Advertisement

Detection of Gaussian Signals in WGN

  • Bernard C. Levy
Chapter

Keywords

False Alarm Detection Problem Toeplitz Matrix Circulant Matrice Stationary Gaussian Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. C. Schweppe, “Evaluation of likelihood functions for Gaussian signals,” IEEE Trans. Informat. Theory, vol. 11, pp. 61–70, Jan. 1965.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    R. L. Stratonovich and Y. G. Sosulin, “Optimal detection of a diffusion process in white noise,” Radio Eng. Electron. Phys., vol. 10, pp. 704–713, June 1965.MathSciNetGoogle Scholar
  3. 3.
    A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Second Edition. New York: Springer Verlag, 1998.MATHGoogle Scholar
  4. 4.
    F. den Hollander, Large Deviations. Providence, RI: American Mathematical Soc., 2000.MATHGoogle Scholar
  5. 5.
    R. M. Gray, A. Buzo, A. H. Gray, Jr., and Y. Matsuyama, “Distortion measures for speech processing,” IEEE Trans. Acoust., Speech, Signal Proc., vol. 28, pp. 367–376, Aug. 1980.Google Scholar
  6. 6.
    B. C. Levy, R. Frezza, and A. J. Krener, “Modeling and estimation of discrete-time Gaussian reciprocal processes,” IEEE Trans. Automatic Control, vol. 35, pp. 1013–1023, Sept. 1990.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation. Upper Saddle River, NJ: Prentice Hall, 2000.Google Scholar
  8. 8.
    H. L. Weinert, Fixed Interval Smoothing for State Space Models. Boston, MA: Kluwer Publ., 2001.MATHGoogle Scholar
  9. 9.
    C. D. Greene and B. C. Levy, “Some new smoother implementations for discrete-time Gaussian reciprocal processes,” Int. J. Control, pp. 1233–1247, 1991.Google Scholar
  10. 10.
    T. Kailath, S. Kung, and M. Morf, “Displacement ranks of matrices and linear equations,” J. Math. Anal. and Appl., vol. 68, pp. 395–407, 1979.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    T. Kailath and A. H. Sayed, “Displacement structure: theory and applications,” SIAM Review, vol. 37, pp. 297–386, Sept. 1995.CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    M. H. Hayes, Statistical Digital Signal Processing and Modeling. New York: J. Wiley & Sons, 1996.Google Scholar
  13. 13.
    P. A. Ruymgaart and T. T. Soong, Mathematics of Kalman-Bucy Filtering, Second Edition. Berlin: Springer-Verlag, 1988.Google Scholar
  14. 14.
    E. Wong and B. Hajek, Stochastic Processes in Engineering Systems. New York: Springer-Verlag, 1985.MATHGoogle Scholar
  15. 15.
    L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. 2: Ito Calculus. Chichester, England: J. Wiley & Sons, 1987.Google Scholar
  16. 16.
    T. Kailath, “A general likelihood-ratio formula for random signals in Gaussian noise,” IEEE Trans. Informat. Theory, vol. 15, pp. 350–361, May 1969.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    T. Kailath and H. V. Poor, “Detection of stochastic processes,” IEEE Trans. Informat. Theory, vol. 44, pp. 2230–2259, Oct. 1998.CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Sixth Edition. Berlin: Springer Verlag, 2003.Google Scholar
  19. 19.
    R. M. Gray, “Toeplitz and circulant matrices: A review.” Technical report available on line at: http://www-ee.stanford.edu/ gray/toeplitz.html, Aug. 2005.Google Scholar
  20. 20.
    S.-I. Amari and H. Nagaoka, Methods of Information Geometry. Providence, RI: American Mathematical Soc., 2000.MATHGoogle Scholar
  21. 21.
    Y. Sung, L. Tong, and H. V. Poor, “Neyman-Pearson detection of Gauss-Markov signals in noise: closed form error exponent and properties,” IEEE Trans. Informat. Theory, vol. 52, pp. 1354–1365, Apr. 2006.CrossRefMathSciNetGoogle Scholar
  22. 22.
    R. Price, “Optimum detection of random signals in noise, with application to scatter-multipath communications, I,” IEEE Trans. Informat. Theory, vol. 2, pp. 125–135, Dec. 1956.CrossRefGoogle Scholar
  23. 23.
    D. Middleton, “On the detection of stochastic signals in additive normal noise– part I,” IEEE Trans. Informat. Theory, vol. 3, pp. 86–121, June 1957.CrossRefGoogle Scholar
  24. 24.
    L. A. Shepp, “Radon-Nikodym derivatives of Gaussian measures,” Annals Math. Stat., vol. 37, pp. 321–354, Apr. 1966.CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    T. E. Duncan, “Likelihood functions for stochastic signals in white noise,” Information and Control, vol. 16, pp. 303–310, June 1970.CrossRefMathSciNetGoogle Scholar
  26. 26.
    T. Kailath, “The innovations approach to detection and estimation theory,” Proc. IEEE, vol. 58, pp. 680–695, May 1970.Google Scholar
  27. 27.
    J. Coursol and D. Dacunha-Castelle, “Sur la formule de Chernoff pour deux processus Gaussiens stationnaires,” Comptes Rendus Académie des Sciences, Paris, vol. 288, pp. 769–770, May 1979.MATHMathSciNetGoogle Scholar
  28. 28.
    R. K. Bahr, “Asymptotic analysis of error probabilities for the nonzero-mean Gaussian hypothesis testing problem,” IEEE Trans. Informat. Theory, vol. 36, pp. 597–607, May 1990.CrossRefMATHMathSciNetGoogle Scholar
  29. 29.
    B. Porat and B. Friedlander, “Parametric techniques for adaptive detection of Gaussian signals,” IEEE Trans. Acoust., Speech, Signal Proc., vol. 32, pp. 780–790, Aug. 1984.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Bernard C. Levy
    • 1
  1. 1.University of CaliforniaDavisUSA

Personalised recommendations