Doctorante / doctorant: “study of riemannian geometry for interference mitigation”

Description L’ENAC, École Nationale de l’Aviation Civile, est la plus importante des Grandes Écoles ou universités aéronautiques en Europe. Elle forme à un spectre large de métiers : des ingénieurs ou des professionnels de haut niveau capables de concevoir et faire évoluer les systèmes aéronautiques et plus largement ceux du transport aérien ainsi que des pilotes de ligne, des contrôleurs aériens ou encore des techniciens aéronautiques. Ses laboratoires de recherche sont à la pointe de l’innovation et travaillent activement en coopération avec des universités internationales de haut niveau pour un transport aérien toujours plus sûr, efficace et durable. L’ENAC est un établissement public à caractère scientifique, culturel et professionnel – grand établissement (EPSCP-GE), sous tutelle de la DGAC (Direction Générale de l’Aviation Civile), Direction du Ministère de la Transition Écologique et Solidaire. L’ENAC comprend une direction générale localisée à Toulouse et 8 sites en France. Pour soutenir sa dynamique en faveur de la promotion de la diversité, l’ENAC facilite l’accueil et l’intégration des travailleurs en situation de handicap. Mission Various phenomena impact signals between their emission and their reception. Some of them might carry useful information, such as the propagation delay, related to the range between emitter and receiver, or the Doppler shift, related to their relative velocities. For instance, this information is used in Radar systems or Global Navigation Satellite Systems (GNSS) to retrieve one’s position and velocity. Usually, the user receives a mixture of signals from which it estimates the individual parameters. In some cases, such as with Code Division Multiple Access (CDMA), a single transmitter can be isolated from others, resulting in an observed signal consisting of the signal of interest (SoI), which is attenuated, delayed, and frequency-shifted. In nominal conditions, the noise can be considered white circular symmetric complex Gaussian, and estimation performance bounds have been derived in that case. However, when spurious signals arrive at the antenna with the SoI, such as replicas of the original signal (multipath, spoofing) or interferences (intentional (jamming) or unintentional), the corresponding estimation problem changes, and if estimators derived under the nominal hypothesis are used, they become misspecified. Usually, the interfering signal has some geometric properties (e.g., constant modulus) which might be interesting to study to mitigate its effects on the estimation of the parameters of interest. The main objective of the thesis is therefore the use of geometric information to improve estimation in identified scenarios. This objective has two main steps: identify geometries corresponding to several interference models, derive the corresponding estimators as well as their performance bounds under well- and miss-specified models. Profile Master en Traitement statistique du signal, estimation