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Christophe Andrieu, ENSEA-ETIS (France)
Patrick Duvaut, ENSEA-ETIS (France)
In this paper we propose an original algorithm for the Bayesian joint estimation and detection of shot noise processes. The solution we propose relies on Markov chain Monte Carlo methods and provides the a posteriori probability density of the unknown parameters conditionally to the observations. The solution we propose provides many degree of freedom for the inclusion of any a priori knowledge.
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TOPGuotong Zhou, Georgia Institute of Technology (U.S.A.)
Periodogram is an important tool to reveal hidden periodicities in a given time series but does not tell whether the resulting spectral lines are associated with constant or random amplitude harmonics. Applications dealing with random amplitude models include Doppler spread targets and detection in the presence of fading. We propose to estimate the variance of the harmonic amplitude and then make the decision based on whether the variance can be regarded as zero in a statistical sense. This is a viable approach because any constant has variance zero whereas any real random process has a positive variance. A rigorous statistical test is formulated and illustrated with simulations.
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Daoud Robert Iskander, SPRC, Queensland University of Technology (Australia)
Abdelhak M. Zoubir, SPRC, Queensland University of Technology (Australia)
In this paper, the design of optimal schemes for detecting deterministic narrowband signals with unknown parameters in correlated interference modelled by the recently developed GBK~distribution is considered. Theoretical derivations of an optimal detector, in the Neyman-Pearson sense, are given for the case where the signal amplitude and phase are unknown. The performance of the detector is then evaluated using extensive computer simulations.
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Jean-Yves Tourneret, ENSEEIHT/GAPSE (France)
Marie Chabert, ENSEEIHT/GAPSE (France)
The problem addressed in the paper is the detection of abrupt changes embedded in multiplicative colored Gaussian noise. The multiplicative noise is modeled by an AR process. The Neyman Pearson detector is developped when the abrupt change and noise parameters are known. This detector constitutes a reference to which suboptimal detectors can be compared. The abrupt change and noise parameters have to be estimated in practical applications. The maximum likelihood estimator for these parameters is then derived. This allows to study the generalized likelihood ratio detector.
ic973693.pdf ic973693.pdf TOPAkbar M. Sayeed, Rice University (U.S.A.)
In many practical detection and classification problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance, the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required for designing the GLRT processors are not available a priori and must be estimated from limited training data. Such design is virtually impossible in general due to two major difficulties: identifying the appropriate nuisance parameters, and estimating the corresponding GLRT statistics. We address this problem by using recent results that relate joint signal representations (JSRs), such as time-frequency and time-scale representations, to quadratic GLRT processors for a wide variety of nuisance parameters. We propose a general data-driven framework that: 1) identifies the appropriate nuisance parameters from an arbitrarily chosen finite set, and 2) estimates the second-order statistics that characterize the corresponding JSR-based GLRT processors.
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Chuang He, Carnegie Mellon University (U.S.A.)
José M.F. Moura, Carnegie Mellon University (U.S.A.)
In our earlier work, we developed a robust detector for multipath constrained environments when the transmitted signal is known. In this paper, we extend these results to the case where the transmitted signal is a random process. The approach we used is to replace the orthogonal projection on the multipath signal subspace S by the orthogonal projection on a representation subspace G, such that G and S are close in the gap metric sense. When the signal is random, S is no longer a subspace but a set with a given structure. The gap metric applies only when S and G are subspaces. In this paper, we introduce the modified deflection as the appropriate measure to be used in the random signal case. We design the representation subspace G to match the multipath signal set S in the modified deflection sense. Wavelet multiresolution tools are used to facilitate the design.
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Assa Ephraty, Tel-Aviv University (Israel)
Joseph Tabrikian, Duke University (U.S.A.)
Hagit Messer, Tel-Aviv University (Israel)
It is not possible, in practice, to precisely model a complex propagation channel, such as shallow water. This lack of accuracy causes a deterioration in the performance of the optimal detector and motivates the search for sub-optimal detectors which are insensitive to uncertainties in the propagation model. We present a novel, robust detector, which measures the degree of spatial-stationarity of the received field, exploiting the fact that a signal propagating in a bounded channel induces non-spatial-stationarity. The performance of the proposed detector is evaluated using both simulated data and experimental data collected in the Mediterranean Sea. This performance is compared to those of three other detectors, employing different extents of prior information. It is shown that when the propagation channel is not completely known, as is the case of the experimental data, the novel detector outperforms the others. That is, this detector couples good performance with robustness to propagation uncertainties.
