Traitement d’antenne tensoriel

Abstract : Source estimation and localization are a central problem in array signal processing, and in particular in telecommunications, seismology, acoustics, biomedical engineering, and astronomy. Sensor arrays, i.e. acquisition systems composed of multiple sensors that receive source signals from different directions, sample the impinging wavefields in space and time. Hence, high resolution techniques such as MUSIC make use of these two elements of diversities: space and time, in order to estimate the signal subspace generated by impinging sources, as well as their directions of arrival. This is generally done through the estimation of second or higher orders statistics, such as the array spatial covariance matrix, thus requiring sufficiently large data samples. Only recently, tensor analysis has been applied to array processing using as a third mode (or diversity), the space shift translation of a reference subarray, with no need for the estimation of statistical quantities. Tensor decompositions consist in the analysis of multidimensional data cubes of at least three dimensions through their decomposition into a sum of simpler constituents, thanks to the multilinearity and low rank structure of the underlying model. Thus, tensor methods provide us with an estimate of source signatures, together with directions of arrival, in a deterministic way. This can be achieved by virtue of the separable and low rank model followed by narrowband sources in the far field. This thesis deals with source estimation and localization of multiple sources via these tensor methods for array processing. Chapter 1 presents the physical model of narrowband elastic sources in the far field, as well as the main definitions and assumptions. Chapter 2 reviews the state of the art on direction of arrival estimation, with a particular emphasis on high resolution signal subspace methods. Chapter 3 introduces the tensor formalism, namely the definition of multi-way arrays of coordinates, the main operations and multilinear decompositions. Chapter 4 presents the subject of tensor array processing via rotational invariance. Chapter 5 introduces a general tensor model to deal with multiple physical diversities, such as space, time, space shift, polarization, and gain patterns of narrowband elastic waves. Subsequently, Chapter 6 and Chapter 8 establish a tensor model for wideband coherent array processing. We propose a separable coherent focusing operation through bilinear transform and through a spatial resampling, respectively, in order to ensure the multilinearity of the interpolated data. We show via computer simulations that the proposed estimation of signal parameters considerably improves, compared to existing narrowband tensor processing and wideband MUSIC. Throughout the chapters we also compare the performance of tensor estimation to the Cramér-Rao bounds of the multilinear model, which we derive in its general formulation in Chapter 7. Moreover, in Chapter 9 we propose a tensor model via the diversity of propagation speed for seismic waves and illustrate an application to real seismic data from an Alpine glacier. Finally, the last part of this thesis in Chapter 10 moves to the parallel subject of multidimensional spectral factorization of seismic ways, and illustrates an application to the estimation of the impulse response of the Sun for helioseismology.
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Francesca Raimondi. Traitement d’antenne tensoriel. Traitement du signal et de l'image. Université Grenoble Alpes, 2017. Français. ⟨NNT : 2017GREAT043⟩. ⟨tel-01691607v2⟩

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