Multidimensional Gaussian probability density and its applications in the degenerate case

We obtain an analytical expression for the probability density of the Gaussian vector with a degenerate covariance matrix. The expression generalizes a similar expression for the nondegenerate case. A definition of the Gaussian vector on the basis of a probability density, which is common for the de...

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Bibliographic Details
Published in:Radiophysics and quantum electronics 2006-07, Vol.49 (7), p.564-571
Main Author: Mikheev, P V
Format: Article
Language:English
Subjects:
Algorithms
Density
Exact solutions
Gaussian
Mathematical analysis
Optimization
Probability
Quantum electronics
Synthesis
Vectors (mathematics)
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Summary:We obtain an analytical expression for the probability density of the Gaussian vector with a degenerate covariance matrix. The expression generalizes a similar expression for the nondegenerate case. A definition of the Gaussian vector on the basis of a probability density, which is common for the degenerate and nondegenerate cases, is given. Examples of using the obtained probability density for the synthesis of optimal signal-processing algorithms are presented.[PUBLICATION ABSTRACT]
ISSN:0033-8443
1573-9120
DOI:10.1007/s11141-006-0090-5