Cette thèse porte sur la localisation de sources spatialement distribuées. Premièrement, des résultats théoriques ont été établis concernant les performances des méthodes à haute résolution en présence d'erreurs de modèle dues à la distribution angulaire de source. Ainsi, le biais d'estimation et l'erreur quadratique moyenne sont exprimées en fonction des paramètres liés à l'erreur de modèle. De plus, les performances ont été étudiées en fonction de la géométrie de l'antenne afin de déterminer les configurations les plus robustes aux sources dispersées.Les résultats théoriques ont été validés par des simulations numériques. Dans un deuxième temps, une nouvelle approche non paramétrique a été proposée pour la localisation de sources distribuées : cette approche exploite les propriétés de parcimonie et de rang-faible de la matrice de covariance spatiale des sources. Cette méthode permet en outre d'estimer la forme de la distribution spatiale des sources. Les résultats de simulations ont permis de mettre en avant l'intérêt de l'hypothèse rang faible par rapport aux critères exploitant uniquement la parcimonie / This thesis focuses on the distributed source localization problem. In a first step, performance of high resolution methods in the presence of model errors due to the angular distribution of source has been studied. Theoretical expressions of the estimation bias and the mean square error of the direction of arrival of sources have been established in terms of model error. The impacts of the array geometry on the performances have studied in order to optimize the robustness of the array to the model error due to distributed sources.Theoretical results have been validated by numerical simulations.In a second step, a new approach for the localization of spatially distributed source has been proposed: the approach is based on the sparsity and low-rank property of the spatial covariance matrix of the sources. The proposed method provides also an estimation of the distribution shapes of the sources. Simulation results exhibit the advantages of exploiting the sparsity and the low rank properties.

In this dissertation, sparse processing of signals for directions-of-arrival (DoAs) estimation is addressed in the framework of Compressive Sensing (CS). In particular, DoAs estimation problem for different types of sources, systems, and applications are formulated in the CS paradigm. In addition, the fundamental conditions related to the ``Sparsity'' and ``Linearity'' are carefully exploited in order to apply confidently the CS-based methodologies. Moreover, innovative strategies for various systems and applications are developed, validated numerically, and analyzed extensively for different scenarios including signal to noise ratio (SNR), mutual coupling, and polarization loss. The more realistic data from electromagnetic (EM) simulators are often considered for various analysis to validate the potentialities of the proposed approaches. The performances of the proposed estimators are analyzed in terms of standard root-mean-square error (RMSE) with respect to different degrees-of-freedom (DoFs) of DoAs estimation problem including number of elements, number of signals, and signal properties. The outcomes reported in this thesis suggest that the proposed estimators are computationally efficient (i.e., appropriate for real time estimations), robust (i.e., appropriate for different heterogeneous scenarios), and versatile (i.e., easily adaptable for different systems).