Periodic Nonuniform Samplings of order N (PNSN) are interleavings of periodic samplings. For a base period T, simple algorithms can be used to reconstruct functions of spectrum included in an union of N intervals δk of length 1/T. In this paper we study the behavior of these algorithms when applied to any function. We prove that they result in N (or less) foldings on , each of δk holding at most one folding.

In Global Navigation Satellite Systems, resilience to multipath remains an important open issue, being the limiting factor in several applications due to the environment specific nature of such harsh propagation conditions. In order to assess the multipath impact into the final system performance, accurate metrics are required. The multipath error envelope (MPEE), even if easy to handle, is limited to the study of the bias of a receiver architecture in a noise free environment. Moreover, when it is a flat zero-valued line, the MPEE becomes less informative about the parameter estimation performance. Considering an unbiased estimator, an alternative way to characterize an architecture is to evaluate its mean square error (MSE) and compare it to the corresponding Cram´er-Rao bound (CRB). In this work, a methodology to use both aforementioned tools is presented. First, the MPEE, which is an understandable metric. Secondly, the MSE convergence to the CRB, where one can clearly interpret the estimation performance in terms of signal-to-noise ratio or minimum path separation. These tools are then applied to a range of known multipath mitigation techniques. In addition, a new alternating projection multipath mitigation approach is proposed and analyzed.

For more than three decades, Global Navigation Satellite System (GNSS) signals have been seen as signals of opportunity as in GNSS Reflectometry (GNSS-R). The study of the reflections from the ground of such signals can indeed lead to many features regarding the reflecting surface and the receiver's height. Due to the nature of the GNSS signal, that is, due to its wavelength, the distortion of the reflected signal may vary significantly depending on the reflecting surface and on the dynamic and height of the receiver. The latter does range from low earth orbit down to ground-based platforms. In this last case, the vicinity to the ground induces important interference between the direct and the reflected path which makes it difficult to process directly in order to obtain altimetry product. In this presentation, after a brief description of the main features of the GNSS-R problem, the feasibility of ground-based single antenna GNSS-R altimetry is studied.

TCP (Transmission Control Protocol) Congestion control mechanism is an essential part of internet communications: it manages how fast the information is sent between two end points. That mechanism aims to achieve a compromise between 3 goals. The first is to achieve the maximum throughput for each flows, the second goal is to reduce the latency between the server and the client, and the last goal is to achieve fairness between each flows. The compromise between these 3 goals is very hard to achieve with human heuristics and basic models because of the ever increasing complexity of internet topologies. We choose to investigate machine learning solution in order optimize the Congestion Control mechanism. In this presentation, the bases of congestion control and the impact of machine learning on that mechanism will be explained.

Earth observation through satellite images is crucial to help economic activities as well as to monitor the impact of human activities on ecosystems. Current satellite systems are subjected to strong computational complexity constraints. Thus, image compression is performed onboard with specifically tailored algorithms while image denoising is performed on the ground. In this letter, we intend to address satellite image compression and denoising with neural networks. The first proposed approach uses a single neural architecture for joint onboard compression and denoising. The second proposed approach sequentially uses a first neural architecture for onboard compression and a second one for on ground denoising. For both approaches, the onboard architectures are lightened as much as possible, following the procedure proposed by Alves de Oliveira et al. (2021). The two approaches are shown to outperform the current satellite imaging system and their respective pros and cons are discussed.

In this paper, we introduce correlation technologies both at RF/mmWave and Base-Band frequencies. At RF and mmWave frequencies power-spectra and energy-spectra metrics are introduced for measuring the power-density of mobile devices and systems. The use of unified power-spectra and energy-spectra metrics leads to innovative Electromagnetic-Thermal sensing solutions for OTA-Testing. At Base-Band frequencies, DSP-based Convolutional-Accelerators are proposed for fast and accurate measurement of EVM (Error Vector Magnitude) using correlation technologies. New ASIC-embedded Smart-Connectors are developed for bringing correlation-based signal processing close to antenna-in-package (AiP) modules. Porting of the DSPbased Convolutional-Accelerators into advanced FD-SOI-ASIC platforms for co-integration with adaptive RF/mmWave Front-End-Modules will enable real-time extraction of auto-correlation and cross-correlation functions of stochastic signals for mobile devices and systems. Perspectives toward optically synchronized interferometric-correlation technologies are drawn for accurate measurements of stochastic EM fields in noisy environments.

Satellite altimeters provide sea-level measurements along satellite track. A mean profile based on the measurements averaged over a time period is then subtracted to estimate the sea-level anomaly (SLA). In the spectral domain, SLA is characterized by a power spectral density (PSD) whose slope in a log-log scale is a parameter of great interest for ocean monitoring. Estimation of this spectral slope is usually done through a cumulated periodogram using a large number of signal samples. The location and dates of the data induce the spatial and temporal resolution of the slope estimates. To improve this resolution, this article studies a new parametric method based on an autoregressive model combined with a warping of the frequency scale (denoted as ARWARP). This ARWARP model provides a PSD estimate, with a lower variance than the classical Fourier-based ones and is reliable in the case of a small sample number. To give a reference in the performance of the SLA slope estimation, the corresponding Cramér-Rao bound is derived. Then, rather than performing linear regression on the spectral estimates, a new estimator of the slope is suggested, based on a model fitting of the PSD. A statistical validation is proposed on simulated SLA signals, showing the performance of slope estimation using this ARWARP spectral estimator, compared to classical Fourier-based methods. Application to Sentinel-3 real data highlights the main advantage of the ARWARP model, making possible SLA slope estimation on a short signal segment, i.e., with a high spatial and/or temporal resolution.

