Performance Analysis of the Total Least Squares ESPRIT Algorithm

IEEE Transactions on Signal Processing

Volumn 39, Issue 5, 1991, Pages 1122-1135

  Ottersten, Björn ^a   Viberg, Mats ^a   Kailath, Thomas ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL TECHNIQUES - LEAST SQUARES APPROXIMATIONS; PROBABILITY - RANDOM PROCESSES;

ASYMPTOTIC ANALYSIS; CRAMER-RAO BOUND; SENSORS ARRAY; SIGNAL SUBSPACE METHODS; TOTAL LEAST SQUARES ESPRIT ALGORITHM; UNIFORM LINEAR ARRAYS;

SIGNAL PROCESSING;

EID: 0026153178     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.80967     Document Type: Article

References (36)

1. R. Roy, A. Paulraj, and T. Kailath, “ESPRIT—A subspace rotation approach to estimation of parameters of cisoids in noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, no. 4, pp. 1340-1342, Oct. 1986.
2. V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. Roy. Astron. Soc, vol. 33, pp. 347-366, 1973.
3. R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” in Proc. RADC Spectrum Estimation Workshop (Rome, NY), 1979, pp. 243-258.
4. G. Bienvenu and L. Kopp, “Principle de la goniometrie passive adaptive,” in Proc. 7'eme Colloque GRESIT (Nice, France), 1979, pp. 106/1-106/10.
5. A. Paulraj, R. Roy, and T. Kailath, “Estimation of signal parameters via rotational invariance techniques—ESPRIT,” in Proc. Nineteenth Asilomar Conf. Circuits, Syst., Comput. (Asilomar, CA), Nov. 1985.
6. A. Paulraj, R. Roy, and T. Kailath, “A subspace rotation approach to signal parameter estimation,” Proc. IEEE, pp. 1044-1045, July 1986.
7. S. Mayrargue, “ESPRIT and TAM are theoretically equivalent,” in Proc. ICASSP 88 (New York, NY), Apr. 1988, pp. 2456-2459.
8. B. D. Rao and K. V. S. Hari, “Performance analysis of ESPRIT, minimum-norm method, and TAM in determining the direction of arrival of plane waves in noise,” Tech. Rep. DAAL-03-86-K-0107-0003, Univ. California, San Diego, CA, 1988; also IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 12. pp. 1990-1995, Dec. 1989.
9. R. H. Roy, “ESPRIT, estimation of signal parameters via rotational invariance techniques,” Ph.D. dissertation, Stanford Univ., Stanford, CA, Aug. 1987.
10. R. Roy and T. Kailath, “ESPRIT—estimation of signal parameters via rotational invariance techniques,” in Singular Value Decomposition and Signal Processing, Proceedings of the International Workshop on SVD and Signal Processing, E. F. Deprettere. Ed. (Les Houches, France), Sept. 21-23, 1987. Amsterdam, The Netherlands: NortH-Holland, 1987.
11. B. Ottersten and T. Kailath, ““Direction-of-arrival estimation for wideband signals using the ESPRIT algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 2, pp. 317-327, Feb. 1990.
12. R. Roy and T. Kailath, “ESPRIT—estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 7, pp. 984-995, July 1989.
13. R. Roy, B. Ottersten, L. Swindlehurst, and T. Kailath, “Multiple invariance ESPRIT,” in Proc. 22nd Asilomar Conf. Signals, Syst., Comput. (Asilomar, CA), Nov. 1988, pp. 583-587.
14. M. Viberg and B. Ottersten, “Sensor array processing based on subspace fitting,” IEEE Trans. Signal Processing, this issue, pp. 1110-1121.
15. B. Ottersten and M. Viberg, “Analysis of subspace fitting based methods for sensor array processing,” in Proc. ICASSP 89 (Glasgow, Scotland), May 1989, pp. 2807-2810.
16. T. W. Anderson, “Asymptotic theory for principal component analysis,” Ann. Math. Stat., vol. 34, pp. 122-148, 1963.
17. R. P. Gutpa, “Asymptotic theory for principal component analysis in the complex case,” J. Indian Stat. Assoc, vol. 3, pp. 97-106, 1965.
18. D. R. Brillinger, Time Series: Data Analysis and Theory, expanded ed. HoldeNDay, 1980.
19. D. J. Jeffries and D. R. Farrier, “Asymptotic results for eigenvector methods,” Proc. Inst. Elec. Eng., E, vol. 132, no. 7, pp. 589-594, June 1985.
20. M. Kaveh and A. J. Baraceli, “The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 331-341, Apr. 1986.
21. B. D. Rao and K. V. S. Hari, “Performance analysis of ESPRIT and TAM in determining the direction of arrival of plane waves in noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 12, pp. 1990-1995, Dec. 1989.
22. A. Swindlehurst and T. Kailath, “2-D parameter estimation using arrays with multidimensional invariance structure,” in Proc. 23nd Asilomar Conf. Signals, Syst., Comput. (Monterey, CA), Nov. 1989.
23. R. O. Schmidt, “A signal subspace approach to multiple emitter location and spectral estimation,” Ph.D. dissertation, Stanford Univ., Stanford, CA, Nov. 1981.
24. P. Stoica and A. Nehorai, “MUSIC, maximum likelihood and Cramér-Rao bound,” in Proc. ICASSP 88 Conf. (New York, NY), Apr. 1988, pp. 2296-2299.
25. M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, no. 2, pp. 387-392, Apr. 1985.
26. G. H. Golub and C. F. Van Loan, “An analysis of the total least squares problem,” SIAM J. Numer. Anal., vol. 17, pp. 883-893, 1980.
27. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins University Press, 1983.
28. T. J. Shan, M. Wax, and T. Kailath, “On spatial smoothing for direction-of-arrival estimation of coherent signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 806-811, Aug. 1985.
29. L. Ljung, System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, NJ, 1987.
30. A. Graham, Kronecker Products and Matrix Calculus with Applications. Chichester, U.K.: Ellis Horwood Ltd., 1981.
31. B. Ottersten and L. Ljung, “Asymptotic results for sensor array processing,” in Proc. ICASSP 89 (Glasgow, Scotland), May 1989, pp. 2266-2269.
32. W. J. Bangs, “Array processing with generalized beamformers,” Ph.D. dissertation, Yale Univ., New Haven, CT, 1971.
33. B. Porat and B. Friedlander, “Analysis of the asymptotic relative efficiency of the MUSIC algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 532-544, Apr. 1988.
34. B. D. Rao and K. V. S. Hari, “Performance analysis of Root-MU-SIC,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 12, pp. 1939-1949, Dec. 1989.
35. B. Ottersten, B. Wahlberg, M. Viberg, and T. Kailath, “Stochastic maximum likelihood estimation in sensor arrays by weighted subspace fitting,” in Proc. 23rd Asilomar Conf. Signals, Syst., Comput. (Monterey, CA), Nov. 1989.
36. M. Viberg, B. Ottersten, and T. Kailath, “Direction-of-arrival estimation and detection using weighted subspace fitting,” in Proc. 23rd Asilomar Conf. Signals, Syst., Comput., Nov. 1989.