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Article de conférence

Estimation du centre et du rayon d'une hypersphère à l'aide d'une loi a priori de Von Mises-Fisher et d'un algorithme EM

Auteurs : Lesouple Julien, Pilastre Barbara, Altmann Yoann et Tourneret Jean-Yves

In Proc. XXVIII ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), Nancy, France, September, 2022.

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Cet article présente une extension d'un algorithme EM (expectation maximization) publié récemment par les auteurs permettant d'estimer conjointement le centre et le rayon d'une hypersphère avec les hyperparamètres d'un modèle statistique prenant en compte le fait que les observations sont localisées sur une partie de l'hypersphère. La méthode proposée repose sur l'ajout de variables latentes ayant une loi a priori de von Mises-Fisher. Ce modèle statistique permet d'exprimer la vraisemblance complète des données, dont l'espérance conditionnée aux données observées possède une distribution connue conduisant à un algorithme EM simple et efficace. Les performances de cet algorithme d'estimation sont évaluées à l'aide de de simulations effectuées dans un cas bi-dimensionnel avec des résultats prometteurs.

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Traitement du signal et des images / Observation de la Terre et Autre

Article de journal

Non-Binary PRN-Chirp Modulation: A GNSS Fast Acquisition Signal Waveform

Auteurs : Ortega Espluga Lorenzo, Vilà-Valls Jordi et Chaumette Eric

IEEE Communications Letters, vol. 26, Issue 9, pp. 2151-2155, September, 2022.

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In this article, we propose a new non-binary modulation which allows both Global Navigation Satellite Systems (GNSS) synchronization and the demodulation of non-binary symbols, without the need of a pilot signal, with the aim to provide a fast first position, velocity and time fix. The waveform is constructed as the product of i) a pseudo-random noise sequence with good auto-correlation and cross-correlation properties, and ii) a chirp spread spectrum family, which allows to demodulate non-binary symbols even if the signal phase is unknown. In order to demodulate the data, a bank of non-coherent matched filters is proposed. Because of the particular modulation structure, the receiver is capable to demodulate the navigation message faster while allowing the basic GNSS signal processing functionalities. Illustrative results are provided to support the discussion.

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Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

Article de conférence

Robust Estimation of Gaussian Mixture Models Using Anomaly Scores and Bayesian Information Criterion for Missing Value Imputation

Auteurs : Mouret Florian, Albughdadi Mohanad Y.S., Duthoit Sylvie, Kouamé Denis et Tourneret Jean-Yves

In Proc. 30th European Signal Processing Conference (EUSIPCO), Belgrade, Serbia, August 29-September 2, 2022.

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The Expectation-Maximization algorithm is a very popular approach for estimating the parameters of Gaussian mixture models (GMMs). A known issue with GMM estimation is its sensitivity to outliers, which can lead to poor estimation performance depending on the dataset under consideration. A common approach to deal with this issue is robust estimation, which typically consists of reducing the influence of the outliers on the estimators by weighting the impact of some samples of the dataset considered as outliers. In an unsupervised context, it is difficult to know which sample from the database corresponds to a normal observation. To that extent, we propose to use within the EM algorithm an outlier detection step that attributes an anomaly score to each sample of the database in an unsupervised way. A modified Bayesian Information Criterion is also introduced to efficiently select the appropriate amount of outliers contained in a dataset. The proposed method is tested on a benchmark remote sensing dataset coming from the UCI Machine Learning Repository. The experimental results show the interest of the proposed robustification when compared to other benchmark imputation procedures.

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Traitement du signal et des images / Autre

A Comparison of Bayesian Estimators for the Parameters of the Bivariate Multifractal Spectrum

Auteurs : Leon Arencibia Lorena, Wendt Herwig, Tourneret Jean-Yves et Abry Patrice

In Proc. 30th European Signal Processing Conference (EUSIPCO), Belgrade, Serbia, August 29-September 2, 2022.

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Multifractal analysis provides the theoretical and practical tools for describing the fluctuations of pointwise regularity in data and has led to many successful applications in signal and image processing. Originally limited to the analysis of single time series or images, a definition of multivariate multifractal analysis, i.e., the joint multifractal analysis of several data components, was recently proposed and was shown to effectively quantify local or transient dependencies in data regularity, beyond linear correlation. However, the accurate estimation of the associated matrix-valued joint multifractality parameters is notoriously difficult, thus limiting its practical usefulness. Leveraging a recent statistical model for bivariate multifractality, the goal of this work is to define and study Bayesian estimators designed to bypass this difficulty. Specifically, we study the original use of two different priors, combined with two different averages (arithmetic and Karcher means), for bivariate multifractal analysis. Monte Carlo simulations with synthetic data allow us to appreciate their relative performance and to conclude that our novel and original estimator based on a scaled inverse Wishart prior and the Karcher mean yields particularly favorable results with up to 5 times smaller rootmean-squared error than previous formulations.

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Traitement du signal et des images / Autre

An EM Algorithm for Mixtures of Hyperspheres

Auteurs : Lesouple Julien, Burger Philippe et Tourneret Jean-Yves

30th European Signal Processing Conference (EUSIPCO), Belgrade, Serbia, August, 2022.

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This paper studies a new expectation maximization (EM) algorithm to estimate the centers and radii of multiple hyperspheres. The proposed method introduces latent variables indicating to which hypersphere each vector from the dataset belongs to, in addition to random latent vectors having an a priori von Mises-Fisher distribution characterizing the location of each vector on the different hyperspheres. This statistical model allows a complete data likelihood to be derived, whose expected value conditioned on the observed data has a known distribution. This property leads to a simple and efficient EM algorithm whose performance is evaluated for the estimation of hypersphere mixtures yielding promising results.

