based lattice versions. All structures are efficient in that their computational cost is proportional to the number of taps. Although these structures are theoretically equivalent, their performance can differ under practical considerations, such as finite-precision effects and regularization. Simulations are included to illustrate this point.
07 May 2001
TL;DR: A fixed point analysis is presented for the steady-state mean square error of a blind adaptive equalizer and the optimal value of the step-size that minimizes this MSE is presented.
Abstract: The steady-state performance of adaptive equalizers can significantly vary when they are implemented in finite precision arithmetic, which makes it vital to analyze their performance in a quantized environment. We present a fixed point analysis for the steady-state mean square error (MSE) of a blind adaptive equalizer and the optimal value of the step-size that minimizes this MSE. Such expressions are useful for selecting the adequate wordlength of a blind equalizer to achieve a specific desired steady-state performance.
01 Jan 2001
TL;DR: An adaptive sigma-delta modulator with a first-order noise shaping filter is shown to be bounded-input bounded-output stable and an analytical expression for the signal-to-noise ratio is derived, and it is shows to be independent of the input signal strength.
Abstract: This work develops an adaptive sigma-delta modu- lator that is based on adapting the quantizer step-size using es- timates of the quantizer input rather than the modulator input. The adaptive modulator with a first-order noise shaping filter is shown to be bounded-input bounded-output stable. Moreover, an analytical expression for the signal-to-noise ratio is derived, and it is shown to be independent of the input signal strength. Simulation results confirm the signal-to-noise ratio performance and indicate considerable improvement in the dynamic range of the modulator compared to earlier structures.