Cet article traite de la mise en œuvre d’un système d’annulation active et adaptative du bruit, applicable aux essais d’émission rayonnée de compatibilité électromagnétique (CEM) ainsi qu’à des applications plus larges. Sous certaines conditions, le système peut isoler les différentes sources de bruit et construire des filtres adaptatifs numériques afin d’éliminer ces interférences. Les résultats de mesures en laboratoire et en environnement ouvert montrent la capacité à supprimer différents types de bruit (blanc, à bande étroite ou plus spécifiques d’un environnement réel) et à restituer un signal situé bien en dessous de ce bruit parasite.

Several precise positioning systems rely on carrier phase measurements, which enable centimeter-level accuracy. However, these measurements are significantly affected by additive noise, degrading the performance of phase-based positioning estimators. To better capture the statistical behavior of carrier phase observations, we pro pose to model phase measurements with a von Mises distribution. Then, to perform precise navigation, it is fun damental to estimate its parameters. To ensure estimation consistency and the respect of the underlying geometric constraints, we propose to perform their estimation within a Lie group framework. Furthermore, we adopt a Bayesian approach, where prior information about the parameters is assumed within the space SO(2)×R+. The proposed method ology provides a full Bayesian formulation that incorpo rates prior knowledge, solved through a Newton algorithm on Lie groups. This approach demonstrates advantages in terms of robustness and precision, especially when dealing with a small number of observations, compared to traditional Euclidean-based and frequentist methods. Further more, we validate the approach through simulations with a real navigation dataset.

Heavy-tailed noise models concern data contaminated with outliers. If the presence of outliers is not considered in the assumed model, the estimation performance of important parameters such as the mean and variance deteriorates. In this work, a misspecified Cramér-Rao bound is derived to show the reduced estimation performance when assuming a Gaussian distribution, although some portion of the data is generated by a Gaussian with inflated variance. This provides insight into one heavy-tailed distribution; the assumption of a different heavy-tailed distribution, the Student’s t distribution, is also investigated. The Cramér-Rao Bound for joint estimation of the location, scale, and shape parameters of the Student’s t-distribution is also derived to quantify the difference in performance when the number of degrees of freedom is unknown. Analysis of the corresponding maximum likelihood estimators and practical implementations of those estimators using the Expectation Maximization algorithm reveals the misspecified estimation performance when the contaminated data is not perfectly modeled by the chosen heavy-tailed distribution. Each of the assumptions is tested on realistic data with labeled outliers to identify the more advantageous assumption between a mixture of Gaussians and a Student’s t distribution when the true distribution of measurements is not necessarily a specific heavy-tailed model.

This thesis investigates carrier-phase enhanced time-delay estimation techniques for achieving centimeter-level inter-satellite ranging accuracy required by the NOIRE mission, a distributed radio interferometry system devised to operate in lunar orbit. The research addresses the fundamental challenge of exploiting carrier-phase information to improve ranging precision beyond conventional methods, which are limited to meter-level accuracy. The theoretical framework develops through three complementary analyses. First, the Conditional Signal Model is revisited explicitly accounting for the hardware-induced and propagation-induced phase components. While these terms were previously thought to be individually unidentifiable, this work demonstrates they can be uniquely determined under appropriate signal structure conditions. This enables the treatment of hardware phase to assess the potential of full propagation phase exploitation. Second, perfect hardware phase compensation is analyzed to establish the theoretical performance limit, representing the optimal case approachable only in specific scenarios. This analysis reveals orders of magnitude improvements through quadratic dependence on carrier frequency. It identifies five distinct operational regions of the Maximum Likelihood Estimator, extending the three regions previously reported in literature. The effects of Doppler, carrier frequency, and sampling frequency variations on estimation performance are systematically characterized. Third, the framework addresses realistic scenarios where phase measurements contain quantifiable uncertainty. A statistically optimal phase-aware estimator is developed through rigorous likelihood maximization. Novel results show performance transitions between conventional and optimal bounds based on phase observation quality. These are compared against both conventional methods and a naive engineering implementation that directly applies phase measurements without statistical weighting. The analysis reveals that under phase uncertainty, both phase-aware and naive implementations converge to a plateau at an error level determined by the uncertainty. Each 10 decibel increase in phase uncertainty elevates plateau levels by approximately 10 decibels, demonstrating a 1:1 correspondence between calibration quality and fundamental performance limits. The naive implementation remains at this error level for any SNR value. In contrast, the phase-aware implementation remains attached to the bound longer, even reaching lower error levels for a short SNR interval, before eventually detaching to form a second plateau at very high SNR. Monte Carlo simulations using GPS L1 C/A and Kasami sequences validate theoretical predictions. They establish quantitative relationships between calibration requirements and achievable accuracy. The results demonstrate that carrier-phase exploitation can theoretically achieve NOIRE mission requirements, though practical implementation requires signal-to-noise ratios exceeding 40 dB for the tested configurations. This analysis provides essential information for mission planning and enables exploration of alternative configurations. It establishes fundamental trade-offs between calibration quality, computational complexity, and system performance.

