CNES is involved in the protection of Radio Astronomy near the far side of the Moon, in a zone defined by ITU as the Shielded Zone of the Moon (SZM). The 2483.5-2500 MHz band has been chosen for lunar in-situ PNT notably since it is the only band recommended by SFCG (Space Frequency Coordination Group) for lunar in situ PNT. This band is also the only GNSS band recommended by SFCG for radiocommunications from Martian orbit to Martian surface. CNES proposed this band for lunar and Martian frequencies to SFCG. Regarding the protection of Radio Astronomy in Shielded Zone of the Moon (SZM), which is more or less the far side of the Moon and above, this 2483.5-2500 MHz band is well adapted, while it is not the case for any part of the other GNSS bands used on Earth: both RNSS L and C bands constitute each an important threat for Radio Astronomy in the SZM. SFCG issued two recommendations concerning the protection of lunar in-situ PNT in its 2483.5-2500 MHz band: Recommendation SFCG 32-2R6, so called “Freqs for lunar region”, and Recommendation SFCG 43-1, so called “Protection of lunar S-band PNT”. Obeying both SFCG RECs 32-2R6 and 43-1simultaneously is mandatory to ensure protection of lunar in-situ PNT from wireless WIFI and 3GPP (like 4G, 5G, …) lunar surface links. Adjacent to the 2483.5-2500 MHz in-situ lunar PNT band recommended by SFCG 32-2R6, the bands 2400-2480 MHz and 2503.5-2655 MHz are among the bands recommended for lunar surface wireless systems. This means that there is a minimum of 3.5 MHz mandatory guard bands on each side of the 2483.5-2500 MHz PNT band in SFCG 32-2R6 for the protection of lunar in-situ PNT. The SFCG REC 43-1 recommends the PNT devices to implement filtering, and that each lunar surface wireless system should not generate an aggregated PFD exceeding -121dBW/m²/MHz at the input of the PNT receiving antenna. The SFCG REC 32-2R6 recommends the Wireless device to implement filtering when necessary to avoid Out Of Band harmfull interference to PNT. The paper details these 2 SFCG recommendations which are fundamental for protection of in-situ lunar PNT. It provides some rules to the implementers to respect both SFCG recommendations. A model of PNT receiver response to interference has been developed by TéSA. Different cases are considered, such as astronauts on the lunar surface in a suit equipped with wireless and PNT devices and related antennas on their backpack, with the wireless transmitters (WIFI and 5G) interfering with the PNT reception. Technical justifications of the PFD limit of SFCG REC 43-1 are also provided. These explanations and rules are valid for in-situ lunar PNT, like the AFS (Augmented Forward Service) of LunaNet, but also for the baseline of the future Chinese insitu lunar PNT service. This paper presents the Wireless to PNT interference simulator developed by TéSA. The interference results from this simulator were used by CNES to participate to the elaboration of REC 32-2R6 and REC 43-1 in order to contribute protecting lunar in-situ PNT and, consequently, Radio Astronomy in the SZM. The SFCG recommendation applicable in the Mars region is REC 22-1R4, “Frequency assignment guidelines for communications in the Mars region” , so called “Freqs for Mars region”. In addition to the 2483.5-2500 MHz orbit to surface band, REC 22-1R4 recommends several surface wireless bands, including 2400-2480 MHz and 2503.5-2620 MHz (likely to be extended up to 2655 MHz in a next version). CNES showed that there would also be Radio Astronomy issues with GNSS L and C bands if one of them were broadcast by a Martian radiocom constellation, since Mars is regularly visible from the Shielded Zone of the Moon. The protection measures for a Martian in-situ PNT in 2483.5-2500 MHz would then be similar to the ones described for lunar in-situ PNT systems. This paper introduces the CCSDS Standard for lunar and Martian 3GPP and WIFI wireless links. This CCSDS Standard specifies to comply with the described SFCG recommendations. The paper finally concludes the systematic need to conduct system studies for each lunar wireless network, combining wireless and PNT, and involving wireless to PNT interference computations.

This work provides a comparative study of the complexity and performance for a range of different types of robust estimators. The interest of this analysis is to find the preferred robust estimator that can define the system time for a swarm of satellites. The Student’s t-distribution is used as a model for the noise corrupting the measurements. The ideal performance of an unbiased estimator for a fixed number of degrees of freedom is known in the form of the Cram´er-Rao Bound (CRB). In this article, two examples of a robust Mestimator and an approximation of the Maximum Likelihood Estimator (MLE) resulting from an Expectation-Maximization algorithm are each tested with respect to the performance bounds. Each estimator is also compared with the Gaussian MLE under Gaussian noise, to identify any losses in efficiency under Gaussian conditions. The complexity of the algorithms is also studied by comparing the time until convergence in the iterative update of the robust estimators.

Global Navigation Satellite Systems rely on estimating the signal propagation delay and Doppler shift to a set of visible satellites, which in turn allows to determine the receiver position, velocity and timing. However, the presence of interfering signals degrades the estimation of such synchronization parameters, reason why robust solutions must be accounted for. One specific kind of interference are jamming, where a powerful signal is emitted in the same bandwidth as the signal of interest. One possible way to mitigate jamming is to resort to an antenna array. Doing so, spatial diversity can help to estimate the most powerful signal, allegedly the interference, and perform detection, localization and mitigation. In our solution, we propose two methods: the first one is an offline one, which uses snapshots where the interference is the most powerful to allow for precise detection and localization of the interferer. The other one is an online one, allowing to perform detection, localization and mitigation in real time of the interfering signal.

