Cross Entropy Approximation of Structured Gaussian Covariance Matrices

@article{Liou2008CrossEA,
  title={Cross Entropy Approximation of Structured Gaussian Covariance Matrices},
  author={Cheng-Yuan Liou and Bruce R. Musicus},
  journal={IEEE Transactions on Signal Processing},
  year={2008},
  volume={56},
  pages={3362-3367}
}
  • C. Liou, B. Musicus
  • Published 1 July 2008
  • Computer Science
  • IEEE Transactions on Signal Processing
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References

SHOWING 1-10 OF 23 REFERENCES
A separable cross-entropy approach to power spectral estimation
TLDR
An approach to power spectrum estimation that is based on a separable cross-entropy modeling procedure that is a generalized version of Capon's maximum-likelihood method and a spectral estimation algorithm that is similar to classical windowing methods is presented.
Effects of estimated noise covariance matrix in optimal signal detection
TLDR
An exact confidence bound is obtained for the realized signal-to-noise ratio which is useful in optimum selection of features in the case of detecting a single signal specified by a real or a complex vector.
Iterative algorithms for optimal signal reconstruction and parameter identification given noisy and incomplete data
We present a new approach to the problem of estimating multiple signal and parameter unknowns given noisy and incomplete data. Using cross-entropy, we fit a separable density to the given model
Estimation of structured covariances with application to array beamforming
The estimation of covariance matrices which are structured, for example, of Toeplitz type, from measurement data is considered. The problem is considered in the context of array beamforming, and
Estimation of structured covariance matrices
TLDR
An iterative algorithm that solves the necessary gradient equations for moderate-sized problems with reasonable computational ease is presented and theoretical convergence properties of the basic algorithm are investigated and robust modifications discussed.
On the uniqueness of the maximum-likeliwood estimate of structured covariance matrices
A generalized Burg technique has been developed recently by Burg, Luenberger, and Wenger for maximum likelihood estimation of structured covariance matrices. Uniqueness of the estimate in the
Expectations of useful complex Wishart forms
TLDR
This paper derives concise formulas for E{WAW},E{W−1AW−1}, and other useful expressions, whereW follows the complex Wishart distribution andA is a deterministic matrix, which need not be symmetric.
A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments
TLDR
Two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate.
Multiple emitter location and signal Parameter estimation
TLDR
The multiple signal classification (MUSIC) algorithm is described, which provides asymptotically unbiased estimates of number of incident wavefronts present and directions of arrival (DOA) (or emitter locations) and strengths and cross correlations among the incident waveforms.
Detection of signals by information theoretic criteria
  • M. Wax, T. Kailath
  • Computer Science
    IEEE Trans. Acoust. Speech Signal Process.
  • 1985
TLDR
Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.
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3
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