The well-known conventional Weighted Least Squares (WLS) and extended Kalman filter (EKF) are the standard estimation methods for positioning with GNSS measurements. However, these estimators are not optimal when the GNSS measurements become contaminated by non-Gaussian errors including multipath (MP) and nonline-of-sight (NLOS) biases. In this paper, we use additional information of the geometric environment provided by a 3D model to build-up a robust solution against biases which may be summed up from MP and NLOS signals in urban environments. We first use a 3D city model to predict lower and upper bounds of these biases. Then, we integrate this information in the position estimation problem. We investigated in two ways of making use of this additional information: the first one is to consider these biases as additive noise and exploiting the bounds to end up with a constrained state estimation by WLS or Kalman filter. The second way is to investigate in the maximum likelihood estimation of both the MP-NLOS bias and the state ending up with a less accurate but acceptable solution. Test results using real GPS signal in Toulouse show that these estimators capable of improving the positioning accuracy compared to the conventional WLS if the NLOS bounds are well-chosen.

The dictionary learning problem aims at finding a dictionary of atoms that best represents an image according to a given objective. The most usual objective consists of representing an image or a class of images sparsely. Most algorithms performing dictionary learning iteratively estimate the dictionary and a sparse representation of images using this dictionary. Dictionary learning has led to many state of the art algorithms in image processing. However, its numerical complexity restricts its use to atoms with a small support since the computations using the constructed dictionaries require too much resources to be deployed for large scale applications. In order to alleviate these issues, this paper introduces a new strategy to learn dictionaries composed of atoms obtained as a composition of K convolutions with S-parse kernels. The dictionary update step associated with this strategy is a non-convex optimization problem. We reformulate the problem in order to reduce the number of its irrelevant stationary points and introduce a Gauss-Seidel type algorithm, referred to as Alternative Least Square Algorithm, for its resolution. The search space of the considered optimization problem is of dimension KS, which is typically smaller than the size of the target atom and is much smaller than the size of the image. The complexity of the algorithm is linear with regard to the size of the image. Our experiments show that we are able to approximate with a very high accuracy many atoms such as modified DCT, curvelets, sinc functions or cosines when K is large (say K = 10). We also argue empirically that, maybe surprisingly, the algorithm generally converges to a global minimum for large values of K and S.

Increasing the sampling rate of Analog-to-Digital Converters (ADC) is a main challenge in many fields and especially in telecommunications. Time-Interleaved ADCs (TI-ADC) were introduced as a technical solution to reach high sampling rates by time-interleaving several low-rate ADCs at the price of a perfect synchronization. Indeed, as the inverse operation of DAC is derived under the assumption of uniform sampling, the desynchronization must be compensated upstream with expensive hardware corrections of the sampling device. In this paper, we propose an alternative framework for TI-ADCs based on a more flexible sampling scheme, known as Periodic Non-uniform Sampling (PNS), that takes into account the desynchronization at the reconstruction stage when the induced delay is known, thus avoiding hardware corrections. The main contribution of this paper is to propose two different strategies for desynchronization estimation, one based on auto-calibration, the other on blind estimation. The proposed method performance is evaluated in terms of signal reconstruction error.

This paper deals with the demodulation of automatic identification system (AIS) signals received by a satellite. More precisely, an error correction algorithm is presented, whose computational complexity is reduced with respect to that of a previously considered approach. This latter approach makes use of the cyclic redundancy check (CRC) of a message as redundancy, in order to correct transmission errors. In this paper, the CRC is also considered as a correction tool, but only a part of it is used for that purpose; the remaining part is only used as an error detection means. This novel approach allows the decoding performance to be adapted to the noise power, and provides a reduction of the computational complexity. Simulation results obtained with and without complexity optimization are presented and compared in the context of the AIS system.

Le démélange d’images hyperspectrales vise à identifier les signatures spectrales d’un milieu imagé ainsi que leurs proportions dans chacun des pixels. Toutefois, les signatures extraites présentent en pratique une variabilité qui peut compromettre la fiabilité de cette identification. En supposant ces signatures potentiellement affectées par le phénomène de variabilité, nous proposons d’estimer les paramètres d’un modèle de mélange linéaire à l’aide d’un algorithme de minimisation alternée (Proximal alternating linearized minimization, PALM) dont la convergence a été démontrée pour une classe de problèmes non-convexes qui contient précisément le problème du démélange d’images hyperspectrales. La méthode proposée est évaluée sur des données synthétiques et réelles.

La caractérisation de la texture d’une image peut être conduite via l’étude des fluctuations de la régularité locale de son amplitude dans le cadre théorique de l’analyse multifractale. Les images étant souvent composées de différentes textures, cette analyse doit être locale. Cet article s’attaque à ce problème en formulant un modèle bayésien par patch reposant sur un modèle semi-paramétrique récemment proposé pour la statistique du logarithme des coefficients dominants. Les estimateurs bayésiens sont obtenus via une procédure d’échantillonnage utilisant un algorithme de Monte-Carlo Hamiltonien. Les performances de ces estimateurs sont illustrées à l’aide de processus synthétiques.

Cet article propose une approche automatique pour estimer le nombre de spectres de composés purs dans les images hyperspectrales. L’estimation est basée sur de récents résultats de la théorie des matrices aléatoires sur les “modèles à variances isolées”. Plus précisément, nous étudions l’écart entre les valeurs propres successives de la matrice de covariance des observations. L’algorithme d’estimation proposé est automatique et robuste à la présence de bruit corrélé. Cette stratégie est validée sur des images synthétiques et réelles. Les résultats expérimentaux sont prometteurs et montrent la pertinence de cette approche par rapport à l’état de l’art.

Dans ce papier, on propose un récepteur exact pour les modulations à phase continue (CPM) basé sur la décomposition/représentation de Laurent. L’approche proposée permet de remédier aux problèmes des interférences inter-symboles et inter-composantes induites par les composantes de Laurent sans introduire un étage supplémentaire dans le récepteur de type filtre blanchissant. Puis, en se basant sur la décomposition de Rimoldi, on proposera une méthode analytique pour construire le nouveau banc de filtre de réception. In this paper, we derive an exact receiver for continuous phase modulations based on Laurent decomposition. The proposed method allows to cancel the inter-symbol and inter-component interference induced by the Laurent components, without the use of an additional processing stage at the receiver side such as whitening filters. Futhermore, based on Rimoldi decomposition, we will propose an analytical method to derive the new receiver filter bank.