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David Declercq, ETIS-ENSEA (France)
Patrick Duvaut, ETIS-ENSEA (France)
This paper introduces a new test statistic of Normality which evaluates the cross covariances between choosen Hermite polynomials which are zero under the null hypothesis. The special form of the test leads to a modified sphericity statistic and we have called it ``Hermite Normality Test'' ($S_H$). We present briefly its asymptotical distribution both under the null and nonnull hypothesis. Large simulations have been made to compare some specific Hermite tests to three other taken in the litterature. If our test is better for a lot nonnormal populations but works worse for some other, the main point is that we defined in fact a wide range of tests which may match different nonnormal distributions.
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Roxana Ojeda, ENST, Dépt. Signal (France)
Jean-François Cardoso, ENST, Dépt. Signal (France)
Eric Moulines, ENST, Dépt. Signal (France)
This paper introduces a Gaussianity test for causal invertible time series. It is based on a quadratic form in differences between sample means and expected values of certain finite memory nonlinear functions of the estimated innovation sequence. The test has, by construction, an interesting property: under reasonable assumptions on the regularity of the stationary process, it is asymptotically invariant with respect to the spectral density of the process. Monte-Carlo experiments are included to illustrate the proposed approach.
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Don H. Johnson, Rice University - ECE Dept. (U.S.A.)
Paulo Gonçalvès, INRIA - FRACTALES (France)
Richard Baraniuk, Rice University - ECE Dept. (U.S.A.)
When applied to continuous-time observations, type-based detection strategies are limited by the necessity to crudely quantize each sample. To alleviate this problem, we smooth the types for both the training and observation data with a linear filter. This post-processing improves detector performance significantly (error probabilities decrease by over a factor of three) without incurring a significant computational penalty. However, this improvement depends on the amplitude distribution and on the quantizer's characteristics.
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Gilles Thonet, EPFL (Switzerland)
Jean-Marc Vesin, EPFL (Switzerland)
A new method for assessing the stationarity of a signal is addressed. The proposed technique is based on the application of time-varying autoregressive models, in which coefficient variations are decomposed upon a set of deterministic basis functions. Stationarity is evaluated by selecting the optimal number of basis functions with a generalized version of Minimum Description Length criterion. Results are then validated with hypothesis testing on the model coefficients. Several simulation results are presented. First, application to synthetic signals confirms the basic assumptions and highlights the main features of the method. Second, relevant conclusions are derived for the study of the stationarity of heart rate time series before the onset of ventricular tachyarrhythmias.
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George A. Saon, CRIN-CNRS (France)
Abdel Belaid, CRIN-CNRS (France)
In this paper we present a stochastic framework for the recognition of binary random patterns which advantageously combine HMMs and Markov random fields (MRFs). The HMM component of the model analyzes the image along one direction, in a specific state observation probability given by the product of causal MRF-like pixel conditional probabilities. Aspects concerning definition, training and recognition via this type of model are developed throughout the paper. Experiments were performed on handwritten digits and words in a small lexicon. For the latter, we report a 89.68% average word recognition rate on the SRTP (Service de Recherche Technique de la Poste) French postal cheque database (7057 words, 1779 scriptors).
ic973725.pdf ic973725.pdf TOPPetar M. Djuric, State University of New York at Stony Brook (U.S.A.)
In this paper the problem of model selection is addressed by the Bayesian methodology and the bootstrap technique. As a rule for choosing the best model from a set of proposed models, the maximum a posteriori principle is used. The evaluation of the maximum a posteriori probability (MAP) of each model amounts to computation of integrals whose integrands may be very peaked functions. We carry out the integration by importance sampling, where the importance function is a multivaraiate Gaussian whose samples are obtained by the bootstrap technique. The performance of the MAP rule is examined by computer simulations, and comparisons with the widely used AIC (Akaike information criterion) and MDL (minimum description length) rules are made.
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Paul T. Troughton, University of Cambridge (U.K.)
Simon J. Godsill, University of Cambridge (U.K.)
We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.
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