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Abstract — This paper considers the problems of channel estimation and adaptive equalization in the novel framework of set-membership parameter estimation. Channel estimation using a class of set-membership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to track time-varying channels are described. Simulation results show that the OBE channel estimators outperform the leastmean-square (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of set-membership 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 updator-shared scheme in a multiple channel environment, referred to as updator-shared parallel adaptive equalization (U-SHAPE). U-SHAPE 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.

Abstract — Set-membership identification (SMI) theory is extended to the more general problem of linear-in-parameters filtering by defining a set-membership 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.

This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking time-varying parameters with incrementally bounded time variations. A linear state-space model is used, with the time-varying parameters represented by the state vector. The OBE algorithm exhibits a selective update property for the time and observation-update 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 state-space equations. In this paper, we use the discrete-time state equation framework and present an optimal bounding ellipsoid (OBE) algorithm for tracking tim...

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 (Set-Membership Adaptive Recursive Techniques) is presented. We show that the class of Optimal Bounding Ellipsoid (OBE) algorithms belong to SMART. An NLMS-like algorithm that features linear complexity and an adaptive step-size 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 mean-square criterion and the deterministic least-squares criterion. In many applications, however, the designer has a priori knowledge about the physical syste...

Abstract—When reliable prior bounds on the acceptable errors between the data and corresponding model outputs are available, bounded-error 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 two-dimensional (2-D) 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.

This paper deals with blind adaptive multiuser detection and interference cancellation for direct sequence-CDMA 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 two-stage blind adaptive receiver architecture which carries out multiuser detection using an Optimal Bounding Ellipsoid (OBE) algorithm and Direction-of-Arrival 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...

This paper presents a modified set theoretic framework for estimating the state of a linear dynamic system based on uncertain measurements. The measurement errors are assumed to be unknown but bounded by ellipsoidal sets. Based on this assumption, a recursive state estimator is (re–)derived in a tutorial fashion. It comprises both the prediction step (time update), i.e., propagation of a set of feasible states by means of the system model and the filter step (measurement update), i.e., inclusion of a new measurement into the current estimate. The main contribution is an efficient square–root formulation of this estimator, which is well suited especially for practical applications. 1

This paper formulates, and provides a solution to, a filtering problem based on certain deterministic constraint imposed on the error sequence. The formulation is called Set-Membership Filtering (SMF) and is a generalization of Set-Membership Identification (SMI) for system identification. A SetMembership Decision Feedback Equalizer (SM-DFE) is proposed as an example of its application to nonlinear systems. This paper also establishes connections of SM-DFE with the Minimum Mean Square Error DFE (MMSE-DFE). Recursive solutions to the general SMF problem are also presented. I. INTRODUCTION Set-membership signal processing and control is a growing field and has seen tremendous increase in research activity in the last decade, see, e.g., [1, 2]. In control systems, for example, design of robust controllers based on identification of a set of feasible plants is now a well established method. In the area of system identification, such methods are termed Set-Membership Identification (SMI)...

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.