Subspace-Based Signal Analysis Using Singular Value Decomposition

Proceedings of the IEEE

Volumn 81, Issue 9, 1993, Pages 1277-1308

  Van Der Veen, Alle Jan ^a   Deprettere, Ed F ^a   Swindlehurst, A Lee ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS); SPURIOUS SIGNAL NOISE; TIME SERIES ANALYSIS; TIME VARYING SYSTEMS;

DIRECTION OF ARRIVAL PROBLEM; SIGNAL ANALYSIS; SINGULAR VALUE DECOMPOSITION; SUBSPACE ORIENTED SCHEME;

SIGNAL PROCESSING;

EID: 0027665717     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.237536     Document Type: Article

References (137)

1. L. Ljung, System Identification — Theory for the User. Englewood Cliffs, NJ: Prentice Hall, 1987.
2. T. Söderstrom and P. Stoica, System Identification. Englewood Cliffs, NJ: Prentice Hall, Inc., 1989.
3. L. Ljung and T. Söderström, Theory and Practice of Recursive Identification. Cambridge, MA: MIT Press, 1983.
4. L. L. Scharf, “The SVD and reduced-rank signal processing,” in SVD and Signal Processing, II: Algorithms, Analysis and Applications, R. J. Vaccaro, Ed. New York: Elsevier, 1991, 3–31.
5. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1991.
6. D.V. Bhaskar Rao and K.S. Arun, “Model based processing of signals: A state space approach,” Proc. IEEE, vol. 80, pp. 283–309, Feb. 1992.
7. A. Nerode, “Linear automaton transformations,” Proc. Amer. Math. Soc., vol. 9, pp. 541–544, 1958.
8. B. L. Ho and R. E. Kalman, “Effective construction of linear, state-variable models from input/output functions,” Regelungs-technik, vol. 14, 545–548, 1966.
9. H. P. Zeiger and A. J. McEwen, “Approximate linear realizations of given dimension via Ho’s algorithm,” IEEE Trans. Automat. Cont., vol. AC-19, p. 153, Apr. 1974.
10. B. C. Moore, “Singular value analysis of linear systems,” in Proc. IEEE Dec. Control, 1979, 66–73.
11. S. Y. Kung, “A new identification and model reduction algorithm via singular value decomposition,” in 12th Asilomar Conf. on Circuits, Systems and Comp.(Asilomar, CA), Nov. 1978, pp. 705–714.
12. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice Hall, 1980.
13. W. J. Rugh, Linear System Theory. A Graduate Course. Englewood Cliffs, NJ: Prentice Hall, 1992.
14. P. R. Halmos, Introduction to Hilbert Space. New York: Chelsea Pub. Co., 1951.
15. G. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1984.
16. R. E. Kalman, P. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory (Int. Series in Pure and Applied Math-ematics). New York: McGraw-Hill, 1970.
17. P. A. Fuhrmann, Linear Systems and Operators in Hilbert Space. New York: McGraw-Hill, 1981.
18. A. J. van der Veen and P. M. Dewilde, “Time-varying system theory for computational networks,” in Algorithms and Parallel VLSI Architectures, II, P. Quinton and Y. Robert, Eds. New York: Elsevier, 1991, pp. 103–127.
19. A. J. van der Veen and P. M. Dewilde, “Time-varying computational networks: Realization, orthogonal embedding and structural factorization,” in Proc. SPIE, “Advanced Signal Processing Algorithms, Architectures, and Implementations,” III, F. T. Luk, Ed., vol. 1770, pp. 164–177, 1992.
20. A. Feintuch and R. Saeks, System Theory: A Hilbert Space Approach. New York: Academic Press, 1982.
21. E. W. Kamen, P. P. Khargonekar, and K. R. Poolla, “A transfer-function approach to linear time-varying discrete-time systems,” SIAM J. Contr. Optimization, vol. 23, no. 4, pp. 550–565, 1985.
22. E. W. Kamen, “The poles and zeros of a linear time-varying system,” Lin. Alg. Applications, vol. 98, pp. 263–289, 1988.
23. B. D. O. Anderson and J. B. Moore, “Detectability and stabilizability of time-varying discrete-time linear systems,” SIAM J. Contr. Optimization, vol. 19, no. 1, pp. 20–32, 1981.