Global Navigation Satellite Systems (GNSS) rely on estimating the signal propagation delay and Doppler shift to a set of visible satellites, which in turn allows to determine the receiver position, velocity and timing. However, the presence of interfering signals degrades the estimation of such synchronization parameters, reason why robust solutions must be accounted for. Considering constant modulus (CM) interferences, which include chirp and continuous wave signals, a recent solution proposed an expectation-maximization (EM) algorithm to estimate both interference and signal parameters, which relies on the von Mises distribution to exploit the interference CM property. In this contribution, we exploit the geometric properties of the CM family using a Riemannian framework, where CM interferences are modeled as a Riemannian manifold. This modeling allows the E-step of the EM algorithm to be replaced by a Riemannian gradient descent over that manifold. Results show that the proposed method improves the estimation performance and reduces the complexity compared to the classical EM approach.

This paper investigates time-delay and Doppler estimation in the presence of unknown heavy-tailed disturbances. Traditional approaches, such as the maximum likelihood estimator, achieve optimal mean squared error performance under the unrealistic assumption of perfect prior knowledge of the noise distribution. To address this limitation, previous work introduced a rank-based and distribution-free R-estimator, which is shown to be parametrically efficient, attaining the classical Cramer-Rao Bound irrespective of the unknown noise distribution, provided it belongs to the family of Complex Elliptically Symmetric distributions. The aim of this paper is to analyse and compare the performance of the R-estimator with an M-estimator, a widely used robust estimation approach. Specifically, we analyse their statistical efficiency for the time-delay and Doppler estimation problem, under various noise conditions. Furthermore, we propose to combine both estimators, leveraging their complementary strengths to enhance estimation performance. Numerical simulations illustrate the benefits of this hybrid approach.

Cet article présente une extension d’une approche plug-and-play pour le recalage de nuages de points 3D. Le problème de recalage de nuages de points 3D est formulé comme un problème inverse, et une approche plug-and-play est utilisée pour conjointement débruiter et recaler les nuages de points. Dans cet article, nous proposons d’optimiser la transformation de recalage en exploitant la structure de groupe de Lie de la transformation rigide SE(3). Des expériences menées sur des nuages de points LiDAR sont présentées mettant en évidence l’amélioration de la méthode par rapport à une méthode existante.

Cet article présente un nouvel algorithme EM (Expectation-Maximization) pour le recalage robuste de nuages de points 2D–3D issus d’une caméra et d’une carte de référence. Nous nous intéressons à l’estimation conjointe des paramètres d’intérêt (i.e., orientation et position de la caméra), de la proportion d’observations aberrantes et de la variance du bruit de mesure. L’approche proposée repose sur un modèle statistique intégrant des variables latentes permettant de gérer les associations inconnues entre points 2D, points 3D et observations aberrantes, via un modèle de mélange. Des résultats obtenus à partir de données synthétiques montrent l’intérêt de cette démarche en termes de rapidité de convergence de l’algorithme proposé et de robustesse face aux mesures aberrantes.

Les observations de phase de la porteuse dans les récepteurs GNSS permettent un positionnement au centimètre près mais sont affectées par un bruit de phase supposé qui suit une distribution de von Mises, dégradant la performance des estimateurs. Nous proposons une approche novatrice contraignant les paramètres de von Mises—localisation angulaire et dispersion—dans l’espace du groupe de Lie SO(2) × R+. Un estimateur du maximum de vraisemblance sur groupes de Lie, résolu via un algorithme de Newton, améliore la rigueur mathématique et la précision, notamment avec peu d’observations, par rapport aux méthodes euclidiennes.

Un réseau IP peut être représenté sous la forme d'un graphe où les noeuds sont des routeurs et les arêtes des liens de communication IP. Ce graphe aide à analyser les interactions et les flux d'information au sein du réseau. Chaque routeur, agissant comme une file d'attente, gère le trafic avec une capacité de mémoire tampon et un débit de sortie. Lorsque le trafic entrant dépasse cette capacité, une congestion se produit, dégradant le service. Identifier ces goulots d'étranglement est crucial pour évaluer la performance du réseau. Cet article explore une méthode de partitionnement de graphe permettant de regrouper les flux partageant un goulot commun à l'aide d'un modèle probabiliste plus général que ceux de la littérature.

L’identification modale des machines tournantes constitue un enjeu majeur pour la conception industrielle, notamment dans le domaine aéronautique. Dans ce contexte, la présence d’harmoniques et la dépendance des modes au régime compliquent l’analyse des signaux. Cet article propose un modèle probabiliste original pour détecter les modes propres à partir d’une carte de détection construite sur un diagramme de Campbell. Deux variantes de l’algorithme EM sont développées : une version classique et une version à classification sous contrainte (CEM) garantissant l’unicité des affectations le long des harmoniques. Les performances sont évaluées à l’aide de données simulées et comparées à la méthode RANSAC. Les résultats montrent que l’approche proposée améliore la précision d’identification et la robustesse aux outliers.