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DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 169 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interiorpoint method, with a simplified analysis of the worstcase complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interiorpoint method will generally be slower; the advantage is that it handles a much wider variety of problems.
Setmembership filtering and a setmembership normalized LMS algorithm with an adaptive step size
 IEEE Signal Process. Lett
, 1998
"... Abstract — Setmembership identification (SMI) theory is extended to the more general problem of linearinparameters filtering by defining a setmembership specification, as opposed to a bounded noise assumption. This sets the framework for several important filtering problems that are not modeled ..."
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Cited by 26 (6 self)
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Abstract — Setmembership identification (SMI) theory is extended to the more general problem of linearinparameters filtering by defining a setmembership specification, as opposed to a bounded noise assumption. This sets the framework for several important filtering problems that are not modeled by a “true ” unknown system with bounded noise, such as adaptive equalization, to exploit the unique advantages of SMI algorithms. A recursive solution for set membership filtering is derived that resembles a variable step size normalized least mean squares (NLMS) algorithm. Interesting properties of the algorithm, such as asymptotic cessation of updates and monotonically nonincreasing parameter error, are established. Simulations show significant performance improvement in varied environments with a greatly reduced number of updates. I.
Setmembership adaptive equalization and an updatorshared implementation for multiple channel communication systems
 IEEE Trans. Signal Processing
, 1998
"... Abstract — This paper considers the problems of channel estimation and adaptive equalization in the novel framework of setmembership parameter estimation. Channel estimation using a class of setmembership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their exte ..."
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Cited by 16 (9 self)
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Abstract — This paper considers the problems of channel estimation and adaptive equalization in the novel framework of setmembership parameter estimation. Channel estimation using a class of setmembership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to track timevarying channels are described. Simulation results show that the OBE channel estimators outperform the leastmeansquare (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of setmembership equalization is introduced along with the notion of a feasible equalizer. Necessary and sufficient conditions are derived for the existence of feasible equalizers in the case of linear equalization for a linear FIR additive noise channel. An adaptive OBE algorithm is shown to provide a set of estimated feasible equalizers. The selective update feature of the OBE algorithms is exploited to devise an updatorshared scheme in a multiple channel environment, referred to as updatorshared parallel adaptive equalization (USHAPE). USHAPE is shown to reduce hardware complexity significantly. Procedures to compute the minimum number of updating processors required for a specified quality of service are presented. I.
Tracking of TimeVarying Parameters using Optimal Bounding Ellipsoid Algorithms
 Proc., 34th Annual Allerton Conf. Communication, Control and Computing, University of Illinois, UrbanaChampaign, Oct 24
, 1996
"... This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a sel ..."
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Cited by 6 (5 self)
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This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a selective update property for the time and observationupdate equations, and necessary and sufficient conditions for state tracking are derived. The interpretability of the optimization criterion is also investigated along with simulation results. 1 Introduction Tracking of time varying parameters is an important problem, both from theoretical as well as practical viewpoints, in adaptive signal processing, communication and control systems. An elegant, convenient and general framework for formulating the problem is provided by linear statespace equations. In this paper, we use the discretetime state equation framework and present an optimal bounding ellipsoid (OBE) algorithm for tracking tim...
Guaranteed robust nonlinear estimation, with application to robot localization
 IEEE Transactions on systems, man and cybernetics; Part C – Applications and Reviews 32 (4) (2003) 374—382, accepted
"... Abstract—When reliable prior bounds on the acceptable errors between the data and corresponding model outputs are available, boundederror estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, even when the model is nonlinear and the ..."
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Cited by 6 (3 self)
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Abstract—When reliable prior bounds on the acceptable errors between the data and corresponding model outputs are available, boundederror estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, even when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or at least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkably robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known twodimensional (2D) environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as byproducts of the procedure. I.
Adaptive multiuser detection and beamforming for interference suppression in CDMA mobile radio systems
 IEEE Transactions on Vehicular Technolgy,pp.1341—1354
, 1999
"... Abstract — This paper considers the problem of interference suppression in directsequence codedivision multipleaccess (DSCDMA) systems over fading channels. An adaptive array receiver is presented which integrates multiuser detection, beamforming, and RAKE reception to mitigate cochannel interfe ..."
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Cited by 6 (0 self)
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Abstract — This paper considers the problem of interference suppression in directsequence codedivision multipleaccess (DSCDMA) systems over fading channels. An adaptive array receiver is presented which integrates multiuser detection, beamforming, and RAKE reception to mitigate cochannel interference and fading. The adaptive multiuser detector is formulated using a blind constrained energy minimization criterion and adaptation is carried out using a novel algorithm based on setmembership parameter estimation theory. The proposed detector overcomes the shortcomings of conventional LMS and RLStype algorithms, namely, that of slow convergence and large computational load, respectively. This is especially the case when strong interferers are present or when the number of adaptive weights is relatively large. DSCDMA systems can have a relatively large number of spatially distributed interferers. Thus beamforming is based on directionofarrival (DOA) estimates provided by an approximate maximumlikelihood estimator (DOAMLE). Unlike previous approaches, the DOAMLE exploits the structure of the DSCDMA signaling scheme resulting in robust performance and simple implementation in the presence of angle spreading. The overall method is suitable for realtime implementation and can substantially improve the interference suppression capabilities of a CDMA system. Index Terms — Adaptive filters, array signal processing, code division multiaccess, direction of arrival estimation, interference suppression, mobile communication. I.
