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64
Determinant maximization with linear matrix inequality constraints
 SIAM Journal on Matrix Analysis and Applications
, 1998
"... constraints ..."
Error Estimations For Indirect Measurements: Randomized Vs. Deterministic Algorithms For "BlackBox" Programs
 Handbook on Randomized Computing, Kluwer, 2001
, 2000
"... In many reallife situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure ..."
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Cited by 29 (13 self)
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In many reallife situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x1 ; : : : ; xn , and then by using the known relation between x i and y to reconstruct the value of the desired quantity y. In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, we describe and compare different deterministic and randomized algorithms for solving this problem in the situation when a program for transforming the estimates e x1 ; : : : ; e xn for x i into an estimate for y is only available as a black box (with no source code at hand). We consider this problem in two settings: statistical, when measurements errors \Deltax i = e x i \Gamma x i are inde...
Astrogeometry, Error Estimation, and Other Applications of SetValued Analysis
 ACM SIGNUM Newsletter
, 1996
"... In many reallife application problems, we are interested in numbers, namely, in the numerical values of the physical quantities. There are, however, at least two classes of problems, in which we are actually interested in sets: ffl In image processing (e.g., in astronomy), the desired blackand ..."
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Cited by 27 (26 self)
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In many reallife application problems, we are interested in numbers, namely, in the numerical values of the physical quantities. There are, however, at least two classes of problems, in which we are actually interested in sets: ffl In image processing (e.g., in astronomy), the desired blackandwhite image is, from the mathematical viewpoint, a set.
Simultaneous Localisation and Map Building
, 1997
"... This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) ..."
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Cited by 22 (0 self)
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This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) problem is currently one of the most important goals of AGV research. Solving this problem would allow anAGV to be deployed easily, with very little initial preparation. The AGV would also be exible and able to cope with modi cations in the environment. A solution to the SLAM problem would enable an AGV to would be truly \autonomous." The thesis examines the SLAM problem from an estimation theoretic point ofview. The estimation approach provides a rigorous framework for the analysis and has also proven to be successful in actual applications. The most signi cant contribution of this thesis is to provide, for the rst time, a detailed development of the theory of the SLAM problem. It is shown that correlations arise between errors in the vehicle and the map estimates, and these correlations are identi ed as fundamentally important to the solution of the SLAM problem. It is demonstrated that ignoring these correlations results in the loss of the fundamental structure of the SLAM problem and leads to inconsistency in map
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.
Ellipsoidal bounds for uncertain linear equations and dynamical systems
 Automatica
, 2004
"... In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. This formulat ..."
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Cited by 11 (0 self)
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In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. This formulation leads to convex optimization problems that can be essentially solved in O(n 3)—n being the size of unknown vector — by means of suitable interior point barrier methods, as well as to closed form results in some particular cases. We further show that the uncertain linear equations paradigm can be directly applied to various statebounding problems for dynamical systems subject to setvalued noise and model uncertainty.
Parallelotopic and Practical Observers for Nonlinear Uncertain Systems
 Int. Journal. Control
, 2002
"... For a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs", we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bound ..."
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Cited by 10 (0 self)
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For a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs", we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially towards an arbitrarily small neighborhood of the origin. Under the hypothesis that bounds are available for the uncertain terms, we build parallelotopic observers providing timevarying bounds for the state variables, even when the system is not observable for unknown inputs These results are illustrated on a biological model of a structured population.
Global optimal attitude estimation using uncertainty ellipsoids
, 2008
"... A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the ..."
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Cited by 7 (5 self)
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A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized.
... Identification and Model Quality Evaluation
 IEEE Transactions on Automatic Control
, 1997
"... Set membership H1 identification is investigated using timedomain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called r ..."
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Cited by 6 (1 self)
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Set membership H1 identification is investigated using timedomain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called radius of information, is solved. For classes of models affine in the parameters, the radius of information is obtained as function of the H1 norm of the unmodeled dynamics. A method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics, thus allowing the actual evaluation of the radius of information. The radius represents a measure of the "predictive ability" of the considered class of models, and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part. The effectiveness of the proposed procedure is tested on some numerical examples and compared with stan...
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...