Over the past four decades, forests have experienced major disturbances, highlighting the need for Near Real-Time (NRT) monitoring. Traditional optical-based detection is cloud-sensitive, whereas Synthetic Aperture Radar (SAR)-based frameworks enable all-weather observation. Yet, SAR monitoring has mainly focused on humid tropical forests, with reduced performance in regions showing strong seasonal backscatter variation, such as tropical savannas. Detecting small-scale forest loss also remains difficult due to the spatial resolution loss from speckle filtering. This paper presents an unsupervised SAR-based disturbance detection method with NRT capabilities, using Bayesian inference. Building on an existing methodology, the approach processes singlepolarization Sentinel-1 SAR time series through Bayesian conjugate analysis. Forest disturbance is framed as a changepoint detection problem, where each new observation updates the probability of forest loss using prior information and a data model. The algorithm uses a hidden Markov chain to adapt recursively to seasonal variation and bypasses spatial filtering, preserving native data resolution and enhancing small-scale forest loss detection. Additionally, a methodology accounts for proximity to past disturbances. The method is tested on two 2020 reference datasets from the Brazilian Amazon and Cerrado savanna. The first covers small validation polygons (0.1–1 ha, excluding selective logging), totaling 2,650 ha in the Amazon and 450 ha in the Cerrado. The second includes larger clearings totaling 11,200 ha in the Amazon, and 12,700 ha in the Cerrado. A further comparison is conducted with operational NRT forest loss monitoring approaches. Results show substantial gains in detecting small-scale disturbances with reduced false alarms. In the Amazon, the method achieves an F1-score of 97.3% versus 93.1% for the current leading NRT approach. In the Cerrado, it reaches an F1-score of 97.4%, far exceeding the 33.3% of the optical-based method. For larger clearings, performance matches existing SAR approaches in the Amazon. While combined optical-SAR monitoring increases true positives, it also raises false alarm rates. In the Cerrado, the proposed method clearly outperforms optical monitoring, and in both regions it improves timeliness relative to individual operational approaches.

Order-Based Modal Analysis estimates resonances at frequencies that are integer multiples of a rotating machine’s speed. These resonances are represented as a cloud of frequency-versus-speed intersections revealing the natural modes of the mechanical structure. This paper shows that grouping these intersections can be cast as inference in a coupled affine Gaussian mixture model where each mode is represented by a straight line shared across all harmonic orders, while a uniform component captures outliers. A dedicated expectation maximisation (EM) algorithm is investigated for this model, estimating mixture weights in closed form and the other model parameters through a one-dimensional search. Cramer–Rao lower bounds are derived for the joint estimation of slopes, intercepts and mixing proportions in the proposed statistical model allowing performance of the estimators of the unknown parameters to be studied. Monte-Carlo simulations illustrate how the variances of EM estimates approach those bounds. Applied to data from an industrial turbomachine, the method extracts modal lines whose characteristics agree with historical benchmarks, despite strong deterministic harmonics and regime-dependent drifts.

A non-parametric method is introduced to estimate the measurement model of dynamical systems. The method uses a neural network trained in an unsupervised manner integrated into a particle filter framework. The network learns the measurement likelihood directly from the distribution of particles. The performance of the resulting neural network particle filter is first evaluated on synthetic data with a known measurement model showing a very interesting performance. The particle filter is then applied to sensor calibration with a specific focus on camera distortion estimation. Experimental results show that the method provides a reliable alternative to traditional parametric calibration techniques.

An online Bayesian changepoint detection framework is proposed to identify structural changes in multiple time series. An existing approach is extended to support asynchronous, multi-source inputs via both deterministic and probabilistic fusion strategies. The resulting framework enables timely, interpretable, and sensor-agnostic detection of forest changes, addressing key limitations of traditional offline and singlesensor methods. Experiments are conducted using both synthetic data and real Sentinel-1 SAR and Sentinel-2 optical data over tropical forests affected by deforestation. Results highlight the benefits of multi-source fusion for accurate and timely disturbance detection.

Accurate signal time-delay estimation is critical in localization, sensor fusion, and communication systems. In multi-sensor contexts, where distributed nodes combine measurements, modeling estimation performance under realistic assumptions is key. A common challenge is global phase misalignment, stemming from hardware imperfections at both transmitter and receiver. While some works assume perfect calibration and others treat phase as completely unknown, we propose a middle-ground model where the phase is partially known, i.e., estimated with uncertainty. This approach is particularly relevant in practical multi-sensor scenarios, where each node may experience different phase conditions. The goal is to quantify how an additional measurement of the unknown phase can enhance time-delay estimation. We derive the corresponding Maximum Likelihood Estimator (MLE) and propose a practical implementation to evaluate its Mean Squared Error. Leveraging existing Cramér-Rao Bound results, we show that the MLE is efficient over a finite SNR range, though not asymptotically consistent or efficient.

Nonlinear regression models play a crucial role in signal processing and multi-sensor applications. Traditionally, performance bounds for these models assume independent Gaussian observations. In practice, the Gaussian assumption fails in multi-sensor systems if some proportion of sensors are corrupted by non-Gaussian noise and outliers. In this context, we extend the Misspecified Cramér-Rao Bound (MCRB) framework to the contaminated Gaussian noise model, where observations are generated from a mixture of nominal Gaussian noise and occasional outliers. Building on previous work with Complex Elliptically Symmetric noise models, we derive analytical MCRB expressions under the mismatched Gaussian assumption and study the asymptotic behavior of the corresponding Misspecified Maximum Likelihood Estimator (MMLE). To demonstrate practical relevance, we apply the theory to joint time-delay and Doppler estimation in GPS signals under contamination. Numerical simulations confirm that the MMLE root mean squared error converges to the theoretical MCRB, which aligns with the classical Gaussian CRB.