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Anne-Emmanuelle Badel, E.N.S. Lyon (France)
Dominique Guégan, ENSAE-CREST (France)
Olivier Michel, E.N.S. Lyon (France)
Ludovic Mercier, ENSAE-CREST (France)
The aim of this paper is to compare different prediction methods for chaotic deterministic systems. We consider three different methods to evaluate the dynamics of the systems~: the Nearest Neighbors, the Radial Basis Functions and the Regression Tree. We use a comparison criterion suited to chaotic systems~: the prediction horizon. The optimal prediction horizon is discussed with respect to the sampling time step. We apply these methods to simulated chaotic system (Lorenz system), experimental chaotic system (Double-Scroll) and to intra-day series of exchange rates, namely DEM/FRF. We provide developments concerning the choice of the parameters involved in chaotic time series prediction.
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TOPSimon J. Godsill, University of Cambridge (U.K.)
In this paper methods are developed for enhancement and analysis of autoregressive moving average (ARMA) signals observed in additive noise which can be represented as mixtures of heavy-tailed non-Gaussian sources and a Gaussian background component. Such models find application in systems such as atmospheric communications channels or early sound recordings which are prone to intermittent impulse noise. Markov Chain Monte Carlo (MCMC) simulation techniques are applied to the joint problem of signal extraction, model parameter estimation and detection of impulses within a fully Bayesian framework. The algorithms require only simple linear iterations for all of the unknowns, including the MA parameters, which is in contrast with existing MCMC methods for analysis of noise-free ARMA models. The methods are illustrated using synthetic data and noise-degraded sound recordings.
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Gary D. Brushe, SAD/CD/DSTO (Australia)
W. Paul Malcolm, SAD/CD/DSTO (Australia)
Langford B. White, SAD/CD/DSTO (Australia)
A hidden Markov model for estimating an a posteriori distribution of the amplitude of communications signals is presented. As the signal to noise ratio decreases the hidden Markov model method is shown to perform significantly better than a conventional histogram method. for characterising the amplitude distribution. The HMM estimation is performed within a Expectation Maximisation method in order to improve the estimates of the transition probabilities used in the HMM and resulting estimated amplitude distribution.
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Harm J.W. Belt, Eindhoven University of Technology (The Netherlands)
Albertus C. den Brinker, Eindhoven University of Technology (The Netherlands)
In this paper we address the problem of approximating functions on a semi-infinite interval by truncated series of orthonormal generalized Laguerre functions. The generalized Laguerre functions contain two parameters, namely a scale factor and an order of generalization. The rate of convergence of a generalized Laguerre series depends on the choice of these parameters. Results concerning the determination of the two parameters are presented.
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Sudhakar Kalluri, University of Delaware (U.S.A.)
Gonzalo Ramiro Arce, University of Delaware (U.S.A.)
Stochastic gradient-based adaptive algorithms are developed for the optimization of Weighted Myriad Filters, a class of nonlinear filters, motivated by the properties of alpha-stable distributions, that have been proposed for robust non-Gaussian signal processing in impulsive noise environments. An implicit formulation of the filter output is used to derive an expression for the gradient of the mean absolute error (MAE) cost function, leading to necessary conditions for the optimal filter weights. An adaptive steepest-descent algorithm is then derived to optimize the filter weights. This is modified to yield an algorithm with a very simple weight update, computationally comparable to the update in the classical LMS algorithm. Simulations demonstrate the robust performance of these algorithms.
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Mei Feng, University of Bremen (Germany)
Karl-Dirk Kammeyer, University of Bremen (Germany)
Higher-Order-Statistics (HOS) are being used in many areas of digital signal processing, e.g. in the field of array processing. The main aim is often to suppress Gaussian noise. Mostly, the corresponding algorithms are applied to short data blocks, because only then the stationarity of the data needed for cumulant estimation is given. In many cases, not enough attention is paid to the fact that for short data blocks the suppression of Gaussian noise is small compared to the estimation error made because of the higher order of the cumulants. In this paper, the property of cumulants to suppress Gaussian noise is studied in detail. With an algorithm for direction-of-arrival (DOA) estimation in the field of array processing, the estimation errors that occur when using HOS are compared with the estimation errors that occur when using 2nd order statistics. A quantitative result will be given to show that for short data blocks the suppression of Gaussian noise with HOS doesn't lead to a better result than using 2nd order statistics.
ic973813.pdf ic973813.pdf TOP
Dirk Maiwald, STN ATLAS Elektronik GmbH (Germany)
Dieter Kraus, STN ATLAS Elektronik GmbH (Germany)
This paper addresses the calculation of moments of complex Wishart and complex inverse Wishart distributed random matrices. Complex Wishart and complex inverse Wishart distributed random matrices are used in applications like radar, sonar, or seismics in order to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively. Moments of these random matrices are often needed e.g. in studies of asymptotic properties of parameter estimates. This paper gives a derivation of the probability density function of complex inverse Wishart distributed random matrices. Furthermore, strategies are outlined for the calculation of the moments of complex Wishart and complex inverse Wishart distributed matrices.