24. I. Gohberg, M. A. Kaashoek, and L. Lerer, “Minimality and realization of discrete time-varying systems,” in Time Variant Systems and Interpolation, I. Gohberg, Ed., vol. OT 56. Basel, Switzerland: Birkhäuser Verlag, 1992, pp. 261–296.
25. B. De Moor, “Mathematical concepts and techniques for modeling of static and dynamic systems,” Ph.D. dissertation, Kath. Univ. Leuven, Belgium, 1988.
26. M. Verhaegen and E. F. Deprettere, “Subspace model identification,” in Algorithms and Parallel VLSI Architectures, vol. B, E. F. Deprettere and A. J. van der Veen, Eds. New York: Elsevier, 1991, 13–32.
27. M. Verhaegen and P. M. Dewilde, “Subspace model identification. Part 1: The output error state space model identification class of algorithms,” Int. J. Contr., vol. 56, no. 5, pp. 1187–1210, 1992.
28. M. Verhaegen and P. M. Dewilde, “Subspace model identification. Part 2: Analysis of the elementary output-error state-space model identification algorithm,” Int. J. Contr., vol. 56, no. 5, pp. 1211–1241, 1992.
29. B. De Moor, M. Moonen, L. Vandenberghe, and J. Vandewalle, “A geometrical approach for the identification of state space models with singular value decomposition,” in Proc. IEEE ICASSP (New York, NY), vol. 4, 1988, pp. 2244–2247.
30. M. Moonen, B. De Moor, L. Vandenberghe, and J. Vandewalle, “On- and off-line identification of linear state-space models,” Int. J. Contr., vol. 49, no. 1, pp. 219–232, 1989.
31. M. Moonen and J. Vandewalle, “QSVD approach to on- and off-line state space identification,” Int.J. Contr., vol. 50, no. 1, pp. 1133–1146, 1990.
32. P. Van Overschee, B. De Moor, and J. Suykens, “Subspace algorithms for system identification and stochastic realization,” in Recent Advances in Mathematical Theory of Systems, Control, Networks and Signal Processing (Proc. Int. Symp. MTNS-91), vol. I, H. Kimura and S. Kodama, Eds. MITA Press, Japan, 1992, pp. 589–594.
33. P. Van Overschee and B. De Moor, “Two subspace algorithms for the identification of combined deterministic and deterministic-stochastic systems,” in Proc.IEEE Conf.on Decision Control (Tucson, AZ), Dec. 1992, pp.511–516.(Also to appear in Automatica (Special Issue on Statistical Signal Processing and Control).
34. 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. 5, pp. 1340–1342, 1986.
35. R. Roy, “ESPRIT,” Ph.D. dissertation, Stanford Univ., Stanford, CA, 1987.
36. R. Roy and T. Kailath, “ESPRIT— Estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 984–995, July 1989.
37. Y. Bresler and A. Macovski, “On the number of signals resolvable by a uniform linear array,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1361–1375, Dec. 1986.
38. M. Wax and I. Ziskind, “On unique localization of multiple sources by passive sensor arrays,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 996–1000, July 1989.
39. R. Prony, “Essai experimental et analytique sur les lois de la dilabilite des fluides elastiques.,” J.de I'Ecole Polytechnique, vol. 1, no.2, pp. 24–76, 1795.
40. E. F. Deprettere, Ed., SVD and Signal Processing: Algorithms, Applications and Architectures. Amsterdam, The Netherlands: North-Holland, 1988.
41. R. J. Vaccaro, Ed., SVD and Signal Processing, II: Algorithms, Analysis and Applications. New York: Elsevier, 1991.
42. G. W. Stewart, “Perturbation theory for the singular value decomposition,” in SVD and Signal Processing, II: Algorithms, Analysis and Applications, R. J. Vaccaro, Ed. New York: Elsevier, 1991, pp. 99–109.
43. F. Li and R. J. Vaccaro, “Performance degradation of DOA estimators due to unknown noise fields,” IEEE Trans. Signal Processing, vol. 40, pp. 686–690, Mar. 1992.
44. M. S. Bartlett, “Tests of significance in factor analysis,” British J. Psych. (Statist. Sect.), vol. 3, pp. 77–85, 1950.
