In this communication we develop a new full Slepian-Bangs formula adapted to observations on Lie Groups (LGs) distributed according to a Gaussian distribution on LGs (CGD), where both the LG mean and LG covariance depend on an unknown LG parameter. This formulation, which can be seen as a generalization on LGs of the full Slepian-Bangs formula for the Euclidean Gaussian distribution, is obtained using LG tools and properties of the CGD. A closed-form expression is then obtained for a modified Wahba’s problem where the observations'covariance matrix depends on the unknown rotation matrix. Such expression is validated through numerical simulations.

Space-based remote sensing facilitates the determination of greenhouse gas concentrations, enhancing the comprehension of carbon fluxes at the Earth’s surface in the context of climate change. High-resolution spectrometers, such as the CNES/UKSA MicroCarb and the upcoming ESA Copernicus Carbon Dioxide Monitoring (CO2M) spectrometers, are crucial tools for this purpose. These instruments require a precise calibration, especially regarding the relative approximation errors of the Instrument Spectral Response Functions (ISRFs). To ease ISRF estimation, parametric models such as Gaussian and Super-Gaussian models have been investigated. However, these models cannot always take into account the diversity of ISRF shapes that are encountered in practical applications. For example, in MicroCarb simulations, the expected performance is not always achieved by these two conventional ISRF estimation methods, even when there is no spectral and radiometric errors. This paper investigates a novel approach based on the sparse representation of ISRFs in a dictionary. This method decomposes the spectral responses of interest as sparse linear combinations of atoms belonging to a dictionary, which are built using representative ISRFs. This new method can be applied both for on-ground ISRF denoising, and in-flight ISRF estimation through the resolution of an appropriate inverse problem. Experiments conducted using realistic simulated datasets associated with the MicroCarb instrument are used to evaluate the performance of the proposed method for on-ground and in-flight ISRF estimation, yielding promising estimation performance compared to the state of the art.

Le domaine de l’observation de l’Espace s’intéresse de près aux signaux très basse fréquence, car ils fournissent d’importantes informations quant à la naissance et aux premiers jours de l’Univers. A ce jour, les interféromètres observant ces signaux se situent à la surface de la Terre, dans des zones arides. Malheureusement, ces signaux sont très sensibles aux interférences terrestres ainsi qu’à l’ionosphère, et sont donc difficilement observables. Une solution à ce problème serait d’observer les signaux directement depuis l’Espace, en déployant un essaim de nanosatellites en orbite autour de la Lune. Cet essaim constitue un Système Spatial Distribué (DSS), fonctionnant en tant qu’interféromètre, dont l’orbite lunaire le préserve des interférences terrestres et de l’ionosphère. Cependant, la configuration de l’essaim de nanosatellites en interféromètre spatial est un défi de taille en termes de communication, notamment en raison de l’absence d’infrastructure dans l’Espace et du volume de données d’observation à propager au sein du système. L’objectif de la thèse est donc de définir une configuration d’architecture fiable, répondant aux contraintes conjointes d’un réseau MANET et d’un système distribué. La thèse commence par caractériser le réseau de l’essaim de nanosatellites et met en avant sa forte hétérogénéité. Ensuite, elle propose des algorithmes permettant de répartir équitablement la charge du réseau, en se basant sur des techniques de division de graphe, et compare les performances de ces algorithmes sur des critères d’équité. Enfin, elle évalue la sensibilité du système aux pannes en termes de robustesse (résistance aux pannes) et de résilience (maintien du fonctionnement en présence de pannes) et étudie l’impact de la division de graphe sur la fiabilité globale de l’essaim. Les algorithmes de division développés dans cette thèse devront garantir la Qualité de Service (QoS) essentielle au bon fonctionnement d’un interféromètre spatial. Pour atteindre cet objectif, des solutions de routage pertinentes devront être minutieusement étudiées et intégrées, afin de s’assurer qu’elles répondent aux exigences strictes de performance et de fiabilité de cette application avancée.

Le domaine de l’observation de l’Espace s’intéresse de près aux signaux très basse fréquence, car ils fournissent d’importantes informations quant à la naissance et aux premiers jours de l’Univers. A ce jour, les interféromètres observant ces signaux se situent à la surface de la Terre, dans des zones arides. Malheureusement, ces signaux sont très sensibles aux interférences terrestres ainsi qu’à l’ionosphère, et sont donc difficilement observables. Une solution à ce problème serait d’observer les signaux directement depuis l’Espace, en déployant un essaim de nanosatellites en orbite autour de la Lune. Cet essaim constitue un Système Spatial Distribué (DSS), fonctionnant en tant qu’interféromètre, dont l’orbite lunaire le préserve des interférences terrestres et de l’ionosphère. Cependant, la configuration de l’essaim de nanosatellites en interféromètre spatial est un défi de taille en termes de communication, notamment en raison de l’absence d’infrastructure dans l’Espace et du volume de données d’observation à propager au sein du système. L’objectif de la thèse est donc de définir une configuration d’architecture fiable, répondant aux contraintes conjointes d’un réseau MANET et d’un système distribué. La thèse commence par caractériser le réseau de l’essaim de nanosatellites et met en avant sa forte hétérogénéité. Ensuite, elle propose des algorithmes permettant de répartir équitablement la charge du réseau, en se basant sur des techniques de division de graphe, et compare les performances de ces algorithmes sur des critères d’équité. Enfin, elle évalue la sensibilité du système aux pannes en termes de robustesse (résistance aux pannes) et de résilience (maintien du fonctionnement en présence de pannes) et étudie l’impact de la division de graphe sur la fiabilité globale de l’essaim. Les algorithmes de division développés dans cette thèse devront garantir la Qualité de Service (QoS) essentielle au bon fonctionnement d’un interféromètre spatial. Pour atteindre cet objectif, des solutions de routage pertinentes devront être minutieusement étudiées et intégrées, afin de s’assurer qu’elles répondent aux exigences strictes de performance et de fiabilité de cette application avancée.

