Algorithmes d’Estimation et de Détection en Contexte Hétérogène Rang Faible

One purpose of array processing is the detection and location of a target in a noisy environment. In most cases (as RADAR or active SONAR), statistical properties of the noise, especially its covariance matrix, have to be estimated using i.i.d. samples. Within this context, several hypotheses are usually made: Gaussian distribution, training data containing only noise, perfect hardware. Nevertheless, it is well known that a Gaussian distribution doesn’t provide a good empirical fit to RADAR clutter data. That’s why noise is now modeled by elliptical process, mainly Spherically Invariant Random Vectors (SIRV). In this new context, the use of the SCM (Sample Covariance Matrix), a classical estimate of the covariance matrix, leads to a loss of performances of detectors/estimators. More efficient estimators have been developed, such as the Fixed Point Estimator and M-estimators.If the noise is modeled as a low-rank clutter plus white Gaussian noise, the total covariance matrix is structured as low rank plus identity. This information can be used in the estimation process to reduce the number of samples required to reach acceptable performance. Moreover, it is possible to estimate the basis vectors of the clutter-plus-noise orthogonal subspace rather than the total covariance matrix of the clutter, which requires less data and is more robust to outliers. The orthogonal projection to the clutter plus noise subspace is usually calculated from an estimatd of the covariance matrix. Nevertheless, the state of art does not provide estimators that are both robust to various distributions and low rank structured.In this Thesis, we therefore develop new estimators that are fitting the considered context, to fill this gap. The contributions are following three axes :- We present a precise statistical model : low rank heterogeneous sources embedded in a white Gaussian noise.We express the maximum likelihood estimator for this context.Since this estimator has no closed form, we develop several algorithms to reach it effitiently.- For the considered context, we develop direct clutter subspace estimators that are not requiring an intermediate Covariance Matrix estimate.- We study the performances of the proposed methods on a Space Time Adaptive Processing for airborne radar application. Tests are performed on both synthetic and real data.