Smart: A Toolbox For SetMembership Filtering
 Proc. 1997 European Conf. Circuit Theory and Design
, 1997
"... This paper presents the concept of SetMembership Filtering (SMF), an extension of SetMembership Identification (SMI) theory to the general filtering problem. A toolbox of adaptive solutions called SMART (SetMembership Adaptive Recursive Techniques) is presented. We show that the class of Optimal Bo ..."
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Cited by 3 (0 self)
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This paper presents the concept of SetMembership Filtering (SMF), an extension of SetMembership Identification (SMI) theory to the general filtering problem. A toolbox of adaptive solutions called SMART (SetMembership Adaptive Recursive Techniques) is presented. We show that the class of Optimal Bounding Ellipsoid (OBE) algorithms belong to SMART. An NLMSlike algorithm that features linear complexity and an adaptive stepsize is also derived as a member of SMART. I. INTRODUCTION Conventional filtering involves determining, or estimating, the filter parameters by optimizing a cost function defined on the parameter space. The choice of the cost function is usually made to facilitate analytical and computational simplicity, rather than to reflect desired performance and a priori knowledge. Examples include the stochastic least meansquare criterion and the deterministic leastsquares criterion. In many applications, however, the designer has a priori knowledge about the physical syste...
Blind Multiuser Detection And Interference Cancellation In DSCDMA Mobile Radio Systems
"... This paper deals with blind adaptive multiuser detection and interference cancellation for direct sequenceCDMA wireless communication systems using antenna arrays. Such techniques have recently been considered as powerful methods for increasing overall system quality, capacity and coverage. With a ..."
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Cited by 2 (1 self)
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This paper deals with blind adaptive multiuser detection and interference cancellation for direct sequenceCDMA wireless communication systems using antenna arrays. Such techniques have recently been considered as powerful methods for increasing overall system quality, capacity and coverage. With a large number of adaptive weights, LMS type algorithms suffer from poor convergence while conventional least squares techniques can be computationally prohibitive. To mitigate these problems, this paper presents a twostage blind adaptive receiver architecture which carries out multiuser detection using an Optimal Bounding Ellipsoid (OBE) algorithm and DirectionofArrival estimation based beamforming using a novel, simple yet robust algorithm referred to as Differential Phase Smoothing. The unique discerning update property of OBE algorithms allows for a reduced complexity receiver. Furthermore, the adaptive multiuser detector also inherits improved convergence and tracking properties. Simu...
Specific Selection of FFT Amplitudes from Audio Sports and News Broadcasting for Classification Purposes
"... In this paper we investigate the problem of classification between sports and news broadcasting. We detect and classify files that consist of speech and music or background noise (news broadcasting), and speech and a noisy background (sports broadcasting). More specifically, this study investigates ..."
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Cited by 2 (2 self)
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In this paper we investigate the problem of classification between sports and news broadcasting. We detect and classify files that consist of speech and music or background noise (news broadcasting), and speech and a noisy background (sports broadcasting). More specifically, this study investigates feature extraction and training and classification procedures. We compare the Average Magnitude Difference Function (AMDF) method, which we consider more robust to background noise, with a novel proposed method. This method uses several spectral audio features which may be considered as specific semantic information. We base the extraction of these features on the theory of computational geometry using an Onion Algorithm (OA). We tested the classification procedure as well as the learning ability of the two methods using a Learning Vector Quantizer One (LVQ1) neural network. The results of the experiment showed that the OA method has a faster learning procedure, which we characterise as an accurate feature extraction method for several audio cases.
Recursive Nonlinear Set–Theoretic Estimation Based on Pseudo– Ellipsoids
 In: Proceedings of the IEEE Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI’2001), Baden–Baden
, 2001
"... In this paper, the problem of estimating a vector x of unknown quantities based on a set of measurements depending nonlinearly on x is considered. The measurements are assumed to be taken sequentially and are corrupted by unknown but bounded uncertainties. For this uncertainty model, a systematic de ..."
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Cited by 2 (1 self)
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In this paper, the problem of estimating a vector x of unknown quantities based on a set of measurements depending nonlinearly on x is considered. The measurements are assumed to be taken sequentially and are corrupted by unknown but bounded uncertainties. For this uncertainty model, a systematic design approach is introduced, which yields closed–form expressions for the desired nonlinear estimates. The estimates are recursively calculated and provide solution sets X containing the feasible sets, i.e., the sets of all x consistent with all the measurements available and their associated bounds. The sets X are tight upper bounds for the exact feasible sets and are in general not convex and not connected. The proposed design approach is versatile and the resulting nonlinear filter algorithms are both easy to implement and efficient. 1