The research activities of the modelling and estimation team are organized in four main interleaved axes:
Our work is focused on methodological studies with the interest and use of various mathematical tools and their application to societal issues in different domains such as Biology and health, Energy, Finance, Statistical physics, and Wireless communications.
Our activities here seek to take into account the nowadays scientific issues concerning the critical mass of data and their heterogeneity. Learning and extracting information from these large multivariate observations is a central challenge in current data systems. The methodological tools used for studying these issues mainly come from robust estimation theory, large random matrices theory, statistical analysis of multichannel data, tensor representations, or even statistical learning.
The works carried out studies and implement these methodological tools for problem-solving in various applications with large-scale data contexts. They can be found in a wide range of applications from antenna processing to financial mathematics problems (optimized detection algorithms, estimation of radar signal sources, robust estimation theory, hyperspectral imaging, biomedical imaging, …).
We are interested in issues related to event detection in signals and the estimation of related quantities. One of the areas that are heavily covered is signal processing for diagnostic. In this context, several approaches are considered by focusing on multivariate systems modeling aspects, subspaces characterization, extraction, characteristics analysis, for decision-making (anomaly detection, breakpoints estimation, …) and performance evaluation (estimators’ limitations, errors, bounds, …).
For this work, different kinds of applications are explored to validate the proposed methodological approaches. They are ranged from electromagnetic systems to medical applications via mechanical systems (converters, electrical machines, bearings, cables, materials, electrocardiograms, phono-cardiograms, etc.). Sometimes, specific analyzes are carried out (vibratory signals analysis, spectral analysis, imaging, etc.).
We are interested in modeling and statistically analyzing special functions that allow complex signals’ description and analysis. For example, the proposed work concerns study of problems related to Bessel functions or orthogonal polynomials’ Fourier transforms calculated over a restricted domain and Pearson random processes studies. This work focuses on modeling and using signals that can be temporally and spatially correlated, non-Gaussian, and non-linear.
Various applications are dealt with. Particular attention is paid to financial series processing, antenna or radar processing problems (sources location, tensors, multi-sensors, non-uniform sampling, etc.), signal processing for biology and medicine, and signal processing for environmental problems.
This work concerns both the field of planning and analyzing numerical experience but also stochastic analysis and optimization. For example, this involves solving minimization of continuous function problems that are not necessarily convex or even probabilities optimization and estimation. Moreover, it will also concern multi-fidelity stochastic simulators solving problems by relying on an original use of sequential Monte Carlo methods.
The application fields concern stochastic simulation for fire safety, the uncertainty propagation study within dynamic continuous-time systems applied to the resource allocation problem in wireless communication systems, the stochastic control application for wind turbine production optimization, or parameters identification in stochastic networks for biomedical and ecological engineering.