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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 183 (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 27 (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.
Comparing different approaches to model error modeling in robust identification
 Automatica
, 2002
"... Technical reports from the Automatic Control group in Linköping are available by anonymous ftp at the address ftp.control.isy.liu.se. This report is contained in the file 2353.pdf. ..."
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Cited by 23 (1 self)
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Technical reports from the Automatic Control group in Linköping are available by anonymous ftp at the address ftp.control.isy.liu.se. This report is contained in the file 2353.pdf.
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.
An Ellipsoid Calculus Based on Propagation and Fusion
"... This paper presents an Ellipsoidal Calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the int ..."
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Cited by 11 (5 self)
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This paper presents an Ellipsoidal Calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degen eracies of the involved ellipsoids and/or affine relations. Examples arising
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 4 (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...
Guaranteed nonlinear parameter estimation via interval computations
 Interval Computation
, 1993
"... The problem of estimating the parameters of a nonlinear model from prior knowledge, experimental data and collateral requirements is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. It is, for instance, possible to characterize ..."
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Cited by 4 (1 self)
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The problem of estimating the parameters of a nonlinear model from prior knowledge, experimental data and collateral requirements is viewed as one of set inversion, which is solved in an approximate but guaranteed way with the tools of interval analysis. It is, for instance, possible to characterize the set of all parameter vectors that are consistent with the data in the sense that the errors between the data and corresponding model outputs fall within known prior bounds. Any collateral requirements that can be expressed as a series of inequalities to be satisfied by the parameters can be taken into account. This is illustrated by asymptotic stability requirements for timeinvariant models whose outputs are linear in their inputs, even if nonlinear in their parameters. The characterization of optimal confidence region in a Bayesian context can also be formulated in the framework of set inversion. Гарантированная оценка нелинейных параметров через интервальные вычисления
Mathematical Modelling In The PostGenome Era: Understanding Genome Expression And Regulation  A System Theoretic Approach
, 2002
"... This paper introduces a mathematical framework for modelling genome expression and regulation. Starting with a philosophical foundation, causation is identified as the principle of explanation of change in the realm of matter. Causation is, therefore, a relationship, not between components, but betw ..."
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Cited by 3 (0 self)
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This paper introduces a mathematical framework for modelling genome expression and regulation. Starting with a philosophical foundation, causation is identified as the principle of explanation of change in the realm of matter. Causation is, therefore, a relationship, not between components, but between changes of states of a system. We subsequently view genome expression (formerly known as `gene expression') as a dynamic process and model aspects of it as dynamic systems using methodologies developed within the areas of systems and control theory. We begin with the possibly most abstract but general formulation in the setting of category theory. The class of models realised are statespace models, input  output models, autoregressive models or automata. We find that a number of proposed `gene network' models are, therefore, included in the framework presented here. The conceptual framework that integrates all of these models defines a dynamic system as a family of expression profiles. It becomes apparent that the concept of a `gene' is less appropriate when considering mathematical models of genome expression and regulation. The main claim of this paper is that we should treat (model) the organisation and regulation of genetic pathways as what they are: dynamic systems. Microarray technology allows us to generate large sets of time series data and is, therefore, discussed with regard to its use in mathematical modelling of gene expression and regulation. 2002 Elsevier Science Ireland Ltd. All rights reserved.
UpdatorShared Adaptive Parallel Equalization (UShAPE) Using SetMembership Identification
 Proc. IEEE Intl. Symp. Circuits and Systems, Atlanta, GA
, 1996
"... Earlier research has shown that the use of setmembership identification (SMI) in adaptive equalization of multipath fading channels results in bit error rate performance comparable to that obtained using the recursive least squares (RLS) algorithm while not requiring to update the equalizer paramet ..."
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Cited by 3 (3 self)
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Earlier research has shown that the use of setmembership identification (SMI) in adaptive equalization of multipath fading channels results in bit error rate performance comparable to that obtained using the recursive least squares (RLS) algorithm while not requiring to update the equalizer parameters at every instant of time. The discerning update strategy of the SMI methodology is exploited in this paper to develop a scheme, referred to here as USHAPE, which shares the processors that update equalizer tap coefficients, resulting in a significant reduction in the hardware requirements of a multiaccess channel equalizer. 1. INTRODUCTION The everincreasing demand for high quality wireless communication services to a large number of users has created a need for novel signal processing techniques to combat distortion in wireless digital communication systems. Adaptive equalization is a common approach to mitigate the effect of multipath fading and the resulting intersymbol interferenc...
SETMEMBERSHIP ADAPTIVE FILTERING WITH PARAMETERDEPENDENT ERROR BOUND TUNING
"... This paper considers setmembership filtering (SMF) when the errorbound specification is hard to determine. Improper errorbound specification could cause overbounding or underbounding, both of which can result in degraded performance for SMF algorithms. This paper introduces a novel variable error ..."
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Cited by 2 (0 self)
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This paper considers setmembership filtering (SMF) when the errorbound specification is hard to determine. Improper errorbound specification could cause overbounding or underbounding, both of which can result in degraded performance for SMF algorithms. This paper introduces a novel variable error bound and presents a different SMF criterion. It is shown that the recursive algorithm derived from this new setmembership filtering criterion has less risk of overbounding/underbounding and outperforms conventional SMF algorithms with one fixed errorbound specification, particularly when insufficient knowledge is available to determine the bound. The proposed algorithm is more suitable to timevariant environments. Frequencydomain equalization for broadband wireless communications is used as an example to illustrate the proposed criterion and recursive solution. Simulation results that show convergence performance and tracking of a timevariant channel are presented.