High resolution algorithms for spectral analysis and array processing




Du, Weixiu

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In this dissertation a novel covariance matrix estimator has been proposed for the covariance-matrix based high resolution spectral estimators. The proposed covariance matrix estimator can fully exploit cross correlations existent among distinct sets of random vectors drawn from different processes to obtain a more stable estimate of the covariance matrix from a short data record corrupted by additive noise. This estimator is derived from a theorem on the Least Squares Linear Prediction of one random vector from another random vector. The theorem can also be interpreted as estimating the auto-covariance matrix of the first random vector from the cross-correlation matrix between the two random vectors and the auto-covariance matrix of the second random vector such that a given optimal criterion is satisfied. Applying this method in conjunction with a high resolution algorithm results in performance improvement of the spectral estimator. The new covariance matrix estimator has been applied in the following three areas: (1) Spatial smoothing for the direction of arrival estimation in the presence of coherent signals. (2) Covariance enhancement by utilizing temporal correlations between array snapshot vectors. (3) Spectral estimation for time sequences. Simulations show that the expected performance improvement can be achieved in terms of resolution, estimation errors and SNR threshold. In addition to the covariance matrix estimator, we also present some other research results in array processing and seismic signal processing. A general transformation matrix based on the vector p-norm has been proposed. This new transformation matrix provides options to satisfy different design specifications in array processing. Finally the velocity estimation problem in seismic signal processing is discussed. The conventional semblance method is found to be the conventional beamforming method for a fixed two-way time. An optimal velocity estimator is proposed based on the Linearly Constrained Minimum Variance beamformer. The optimal velocity estimator demonstrates the high discrimination power (resolution) both for noise free data and noisy data. When the new covariance estimator is used in conjunction with the optimal velocity estimator, we can achieve a resolution with deeper notch. This fact once more demonstrates the advantages of the proposed covariance matrix estimator.



Analysis of covariance