The Modified Cramér-Rao Bound (MCRB) proves to be of significant importance in non-standard estimation scenarios, when in addition to unknown deterministic parameters to be estimated, observations also depend on random nuisance parameters. Given the interest of applications that involve estimation on Lie Groups (LGs), as well as the relevance of nonstandard estimation problems in many practical scenarios, the main concern in this communication is to derive an intrinsic MCRB on LGs (LG-MCRB). For this purpose, a modified unbiasedness constraint must be defined, yielding a modified Barankin Bound. A closed-form formula of the LG-MCRB is then provided for a LG Gaussian model on $S O(2)$, representing $2 D$ rotation matrices, while considering non-Gaussian random nuisance parameters. The validity of this expression is then assessed through numerical simulations, and compared with the intrinsic CRB on LGs for a simplified illustrative scenario, involving a concentrated Gaussian prior distribution on the random nuisance parameters.

Forest loss is a global issue that requires real-time surveillance to prevent further vegetation loss. This study presents an unsupervised SAR-based technique that leverages Bayesian inference and infinite state Markov chains to identify forest loss, overcoming the limitations of current methods. Our approach significantly improves accuracy and reduces false alarm rates compared to existing Near Real-Time (NRT) forest loss monitoring systems and enlarges the conditions of operability.

The computation of a common reference time for a swarm of nanosatellites is restricted by the quality and availability of the timing measurements made with inter-satellite links. The presence of anomalies or absence of communication links is demonstrated to harm the stability of the time scale. The Least Squares (LS) estimator is introduced as a method of preprocessing measurement noise by using all available clock comparisons in the swarm. This estimator also provides filtered measurements when inter-satellite links are missing as long as each satellite maintains at least one link with another. Anomaly detection and removing corrupted satellite links are shown to be compatible with the LS estimator to mitigate the impact of anomalous measurements. When a satellite becomes completely isolated for some period of time, a correction at the beginning and the end of the isolation period are both detailed. The correction is simple and just requires resetting the weights of missing clocks and clocks being reintroduced. Continuity is shown to be maintained when a large portion of clocks are removed and later reintroduced at the same time.

Nous proposons de partitionner l’architecture d’un réseau ad-hoc mobile en plusieurs groupes, afin de re-distribuer équitablement la charge entre les membres du réseau. Notre étude porte sur un essaim de nanosatellites fonctionnant commue un télélescope spatial distribué, placé en orbite lunaire. Chaque nanosatellite de l’essaim collecte des données d’observation de l’espace, puis les échange avec les autres membres de l’essaim. Les données recueillies sont ensuite combinées localement afin de produire l’image globale observée par l’essaim. Cependant, un système fondé sur ce mode opératoire est particulièrement sensible aux pertes de paquets et aux pannes d’énergie. En effet, la transmission simultanée d’un important volume de données peut entraîner des problèmes de communication, notamment en surchargeant le canal radio ou en augmentant le risque de collisions, menant dans les deux cas à des pertes de paquets. La consommation énergétique totale de l’essaim est également proportionnelle au nombre de paquets transmis : il faut alors trouver une solution pour limiter le nombre de transmissions afin d’économiser l’énergie des nanosatellites. La principale contribution de ce papier est de proposer une approche basée sur la division équitable du réseau en plusieurs groupes de nanosatellites. Nous comparons les performances de trois algorithmes de division de graphe : Random Node Division (RND), Multiple Independent Random Walks (MIRW), et Forest Fire Division (FFD). Nos résultats montrent que MIRW obtient les meilleurs scores en termes d’équité, peu importe le nombre de groupes produit.

In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for highorder Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs.We implement the proposed SBND system for two polar codes (64, 32) and (128, 64), using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.

In this work, we investigate the construction of channel decoders based on machine learning solutions, and more specifically, Support Vector Machines (SVM). The channel decoding problem being a high-dimensional multiclass classification problem, previous attempts were made in the literature to construct SVM-based channel decoders. However, existing solutions suffer from a dimensionality curse, both in the number of SVMs involved –which are exponential in the block length–and in the training dataset size. In this work, we revisit SVMbased channel decoders by alleviating these limitations and prove that the suggested SVM construction can achieve optimal Bit Error Probability (BEP) by attaining the performance of the bit-Maximum A Posteriori (MAP) decoder in the Additive White Gaussian Noise (AWGN) channel.

Time-delay and Doppler estimation is an operation performed in a plethora of engineering applications. A common hypothesis underlying most of the existing works is that the noise of the true and assumed signal model follows a centered complex normal distribution. However, everyday practice shows that the true signal model may differ from the nominal case and should be modeled by a non Gaussian distribution. In this paper, we analyse the asymptotic performance of the time-delay and Doppler estimation for the non-nominal scenario where the true noise model follows a centered complex elliptically symmetric (CES) distribution and the receiver assumed that the noise model follows a centered complex normal distribution. It turns out that performance bound under the misspecified model is equal to the one obtained for the well specified Gaussian scenario. In order to validate the theoretical outcomes, Monte Carlo simulations have been carried out.

In this talk, I will introduce a method for sequentially estimating both random and deterministic parameters within linear Gaussian discrete-time state space models. Following that, the performance of the obtained joint Maximum-a-posteriori Maximum likelihood estimator is assessed using hybrid Cramér-Rao bounds on two illustrative examples. Moving forward, I will exhibit the link between the Modified Cramér-Rao bound, a ubiquitous bound in non-standard estimation problems, and the hybrid Cramér-Rao bound under a mild constraint. Leveraging this link enables us to derive a recursive estimation scheme of the Modified Cramér-Rao bound (under constraint) for Markovian Dynamic Systems. Finally, I will discuss the extension of the Modified Cramér-Rao bound to matrix Lie groups.