Location-based services, safety-critical applications, and modern intelligent transportation systems require reliable, continuous, and precise positioning, navigation, and timing (PNT) information. Global Navigation Satellite Systems (GNSS) are the main source of positioning data in open sky conditions; however, their vulnerabilities to radio interferences and signal propagation limit their use in challenging environments. Consequently, enhancing conventional GNSS-based PNT solutions to incorporate additional sensing modalities and exploit other available signals of opportunity has become necessary for continuous and reliable navigation. Articles in the special issue span detection methods, estimation algorithms, signal optimization, and the application of machine learning, providing comprehensive insights into enhancing navigation and positioning accuracy.

Forests worldwide have undergone significant transformations due to forest loss, highlighting the critical need for real-time forest monitoring to prevent further vegetation loss and facilitate prompt interventions. Traditionally, forest loss monitoring relied on optical imagery, which is obstructed by its susceptibility to cloud coverage, especially in tropical regions. In recent times, Synthetic Aperture Radar (SAR)-based systems have emerged to enable all-weather operability. However, SAR-based approaches encounter challenges, such as the alterations in backscatter caused by factors like soil moisture variations. Moreover, accurately detecting small-scale disturbances remains problematic for SAR systems, partly due to the spatial filtering techniques employed to mitigate the effects of speckle. Additionally, monitoring forest loss in regions characterized by pronounced seasonality in backscatter signals, such as dry forests and savannas, poses limitations, resulting in substantial under-monitoring of these extensive carbon sinks. This study introduces an unsupervised SAR-based method for detecting forest loss, employing Bayesian inference through an infinite state Markov chain.

In this article, the principles of robust estimation are applied to the standard basic time scale equation to obtain a new method of assigning weights to clocks. Specifically, the Student’s t-distribution is introduced as a new statistical model for an ensemble of clocks that are experiencing phase jumps, frequency jumps or anomalies in their measurement links. The proposed robust time scale is designed to mitigate the effects of these anomalies without necessarily identifying them, but through applying a method of robust estimation for the parameters of a Student’s t-distribution. The proposed time scale algorithm using the Student’s t-distribution (ATST) is shown to achieve comparable robustness to phase jumps, frequency jumps, and anomalies in the measurements with respect to the AT1 oracle time scale. The AT1 oracle is a special realization of the AT1 time scale which corrects all anomalies by having prior knowledge of their occurrences. The similar performance of ATST and AT1 oracle suggests that the ATST algorithm is efficient for obtaining robustness with no prior knowledge or detection of the occurrences of anomalies.

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its ability to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space, which is referred to as Hyperbolic Local Outlier Probability (HLoOP). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The proposed HLoOP combines the notion of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method computes the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The proposed HLoOP algorithm is tested on the WordNet dataset and desmonstrated promising results. The code and data will be made available upon request for reproducibility.

Robust estimation methods are useful in mitigating the impact of anomalies in clock data. Such anomalous clock data is assumed to be well modeled by a Student’s t-distribution. This paper derives a lower bound on the performance of the misspecified Gaussian model using the theory of the Misspecified Cram´er-Rao bound (MCRB). The results of these derivations are verified by analyzing the Mean Square Error (MSE) of the misspecified Gaussian Maximum Likelihood Estimator (MLE) when using data generated by the Student’s t-distribution. The derived MCRB indicates a constraint on the MSE when assuming a Gaussian distribution. The MLE for the mean of the Student’s t-distribution is obtained with an Expectation maximization algorithm and is shown to obtain a lower MSE than the MCRB and hence, the misspecified estimator. This indicates an improvement in performance if anomalous clock data is appropriately accounted for in the statistical model.

State estimation with Kalman Filters (KF) regularly encounters covariance matrices that are unknown or empirically determined, causing sub-optimal performances. Solutions to lift these uncertainties are opening up to estimation techniques based on the hybridization of KF with deep learning methods. In fact, inferring covariance matrices from neural networks gives rise to enforcing symmetric positive definite outputs. In this work, a new Recurrent Neural Network (RNN) model is explored, based on the geometric properties of the Riemannian Symmetric Positive Definite (SPD) manifold. To do so, a neuron function is defined based on the Riemannian exponential map, depending on unknown weights lying on the tangent space of the manifold. In this way, a Riemannian cost function is deduced, enabling to learn the weights as Euclidean parameters with a conventional Gauss-Newton algorithm. It involves the computation of a closedform Jacobian. Through optimization on a simulated covariance dataset, we demonstrate the possibilities of this new approach for RNNs.