Enhanced Covariance Matrix Research Articles

Robust DOA Estimator Under Non-Gaussian Noise and Insufficient Sample Support

In this paper, we develop a robust algorithm for improving the accuracy of direction-of-arrival estimation under non-Gaussian noise and insufficient sample support. (The number of sensors is large, while the number of samples is relatively small.) Unlike the traditional peak-search techniques, our approach is based on an enhanced covariance matrix estimation, where we exploit the thoughts of the M-estimator and the shrinkage estimator, but devise a new target matrix equation and iterative solution procedure. Numerical results indicate that the proposed algorithm significantly performs better than the existing methods in the presence of non-Gaussian noise and finite samples.

Null widening method for conformal array based on covariance matrix enhancement

Conformal arrays are widely used in various aircrafts since they do not affect the aerodynamic performance of the carriers. When conformal arrays are used to suppress fast-moving interference, it is possible that the weight mismatches the data of measurement due to the perturbation of the interference location. Traditional null widening methods are based on linear or planar arrays and cannot be applied to conformal arrays directly. Therefore, a null widening method used for conformal arrays is proposed in this article. In the method, the spatial spectrum of the signal is first calculated, and then the convolution of spatial spectrum in the interference region and 2-D window function is calculated to enhance the spatial spectrum. Next, the enhanced covariance matrix is calculated based on the convolution results. Finally, the sample matrix inversion (SMI) method is used to calculate the weight. This method can be used for common conformal arrays and can form two-dimensional nulls in space. Based on the numeral simulation results, it is verified that the proposed method can form widened nulls and improve the robustness of interference suppression effectively.

Robust adaptive beamforming based on subspace method

The performance of adaptive beamformers is susceptible to the steering vector mismatches and covariance matrix uncertainties. In contrast to traditional subspace methods, the proposed subspace method is robust against model mismatches. The signal-plus-interference covariance matrix (SICM) is reconstructed by projecting the enhanced covariance matrix onto the signal-plus-interference subspace which is formed using the property of covariance matrix. The array steering vector is adjusted by projecting the presumed steering vector onto the signal subspace which is structured using the major eigenvectors of the enhanced covariance matrix. The major eigenvectors are selected when the correlation coefficient between the presumed steering vector and the eigenvector exceeds a certain threshold. By combining the reconstructed SICM with the adjusted array steering vector, the proposed beamformer can provide robust performance. In comparison with many existing robust techniques, the proposed method performs well in both high and low signal-to-noise ratio scenarios. Several examples are carried out to illustrate the superiority of our method.

Detection of the number of two‐dimensional harmonics in additive colored noise

ABSTRACTThis paper proposes a novel method to detect the number of two‐dimensional (2D) harmonics in additive colored noise based on the enhanced covariance matrix. We define an enhanced covariance matrix using the covariances of the observed signal. We get a special inherent relation between the number of 2D harmonics in additive colored noise and the eigenvalues of the enhanced covariance matrix, which can be used to detect the number of 2D harmonics in additive colored noise by analyzing the eigenvalues of the enhanced covariance matrix. The proposed method has a super resolution and does not need to assume the color and distribution of the additive noise. The effectiveness of the proposed method has been validated by both the theoretical analysis and extensive simulations. Copyright © 2012 John Wiley & Sons, Ltd.

Modified projection approach for robust adaptive array beamforming

A novel modified projection method is proposed in this paper, which is robust against the signal steering vector mismatch and covariance matrix uncertainty. First, an enhanced covariance matrix estimate based on a shrinkage method is obtained. Then, the desired signal subspace is estimated from the eigenvectors of the enhanced covariance matrix, and a calibrated steering vector of the desired signal is obtained in sequence by projecting the presumed one onto the new estimated desired signal subspace. Finally, the robust adaptive beamformer weight is obtained from the estimated covariance matrix and the calibrated steering vector. Compared with the traditional projection method, the proposed method can work well even at low signal-to-noise ratio. Also, it is not necessary to estimate the number of sources. Simulation results demonstrate the efficiency of the proposed robust method compared with some of the existing ones.

Fully Automatic Computation of Diagonal Loading Levels for Robust Adaptive Beamforming

The main drawback of the conventional diagonal loading (DL) approaches is that there is no clear guideline on how to choose the DL level reliably or how to select user parameters appropriately. An algorithm that can be used to compute the DL level completely automatically from the given data without the need of specifying any user parameter is considered. In this algorithm an enhanced covariance matrix estimate obtained via a shrinkage method, instead of the sample covariance matrix, is used in the standard Capon beamforming formulation. The performance of the resulting beamformer is illustrated via numerical examples, and it is compared with several other adaptive beamformers.

Risk evaluation with enhanced covariance matrix

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a ‘potential’ or ‘objective’ function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distributions. The method is tested using historical data from both the New York and Warsaw stock exchanges.