On Detection and Estimation of Multiple Sources in Radar Array Processing

Abstract: This thesis deals with detection and estimation problems in sensor array signal processing. We treat the multiple hypothesis problem for complex sinusoids observed in spatially colored noise. The detection scheme protects against false alarms by allowing the user to set the thresholds such that a specified probability of over-estimation is obtained. The method relies on using the Sequentially Rejective Bonferroni Test for bounding the false alarm probability. As test statistics, generalized likelihood ratios are used together with the Nonlinear Weighted Least Squares, NWLS, estimates. The NWLS method is shown to be consistent and the asymptotic multivariate Gaussian distribution of the parameter estimates is derived under a large class of noise distributions. We also treat adaptive data reduction with minimal information loss via linear transformations. This is investigated for both stochastic and deterministic source signal models observed in complex Gaussian colored noise. The criterion used is preservation of the Cramér-Rao Bounds, CRB. The optimal transformation depends on the unknown noise covariance matrix as well as the unknown directions of arrival. However, as is shown, one may use the array covariance matrix instead of the noise covariance matrix, without affecting the CRB. The transformation results in lower computational complexity and a reduced sensitivity to colored noise. To further reduce the computational load, we present an approach that combines the information preserving linear transformation with a uniform linear array interpolation. This enables the use of computationally efficient approaches for direction estimation such as the Root-MUSIC, ESPRIT or IQML methods. Finally, we treat a different problem, namely the classification problem. Therein, it is often desirable to reduce the number of features used for classifying a set of data. We propose a linear transformation that reduces the feature dimension so that the separation between the classes is retained, as measured by all pairwise Mahalanobis distances between the classes. In the two class case, it coincides with the well known Fisher linear discriminant function. The proposed method is found to perform well in comparison to other established techniques.

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