The extended least squares criterion: minimization algorithms and applications

IEEE Transactions on Signal Processing

Volumn 49, Issue 1, 2001, Pages 74-86

  Yeredor, Arie ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Ar modeling; Arx system identification; Constrained total least squares (ctls); Extended least squares (xls); Least squares; Structured total least squares (stls); Total least squares (tls)

Indexed keywords

AUTOREGRESSIVE (AR) METHODS; EXTENDED LEAST SQUARES (XLS) CRITERION;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; LEAST SQUARES APPROXIMATIONS; REGRESSION ANALYSIS;

DIGITAL SIGNAL PROCESSING;

EID: 0035123916     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.890344     Document Type: Article

References (32)

1. G. H. Golub and C. F. Van Loan, "An analysis of the total least squares problem," SIAM J. Numer. Anal., vol. 17, no. 4, pp. 883-893, 1979.
2. Matrix Computations, 2nd ed. Baltimore, MD: John Hopkins Univ. Press, 1989.
3. S. Van Huffei and J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis, Frontiers in Applied Mathematics Series. Philadelphia, PA: SIAM, 1991, vol. 9.
4. D. Tufts, R. Kumaresan, and I. Kirsteins, "Data adaptive signal estimation by singular value decomposition of a data matrix," P roc. IEEE, vol. 70, pp. 684-685, 1982.
5. T. J. Abatzoglou and J. M. Mendel, "Constrained total least squares," in Proc. ICASSP, 1987, pp. 1485-1488.
6. Y. Hua and T. P. Sarkar, "On the total least squares linear prediction method for frequency estimation," IEEE Trans. AcousL, Speech, Signal Processing, vol. 38, pp. 2186-2189, 1990.
7. T. J. Abatzoglou, J. M. Mendel, and G. A. Harada, "The constrained total least squares technique and its application to harmonic superresolution," IEEE Trans. Signal Processing, vol. 39, pp. 1070-1087, 1991.
8. S. Van Huffel, "Enhanced resolution based on minimum variance estimation and exponential data modeling," Signal Process., vol. 33, no. 3, pp. 333-355, 1993.
9. B. De Moor, "Total least squares for affinely structured matrices and the noisy realization problem," IEEE Trans. Signal Processing, vol. 42, pp. 3104-3113, Nov. 1994.
10. K. Steiglitz and L. E. NcBride, "Techniques for the identification of linear systems," IEEE Trans. Automat. Contr., vol. AC10, pp. 461164, 1965.
11. Y. Bresler and A. Macovski, "Exact maximum likelihood parameter estimation of superimposed exponential signals in noise," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP34, pp. 1081-1089, Aug. 1986.
12. J. H. McClellan and D. Lee, "Exact equivalence of the Steiglitz-McBride iteration and IQML," IEEE Trans. Signal Processing, vol. 39, pp. 509-512, Feb. 1991.
13. P. Lemmerling, B. De Moor, and S. Van Huffel, "On the equivalence of constrained total least squares and structured total least squares," IEEE Trams. Signal Processing, vol. 44, pp. 2908-2911, Nov. 1996.
14. J. A. Cadzow and D. M. Wilkes, "Enhanced sinusoidal and exponential modeling," SVD Signal Process. II: Algorithms, Anal., Applicat., pp. 335-352, 1991.
15. J. A. Cadzow and D. M. Wilkes, "Constrained total least squares: Signal and system modeling," in Proc. ICASSP, vol. 5, 1992, pp. 277-280.
16. J. A. Cadzow, "Total least squares, matrix enhancement, and signal processing," Digital Signal Process., vol. 4, pp. 21-39, 1994.
17. B. De Moor, "Structured total least squares and L2 approximation problems," Linear Algebra Applicat., Special Issue on Numerical Linear Algebra Methods in Control, Signals, Systems, vol. 188/189, pp. 163-205, 1993.
18. P. Lemmerling, "Structured total least squares: analysis, algorithms and applications," Ph.D. dissertation, Dept. Elect. Eng., Katholieke Univ., Leuven, Belgium, 1999.
19. L. Ljung, System Identification. Englewood Cliffs, NJ: Prentice-Hall, 1987.
20. W. A. Fuller, Measurement Error Models. New York: Wiley, 1987.
21. J. S. Lim and A. V Oppenheim, "All-pole modeling of degraded speech," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP26, pp. 197-210, Mar. 1978.
22. B. De Moor and P. Lemmerling, "A new trade-off in linear system identification: Misfit versus latency," in Proc. MTNS, Padova, Italy, 1998.
23. A. Yeredor, "The extended least squares criterion for discriminating measurement errors from model errors: Algorithms, applications, analysis," Ph.D. dissertation, Tel-Aviv University, Tel-Aviv, Israel, Fac. Eng., Dept. Elect. Eng.-Systems, 1997.
24. A. Yeredor and E. Weinstein, "The extended least squares and the joint maximum a posteriori-maximum likelihood estimation criteria," in Proc. ICASSP, vol. 4, Phoenix, AZ, USA, 1999, pp. 1813-1816.
25. A. Yeredor, "The joint MAP - ML estimation criterion and its relation to ML and to extended least squares," IEEE Trans. Signal Processing, vol. 48, pp. 3484-3492, Dec. 2000.
26. J. A. Cadzow, "Signal enhancement: A composite property mapping algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 49-62, Jan. 1988.
27. E. M. Dowling, R. D. DeGroat, and D. A. Linebarger, "Total least squares with linear constrains," in Proc. ICASSP, vol. 5, 1992, pp. 341-344.
28. "Exponential parameter estimation in the presence of known components and noise," IEEE Trans. Antennas Propagat., vol. 42, pp. 590-599, May 1994.
29. H. Chen, S. Van Huffel, D. Van Ordmondt, and R. De Beer, "Parameter estimation with prior knowledge of known signal poles for the quantification of NMR spectroscopy data in the time domain," J. Magn. Reson. A, vol. 119, pp. 225-234, 1996.
30. H. Chen, S. Van Huffel, and J. Vandewalle, "Improved methods for exponential parameter estimation in the presence of known poles and noise," IEEE Trans. Signal Processing, vol. 45, pp. 1390-1393, May 1997.
31. S. Van Huffel and H. Zha, "The restricted total least squares problem: Formulation, algorithms and properties," SIAM J. Matrix Anal. Appl., vol. 12, pp. 292-309, 1991.
32. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," Ann. R. Stat. Soc., vol. Ser.3g, pp. 1-38, 1977.