A solution to linear estimation problems using approximate karhunen-loeve expansions

IEEE Transactions on Information Theory

Volumn 46, Issue 4, 2000, Pages 1677-1682

  Navarro Moreno, Jesus ^a   Ruiz Molina, Juan Carlos ^a   Valderrama, Mariano J ^b  

^a UNIVERSITY OF JAÉN   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Approximate karhunen loeve expansions; Linear least mean squared error estimation problems

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; ESTIMATION; PROBLEM SOLVING; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE;

KARHUNEN-LOEVE EXPANSION; LINEAR LEAST MEAN SQUARED ERROR;

SIGNAL FILTERING AND PREDICTION;

EID: 0034228446     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.850715     Document Type: Article

References (19)

1. T. T. Kadota, Optimum estimation of nonstationary Gaussian signal in noise, IEEE Trans. Inform. Theory, vol. IT-15, pp. 253-257, Mar. 1969.
2. W. A. Gardner and L. E. Franks, An alternative approach to linear least squares estimation of continuous random processes, in 5th Anna. Princeton Conf. Information Sciences and Systems, 1971.
3. T. E. Fortmann and B. D. O. Anderson, On the approximation of optimal realizable linear filters using a Karhunen-Loeve expansion, IEEE Trans. Inform. Theory, vol. IT-19, pp. 561-564, July 1973.
4. S. Cambanis, A general approach to linear mean-square estimation problems, IEEE Trans. Inform. Theory, vol. IT-19, pp. 110-114, Jan. 1973.
5. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1. New York: Wiley, 1968.
6. V. S. Pugachev, Theory of Random Functions. Reading, MA: AddisonWesley, 1965.
7. W. A. Gardner, A simple solution to smoothing, filtering, and prediction problems using series representations,"lEEETrans. Inform. Theory, vol. IT-20, pp. 271-274, Mar. 1974.
8. J. C. Ruiz-Molina and M. J. Valderrama, On the derivation of a suboptimal filter for signal estimation, Statist. Prob. Lett., vol. 28, pp. 239-243, 1996.
9. S. Watanabe, Karhunen-Loeve expansion and factor analysis. Theoretical remarks and applications, in Trans. 4h Prague Conf. Information Theory, 1965.
10. R. Gutiérrez, J. C. Ruiz-Molina, and M. J. Valderrama, On the numerical expansion of a second order stochastic process, Appl. Stochastic Models Data Anal., vol. 8, no. 2, pp. 67-77, 1992.
11. W. A. Gardner, On 'A general approach to linear mean-square estimation problems', IEEE Trans. Inform. Theory, vol. IT-19, p. 114, Jan. 1973.
12. V A. Segalescu, M. Zibulski, and Y. Y Zeevi, On the role of biorthonormality in representation of random processes, IEEE Trans. Inform. Theory, vol. 42, no. 1, pp. 288-290, 1996.
13. J. C. Ruiz-Molina, J. Navarro, and M. J. Valderrama, Differentiation of the modified approximative Karhunen-Loeve expansion of a stochastic process, Statist. Prob. Lett., vol. 42, pp. 91-98, 1999.
14. C. T. H. Baker, The Numerical Treatment of Integral Equations. Oxford, U.K.: Oxford Univ. Press, 1977.
15. C. W. Helstrom, Elements of Signal Detection & Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1995.
16. A. B. Baggeroer, State variable analysis procedures, in Detection, Estimation, and Modulation Theory. Part II, H. L. Van Trees, Ed. New York: Wiley, 1971, sec. Appendix A, pp. 286-327.
17. L. Ljung and T. Söderström, Theory and Practice of Recursive Estimation. Cambridge, MA: MIT Press, 1983.
18. T. Kailath, L. Ljung, and M. Morf, Recursive input-output and state-space solutions for continuous-time linear estimation problems, IEEE Trans. Automat. Contr., vol. AC-28, pp. 897-906, Sept. 1983.
19. J. C. Ruiz-Molina, J. Navarro-Moreno, and A. Oya, Signal detection using approximative Karhunen-Loeve expansions, IEEE Trans. Inform. Theory, 1999, submitted for publication.