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Traitement du signal et des images / Observation de la Terre et Autre

Article de journal

A novel image representation of GNSS correlation for deep learning multipath detection

Auteurs : Blais Antoine, Couellan Nicolas et Evgenii Munin

Array, vol. 14, Art. no 100167, July, 2022.

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This paper proposes a novel framework for multipath prediction in Global Navigation Satellite System (GNSS) signals. The method extends from dataset generation to deep learning inference through Convolutional Neural Network (CNN). The process starts at the output of the correlation stage of the GNSS receiver. Correlations of the received signal with a local replica over a (Doppler shift, propagation delay)-grid are mapped into grey scale 2D images. They depict the received information possibly contaminated by multipath propagation. The images feed a CNN for automatic feature construction and multipath pattern detection. The issue of unavailability of a large amount of supervised data required for CNN training has been overcome by the development of a synthetic data generator. It implements a well-established and documented theoretical model. A comparison of synthetic data with real samples is proposed. The complete framework is tested for various signal characteristics and algorithm parameters. The prediction accuracy does not fall below 93% for C/N0 ratio as low as 36 dBHz, corresponding to poor receiving conditions. In addition, the model turns out to be robust to the reduction of image resolution. Its performance is also measured and compared with an alternative Support Vector Machines (SVM) technique. The results show the undeniable superiority of the proposed CNN algorithm over the SVM benchmark.

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Traitement du signal et des images / Localisation et navigation

Generalized Frequency Estimator with Rational Combination of Three Spectrum Lines

Auteurs : Gigleux Benjamin, Vincent François et Chaumette Eric

IET Radar Sonar Navigation, vol. 16, issue 7, pp.1107-1115, July, 2022.

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The popular Discrete Fourier Transform (DFT) is known to be a sub‐optimal frequency estimation technique for a finite transform length. In order to approach the Cramer‐Rao Lower Bound (CRLB), many refinement techniques have been considered, but little considering both zero padding or tapering, also known as windowing or apodisation. In this paper, a frequency estimator with closed‐form combination of three DFT samples is generalized to zero padding and tapered data within the class of cosine windowing. Root Mean Squared Error (RMSE) is shown to approach the CRLB in the case of a single tone signal with additive white Gaussian noise. Compared to state‐of‐the‐art techniques, the proposed algorithm improves the frequency RMSE up to 1 dB when using significant zero‐padding lengths (K ≥ 2 N) and for small to moderate SNR, which is the most challenging case for practical radar applications.

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Traitement du signal et des images et Réseaux / Systèmes de communication aéronautiques, Localisation et navigation et Systèmes spatiaux de communication

A Bayesian Framework for Multivariate Multifractal Analysis

Auteurs : Leon Arencibia Lorena, Wendt Herwig, Tourneret Jean-Yves et Abry Patrice

IEEE Transactions on Signal Processing, vol. 70, pp. 3663 - 3675, June, 2022.

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Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it has proven useful in an increasing range of applications, yet so far involving only univariate data (scalar valued time series or single channel images). Recently the theoretical ground for multivariate multifractal analysis has been devised, showing potential for quantifying transient higher-order dependence beyond linear correlation among collections of data. However, the accurate estimation of the parameters associated with a multivariate multifractal model remains challenging, especially for small sample size data. This work studies an original Bayesian framework for multivariate multifractal estimation, combining a novel and generic multivariate statistical model, a Whittle-based likelihood approximation and a data augmentation strategy allowing parameter separability. This careful design enables efficient estimation procedures to be constructed for two relevant choices of priors using a Gibbs sampling strategy. Monte Carlo simulations, conducted on synthetic multivariate signals and images with various sample sizes and multifractal parameter settings, demonstrate significant performance improvements over the state of the art, at only moderately larger computational cost. Moreover, we show the relevance of the proposed framework for real-world data modeling in the important application of drowsiness detection from multichannel physiological signals.

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Traitement du signal et des images / Observation de la Terre et Autre

Article de conférence

Effective AM/AM and AM/PM curves derived from EVM simulations or measurements on constellations

Auteur : Sombrin Jacques B.

In Proc. 99th ARFTG Microwave Measurement Conference, Denver, Colorado USA, June 24th, 2022.

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Non-linear amplifiers distort signal constellations through their amplitude (AM/AM) and phase (AM/PM) curves versus input amplitude. This causes an increase in the average Error Vector Magnitude (EVM) of the amplified signal. Most commercial EVM simulation software and measurement devices display the ideal and distorted constellations. When computing separate EVMs for each value of ideal symbol power, it is possible to obtain a representation of the effect of AM/AM and AM/PM curves on the constellation. A new type of display, with the distorted constellation folded up on the real axis, is proposed to get a direct representation of the amplifier non-linearity. This can also be used for nonlinear equalization of the signal to improve the EVM.

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Communications numériques / Systèmes spatiaux de communication

Attention Networks for Time Series Regression and Application to Congestion Control

Auteurs : Perrier Victor, Lochin Emmanuel, Tourneret Jean-Yves et Gélard Patrick

In Proc. 4th International Workshop on Network Intelligence (IFIP Networking), Catania, Italy, June 13-16, 2022.

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This paper studies a new attention-based recurrent architecture, lighter and less computationally expensive than a global attention network. This type of architecture achieves better performance than commonly used recurrent networks for time series regression. An application to congestion control is considered, where the history of round trip times (RTT) evolution history is used to monitor congestion control. The performance of the proposed new congestion control strategy is evaluated with both synthetic and real traces, showing that it can be efficiently used to estimate the congestion state of a network.

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Réseaux / Systèmes spatiaux de communication

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