A convex optimization approach to the rational covariance extension problem

SIAM Journal on Control and Optimization

Volumn 37, Issue 1, 1999, Pages 211-229

  Byrnes, Christopher I ^a   Gusev, Sergei V ^b   Lindquist, Anders ^c  

^a WASHINGTON UNIVERSITY   (United States)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^c ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Partial stochastic realization; Rational covariance: Extension; Spectral estimation; Speech processing; Stochastic modeling; Trigonometric moment problem

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBLEM SOLVING; SPEECH PROCESSING;

PARTIAL STOCHASTIC REALIZATION; RATIONAL COVARIANCE EXTENSION; SPECTRAL ESTIMATION; TRIGONOMETRIC MOMENT PROBLEM;

OPTIMIZATION;

EID: 0032154818     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012997321553     Document Type: Article

References (32)

1. N. I. AKHIEZER, The Classical Moment Problem and Some Related Questions in Analysis, Hafner Publishing, New York, 1965.
2. M. AOKI, State Space Modeling of Time Series, Springer-Verlag, Berlin, 1987.
3. C. G. BELL, H. FUJISAKI, J. M. HEINZ, K. N. STEVENS, AND A. S. HOUSE, Reduction of speech spectra by analysis-by-synthesis techniques, J. Acoust. Soc. Amer., 33 (1961), pp. 1725-1736.
4. C. I. BYRNES AND A. LINDQUIST, On the geometry of the Kimura-Georgiou parameterization of modelling filter, Internat. J. Control, 50 (1989), pp. 2301-2312.
5. C. I. BYRNES AND A. LINDQUIST, Toward a solution of the minimal partial stochastic realization problem, C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 1231-1236.
6. C. I. BYRNES AND A. LINDQUIST, On the partial stochastic realization problem, IEEE Trans. Automat. Control, AC-42 (1997), pp. 1049-1070.
7. C. I. BYRNES, A. LINDQUIST, S. V. GUSEV, AND A. S. MATEEV, A complete parametrization of all positive rational extensions of a covariance sequence, IEEE Trans. Automat. Control, AC-40 (1995), pp. 1841-1857.
8. J. A. CADZOW, Spectral estimation: An overdetermined rational model equation approach, Proc. IEEE, 70 (1982), pp. 907-939.
9. C. CARATHÉODORY, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann., 64 (1907), pp. 95-115.
10. C. CARATHÉODORY, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Functionen, Rend. Circ. Mat. Palermo (2), 32 (1911), pp. 193-217.
11. P. DELSARTE, Y. GENIN, Y. KAMP, AND P. VAN DOOREN, Speech modelling and the trigonometric moment problem, Philips J. Res., 37 (1982), pp. 277-292.
12. P. ENQVIST, forthcoming Ph.D. dissertation, Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden.
13. T. T. GEORGIOU, Partial Realization of Covariance Sequences, Ph.D. thesis, Center for Mathematical Systems Theory, University of Florida, Gainesville, FL, 1983.
14. T. T. GEORGIOU, Realization of power spectra from partial covariance sequences, IEEE Trans. Acoust. Speech Signal Process., ASSP-35 (1987), pp. 438-449.
15. Y. L. GERONIMUS, Orthogonal Polynomials, Consultants Bureau, New York, 1961.
16. U. GRENANDER AND G. SZEGÖ, Toeplitz Forms and Their Applications, University of California Press, Berkeley, CA, 1958.
17. U. GRENANDER AND M. ROSENBLATT, Statistical Analysis of Stationary Time Series, Almqvist & Wiksell, Stockholm, 1956.
18. R. E. KALMAN, Realization of covariance sequences, in Proc. Toeplitz Centennial, Tel Aviv, Israel, 1981, Oper. Theory Adv. Appl. 4, Birkhäuser, Basel, 1982, pp. 331-342.
19. S. A. KASSAM AND H. V. POOR, Robust techniques for signal processing, Proc. IEEE, 73 (1985), pp. 433-481.
20. S. M. KAY AND S. L. MARPLE, JR., Spectrum analysis - A modern perspective, Proc. IEEE, 69 (1981), pp. 1380-1419.
21. H. KIMURA, Positive partial realization of covariance sequences, in Modelling, Identification and Robust Control, C. I. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam, 1987, pp. 499-513.
22. A. LINDQUIST AND G. PICCI, Canonical correlation analysis, approximate covariance extension, and identification of stationary time series, Automatica J. IFAC, 32 (1996), pp. 709-733.
23. D. G. LUENBERGER, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, Reading, MA, 1984.
24. J. D. MARKEL AND A. H. GRAY, Linear Prediction of Speech, Springer-Verlag, Berlin, 1976.
25. J. MAKHOUL, Linear prediction: A tutorial review, Proc. IEEE, 63 (1975), pp. 561-580.
26. M. MINOUX, JR., Mathematical Programming: Theory and Algorithms, John Wiley, New York, 1986.
27. B. PORAT, Digital Processing of Random Signals, Prentice-Hall, Englewood Cliffs, NJ, 1994.
28. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
29. L. R. RABINER AND R. W. SCHAFER, Digital Processing of Speech Signals, Prentice-Hall, Englewood Cliffs, NJ, 1978.
30. I. SCHUR, On power series which are bounded in the interior of the unit circle I and II, J. Reine Angew. Math., 148 (1918), pp. 122-145.
31. O. TOEPLITZ, Über die Fouriersche Entwicklung positiver Funktionen, Rend. Circ. Mat. Palermo (2), 32 (1911), pp. 191-192.
32. P. VAN OVERSCHEE AND B. DE MOOR, Subspace algorithms for stochastic identification problem, IEEE Trans. Automat. Control, AC-27 (1982), pp. 382-387.