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.

Time-delay and Doppler estimation is crucial in various engineering fields, as estimating these parameters constitutes one of the key initial steps in the receiver’s operational sequence. Due to its importance, several expressions of the Cramér–Rao Bound (CRB) and Maximum Likelihood Estimation (MLE) have been derived over the years. Previous contributions started from the assumption that the transmission process introduces an unknown phase, which hindered the explicit consideration of the time-delay parameter in the carrier-phase component in theoretical derivations. However, this contribution takes into account this additional term under the assumption that such an unknown phase is inferred and compensated for. This new condition leads to the derivation of a novel MLE. Subsequently, a closed-form expression of the achievable Mean Squared Error (MSE) for the time-delay and Doppler parameters is provided for the asymptotic region, assuming the signal is band-limited. Both expressions are validated via Monte Carlo simulations. This analysis reveals five distinct regions of operation of the MLE, refining existing knowledge and providing valuable insights into time-delay estimation

This study investigates the Unsplittable Multi-Commodity Flow (UMCF) as a routing algorithm for LEO constellations. Usually, LEO routing schemes enable the Floyd-Warshall algorithm (Shortest Path) to minimize the end-to-end latency of the flows crossing the constellation. We propose to solve the UMCF problem associated with the system as a solution for routing over LEO. We use a heuristic algorithm based on randomized rounding known in the optimization literature to efficiently solve the UMCF problem. Furthermore, we explore the impact of choosing the first/last hop before entering/exiting the constellation. Using network simulation over Telesat constellation, we show that UMCF maximizes the end-to-end links usage, providing better routing while minimizing the delay and the congestion level, which is an issue today over new megaconstellations.

EVM (Error Vector Measurement) is used to measure the end-to-end quality of digital communication links. It comes from noise, linear and non-linear distortion, and interference if any. I propose a method to discriminate between random noise that is independent of the signal and distortion that depends on the signal. Interference is more complex to discriminate as it is not random but can be either synchronous with the signal or not. Echoes such as multipath cause linear distortion if they are static. However, variable echoes, such as those created in a reverberation chamber must be treated specifically.

Since time-delay and phase estimation is a fundamental task in a plethora of engineering fields, several CRB and MLE expressions have been derived for the past decades. In all these previous works, a common hypothesis is that the wave transmission process introduces an unknown phase which prevents from estimating both delay and transmission phase components. By revisiting this problem, including the derivation of the MLE and the associated CRB, we show that this well-admitted assertion is not true strictly: both informations can be estimated, but generally with a sub-optimal achievable MSE in the asymptotic region. Moreover, since practical problems exist where the transmission phase can be estimated apart, adding this additionnal measure to the observation model provides a setting allowing to explore the contribution of each signal component (carrier frequency, baseband signal and transmission phase measure) to the achievable MSE of time-delay and phase estimation in the asymptotic region.

A fusion method was recently proposed for ultrasound and magnetic resonance images for endometriosis diagnosis. This method combined the advantages of each modality, i.e., the good contrast and signal to noise ratio of the MR image and the good spatial resolution of the US image. The method was based on an inverse problem, performing a superresolution of the MR image and a denoising of the US image. A polynomial function was introduced to model the relationships between the gray levels of the MR and US images. This paper studies the potential interest of replacing this polynomial function by a non-parametric transformation built using the theory of reproducing kernel Hilbert spaces. Simulations conducted on a phantom and synthetic data allow the performance of the resulting fusion method to be appreciated.

In this work, we investigate the problem of neuralbased error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We improve on previous works in terms of allowing full decoding of the message rather than codewords, allowing thus the application to nonsystematic codes, and proving that the single-message training property is still viable. The suggested system is implemented and tested on polar codes of sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise Ratio (SNR) regime.