Radiophysics and Quantum Electronics

, Volume 49, Issue 7, pp 564–571 | Cite as

Multidimensional Gaussian probability density and its applications in the degenerate case

  • P. V. Mikheev


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.


Probability Density Antenna Array Arrival Direction Conditional Probability Density Gaussian Vector 
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  1. 1.
    D. Middleton, An Introduction to Statistical Communication Theory, McGraw-Hill, New York (1960).zbMATHGoogle Scholar
  2. 2.
    S. Zacks, Theory of Statistical Inference, Wiley, New York (1971).zbMATHGoogle Scholar
  3. 3.
    V. P. Repin and G. P. Tartakovsky, Statistical Synthesis Under a Priori Uncertainty and Adaptation of Information Systems [in Russian], Sovetskoe Radio, Moscow (1977).Google Scholar
  4. 4.
    R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays, Wiley, New York (1980).Google Scholar
  5. 5.
    H. Cramér, Mathematical Methods of Statistics, Princeton Univ. Press, Princeton, NJ (1999).zbMATHGoogle Scholar
  6. 6.
    C. R. Rao, Linear Statistical Inference and its Applications, Wiley, New York (1973).zbMATHGoogle Scholar
  7. 7.
    V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Calculations [in Russian], Nauka, Moscow (1984).Google Scholar
  8. 8.
    V. I. Tikhonov, Statistical Radioengineering [in Russian], Radio i Svyaz’, Moscow (1982).Google Scholar
  9. 9.
    V. V. Voevodin, Linear Algebra [in Russian], Nauka, Moscow (1980).Google Scholar
  10. 10.
    H. Bremermann, Distributions, Complex Variables, and Fourier Transforms, Addison-Wesley, Reading, Ma (1965).zbMATHGoogle Scholar
  11. 11.
    S. L. Marple, Jr., Digital Spectral Analysis; With Applications, Prentice-Hall, Englewood Cliffs, NJ (1987).Google Scholar
  12. 12.
    F. R. Gantmacher, The theory of Matrices, Vols. 1 and 2, Chelsea, New York(1959).zbMATHGoogle Scholar
  13. 13.
    P. Lancaster, Theory of Matrices, Academic Press, New York (1969).zbMATHGoogle Scholar
  14. 14.
    G. A. F. Seber, Linear Regression Analysis, Wiley, New York (1977).zbMATHGoogle Scholar
  15. 15.
    F. R. Gantmacher and V. N. Manzhos, Theory and Techniques of Radar Information Processing against the Noise Background[in Russian], Radio i Svyaz’, Moscow (1981).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • P. V. Mikheev
    • 1
  1. 1.Nizhny Novgorod Research Institute of RadioengineeringNizhny NovgorodRussia

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