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Moritz Harteneck, SPD/EEE/University Strathclyde (U.K.)
Robert W. Stewart, SPD/EEE/University Strathclyde (U.K.)
John G. McWhirter, DRA Malvern (U.K.)
Ian K. Proudler, DRA Malvern (U.K.)
In this paper we present a pole estimation algorithm which is based on an overdetermined adaptive IIR filter with an additional postprocessing stage to extract the pole locations from the adaptive weights. The adaptive filtering algorithm used, is a pseudo-linear regression algorithm which is solved by a time-recursive QR decomposition. Two pole classification schemes are presented to separate the true poles and the superfluous poles. The classification schemes are based on the occurrence of pole-zero cancelation and on the pole movement in the z-plane. Floating point simulations are presented to demonstrate the performance of the proposed algorithm.
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Joseph M. Francos, BGU (Israel)
Benjamin Friedlander, University of California, Davis (U.S.A.)
This paper considers the problem of estimating the parameters of two-dimensional moving average random fields. We first address the problem of expressing the covariance matrix of a moving average random field, in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed form expression for the Cramer-Rao lower bound on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the moving average model is developed. The algorithm initially fits a two-dimensional autoregressive model to the observed field, then uses the estimated parameters to compute the moving average model.
ic973825.pdf ic973825.pdf TOPThomas L. Marzetta, Bell Labs (U.S.A.)
The Barankin bound is the greatest lower bound on the variance of any unbiased estimate for a nonrandom parameter. Computing this bound yields, as a byproduct, an unbiased estimator that is at least locally best in the following sense. The estimator formula contains a reference parameter; when the unknown parameter happens to be equal to the reference, the variance of the estimate achieves the Barankin bound. If the dependence of the Barankin estimate on the reference parameter vanishes, then the estimate is also uniformly minimum variance. We obtain a simple derivation of the Barankin bound as the solution of an unconstrained convex quadratic optimization problem. In contrast the standard form of the Barankin bound involves the maximization of a ratio of quadratic quantities. For the case of PET inversion and natural gamma ray spectrometry, the Barankin estimate is only locally minimum variance, but it can be a viable alternative to the maximum likelihood estimate.
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Philippe Pango, INRS, Univ. du Québec (Canada)
Benoît Champagne, INRS, Univ. du Québec (Canada)
In this paper, we analyse the issue of efficiently using Givens rotations to perform amore accurate SVD-based subspace tracking. We propose an alternative type of decomposition which allows a more versatile use of Givens rotations. We also show the direct effect of the latter on the tracking error, and develop a cross-terms cancellation concept which leads to aclass of high performance algorithms with very low complexity: $O(N^2)$ if signal and noise subspaces are tracked, $O(Nr)$ if only the signal subspace is tracked, where $N$ is the data vector dimension, and $r$ the number of sources. Comparative simulation experiments support the theoretical work.
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Juan Guillermo Gonzalez, University of Delaware (U.S.A.)
Daniel Leo Lau, University of Delaware (U.S.A.)
Gonzalo Ramiro Arce, University of Delaware (U.S.A.)
In this paper we introduce a general framework for edge preserving filters, derived from the powerful class of M-estimators. First, we show that under very general assumptions, any location estimator generates an edge preserving filter if we approximate the estimate by one of the input samples. Based on this premise, we propose the family of S-estimators or S-filters, as a selection-type class of filters arising from a computationally tractable selectification of location M-estimators. S-filters inherit the richness of the theory underlying the M-estimators framework, providing a very flexible family of robust estimators with edge preservation capabilities. Several properties of S-filters are studied. Sufficient and necessary conditions are given for an S-filter to present edge enhancing capabilities, and several novel filters within this framework are introduced and illustrated. Data, figures and source code utilized in this paper are available at: http://www.ee.udel.edu/signals/robust
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Gema Piñero, Univ. Pol. Valencia (Spain)
Luis Vergara, Univ. Pol. Valencia (Spain)
A parametric method based on spatial filter techniques (beamforming) is proposed to estimate the propagation speed of acoustic waves. The propagation speed estimate is analyzed for the case of narrowband signals and compared to the maximum likelihood estimate (MLE) of the propagation speed. It is shown that for an array of 3 sensors our estimate coincides with the ML estimate but its performance analysis is simpler and its computational cost is much more reduced. The proposed estimate is also applied to the wideband waves propagating along a car exhaust. It is shown that the signal-to-noise ratio and the magnitude of the relative aperture (distance between the array sensors respect to the wavelength) for each frequency could limit the good performance of the speed estimator. Good results have been achieved when these limitations have been taken into account.
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Shlomo Dubnov, IRCAM (France)
Naftali Tishby, The Hebrew University (Israel)
In this paper we describe a sound classification method, which seems to be applicable to a broad domain of stationary, non-musical sounds, such as machine noises and other man made non periodic sounds. The method is based on matching higher order spectra (HOS) of the acoustic signals and it generalizes our earlier results on classification of sustained musical sounds by higher order moments. An efficient ``decorrelated matched filter'' implemetation is presented. The results show good sound classification statistics and a comparison to spectral matching methods is also discussed.
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