Goniométrie parcimonieuse de sources radioélectriques : modèles, algorithmes et mises en œuvre robustes

This thesis deals with the direction-of-arrival (DOA) estimation of non-cooperative radio transmitters from signals received on an antenna array. The applications targeted in this work are the airborne scenario, characterized by a number of sources higher than the number of sensors, and the urban environment scenario, characterized by coherent multipath.Conventional direction-of-arrival estimation methods such as beamforming and Capon method or high resolution methods such as MUSIC are not efficient in such scenarios. The maximum likelihood method suffers from a computational complexity incompatible with current operational systems.In order to overcome these limitations, the problem of direction-of-arrival estimation is treated here with a sparse formalism, perfectly adapted to the use of calibration tables in operational systems. After having shown the interests of an approach based on a regularization by the L0 norm, this thesis tackles the technical issues that are the regularization parameter and the global convergence of optimization algorithms. To this end, we construct and statistically study sparse representations adapted to i) airborne scenarios, and ii) urban environments. The equivalence with the maximum likelihood given by a constrained formulation then allows us to determine a theoretical admissible interval for the regularization parameter. We also study the minimizers and error surfaces of different optimization criteria. This allows us to propose iterative minimization schemes that increase the probability of global convergence and thus are less sensitive to initialization. In that respect, the proposed ALICE-L0 algorithm enables to separate close sources.