How many photons per pixel do we need to construct an image? This apparently simple question is rather complicated to answer as it is dependent on what you want to use the image for. Computational imaging and sensing combines measurement and computational methods often when the measurement conditions are weak, few in number, or highly indirect (e.g. when the measurements are few in number, the information of interest is indirectly observed, or in challenging observation conditions). The recent surge in the development of sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low flux imaging and sensing.

This paper studies a new variational marginalized particle filter for jointly estimating the state and the system mode parameters of jump Markov nonlinear systems. Contrary to the Markovian assumption usually considered to model the evolution of the system modes, we introduce conjugate prior distributions for the system mode parameters. The joint posterior distribution of the state and system mode parameters is then marginalized with respect to the mode variables. The remaining state vector is sampled using a sequential Monte Carlo algorithm, and the mode parameters are sampled using variational Bayesian inference. In order to obtain analytical solutions for the different variational distributions, we use an extended factorized approximation simplifying the variational distributions. A comprehensive simulation study is conducted to compare the performance of the proposed approach with the state-of-the-art for a modified nonlinear benchmark model and maneuvering target tracking scenarios.

Le problème de la transmission de ressources indivisibles au travers d’un réseau est un problème générique présent dans de nombreuses applications. En effet, ce type de problème se retrouve dans des industries telles que le transport de fret ou encore les télécommunications (réseaux optiques, communications satellitaires, ...). L’amélioration des méthodes de résolution pour ce problème représente donc un enjeu important qu’il convient d’aborder sous plusieurs angles. Premièrement, améliorer la qualité des solutions trouvées permet d’augmenter l’efficacité des systèmes que ce problème affecte. Deuxièmement, accélérer la résolution de ce problème est important dans les applications où le temps de calcul est très restreint, mais aussi lorsque les instances du problème de transmission considéré sont de grande taille. Ce dernier point représente un enjeu important dans l’application industrielle qui motive cette thèse : la constellation de satellites de télécommunication Telesat. En effet, cette industrie tend à construire des constellations contenant de plus en plus de satellites afin d’augmenter le débit internet que le système est capable de transmettre. On peut ainsi constater cette évolution en comparant les 66 satellites de la constellation Iridium (2018) avec les 288 satellites de la constellation Telesat (à venir en 2022) ou encore les 10 000 satellites envisagés dans la constellation Starlink (annoncée pour 2024). En parallèle de l’augmentation du nombre de satellites, on constate aussi une augmentation du nombre d’utilisateurs de ces constellations. Celle ci s’explique à la fois par l’accroissement de la richesse de la population, l’essor de nouvelles applications telles que les accès internet dans les avions ou les bateaux mais aussi tout simplement par l’augmentation de la capacité et de la qualité des services de télécommunication par satellite. La combinaison de ces facteurs tend à créer des problèmes de transmission de ressources de plus en plus difficiles à résoudre ce qui nécessite des algorithmes de résolution plus performants. Or, dans le cadre de la constellation Telesat que nous étudions en partenariat avec Thalès Alenia Space et le Centre National d’études spatiales, le débit total transmis par la constellation est estimé aux alentours de 7 Térabits par seconde. Si l’on considère qu’un utilisateur moyen demande aux alentours de 5 Mégabits par seconde, une hausse de 5% de la capacité de transmission de la constellation due à une meilleure gestion des ressources de communications représente une possibilité d’accès au service de la constellation pour des centaines de milliers d’utilisateurs supplémentaires. Ce chiffre peut sembler faible en comparaison avec la population mondiale actuelle, mais une telle constellation n’est pas destinée à concurrencer le réseau Internet terrestre chargé de fournir la majeure partie du débit demandé. En effet, le rôle de la constellation Telesat est de compléter le réseau terrestre dans les zones où celui-ci est trop cher à construire ou pour les utilisateurs inaccessibles tels que ceux au milieu des océans. Dans cette thèse, nous nous intéressons au problème de transmission de la ressource indivisible qu’est le débit des utilisateurs dans une constellation. Ce problème correspond à un problème classiquement étudié dans la littérature des problèmes de flots, sous le nom de problème de flot insécable. Bien que ses propriétés théoriques soient bien connue et que de nombreuses approches de résolution existent, celles-ci manquent d’efficacité lorsque la taille du problème est importante. Nous tentons de combler cette lacune en proposant des algorithmes présentant de bonnes performances sur de grandes instances de ce problème. D’autre part, l’introduction de la dynamique de la constellation dans le problème nous mène à nous intéresser au problème de flot insécable dynamique. Ce problème est peu étudié dans la littérature, c’est pourquoi nous étendons l’ensemble des méthodes de résolution testées sur ce problème en proposant différentes approches et en les comparant expérimentalement sur des jeux d’instances que nous proposons. Enfin, nous étudions des méthodes de décomposition permettant de renforcer la relaxation linéaire du problème flot insécable. En effet, cette relaxation linéaire est à la base de la plupart des méthodes de résolution proposées dans la littérature. Le calcul d’une relaxation puissante est donc un enjeu de la résolution du problème de flot insécable. Après avoir présenté et réimplémenté deux méthodes de la littérature, nous proposons une nouvelle méthode de décomposition s’inspirant des deux méthodes précédentes. Une étude empirique montre que la nouvelle méthode proposée possède un avantage compétitif important sur les grandes instances du problème de flot insécable.