45. M. S. Bartlett, “A note on the multiplying factors for various x2approximations,” J. Roy. Statist. Soc., Ser. B, vol. 16, pp. 296–298, 1954.
46. T. W. Anderson, “Asymptotic theory for principal component analysis,” Ann. Math. Statist., vol. 34, pp. 122–148, 1963.
47. H. Akaike, “Information theory and an extension of the Maximum Likelihood principle,” in Proc. 2nd Int. Symp. on Information Theory, 1973, pp. 267–281.
48. J. Rissanen, “Modeling by shortest data description,” Automat-ica, vol. 14, pp. 465–471, 1978.
49. J. Rissanen, “A universal prior for the integers and estimation by Minimum Description Length,” Annals Statist., vol. 11, pp. 417–431, 1983.
50. L. C. Zhao, P. R. Krishnaiah, and Z. D. Bai, “On the detection of the number of signals when the noise covariance matrix is arbitrary,” J. Multivariate Anal., vol. 20, no. 1, pp. 1–25, 1986.
51. R. O. Schmidt, “A signal subspace approach to multiple emitter location and spectral estimation,” Ph.D. dissertation, Stanford University, Stanford, CA, 1981.
52. M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 387–392, Apr. 1985.
53. M. Viberg, B. Ottersten, and T. Kailath, “Detection and estimation in sensor arrays using weighted subspace fitting,” IEEE Trans. Signal Processing, vol. 39, pp. 2436–2449, Nov. 1991.
54. M. Wax and I. Ziskind, “Detection of the number of coherent signals by the MDL principle,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 1190–1196, Aug. 1989.
55. M. Wax, “Detection and localization of multiple sources via the stochastic signals model,” IEEE Trans. Signal Processing, vol. 39, pp. 2450–2456, Nov. 1991.
56. S. Van Huffel and J. Vandewalle, The Total Least Squares problem: Computational Aspects and Analysis. Philadelphia, PA: SIAM, 1991.
57. B. C. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 17–32, Feb. 1981.
58. L. Pernebo and L. M. Silverman, “Balanced systems and model reduction,” in Proc. IEEE Conf. Dec. Control, 1979, pp. 865–867.
59. S. Y. Kung and D. W. Lin, “Recent progress in linear system model-reduction via Hankel matrix approximation,” in Proc. ECCTD Circuit Theory and Design, (The Hague), 1981, pp. 222–233.
60. S. Y. Kung, K. S. Arun, and D. V. Bhaskar Rao, “State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem,” J. Opt. Soc. Amer., vol. 73, pp. 1799–1811, Dec. 1983.
61. S. Y. Kung, C. K. Lo, and R. Foka, “A Toeplitz approximation approach to coherent source direction finding,” in Proc. IEEE ICASSP, 1986, pp. 193–196.
62. S. Mayrargue, “ESPRIT and TAM (Toeplitz approximation method) are theoretically equivalent,” in Proc. IEEE ICASSP, vol. 4 (New York), 1988, pp. 2456–2459.
63. S. Mayrargue and J. P. Jouveau, “A new application of SVD to harmonic retrieval,” in SVD and Signal Processing, E. F. Deprettere, Ed. Amsterdam, The Netherlands: North-Holland, 1988, pp. 467–472.
64. D. V. Bhaskar 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. AcoustSpeech, Signal Processing, vol. 37, pp. 1990–1995, Dec. 1989.
65. D. V. Bhaskar Rao, “Relationship between matrix pencil and state space based harmonic retrieval methods,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 177–179, Jan. 1990.
66. H. Ouibrahim, D. D. Weiner, and T. K. Sarkar, “A general approach to direction finding,” in Proc. IEEE MILCON, 1986, pp. 41.4.1-41.4.5.
67. Y. Hua and T. K. Sarkar, “Matrix pencil method and its performance,” in Proc. IEEE ICASSP, 1988, pp. 2476–2479.
68. Y. Hua and T. K. Sarkar, “Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 814–824, May 1990.
69. M. Moonen, P. Van Dooren, and J. Vandewalle, “An SVD updating algorithm for subspace tracking,” SIAMJ. Matrix Anal. Appl., vol. 13, no. 4, 1992.
70. M. Moonen, F. Van Poucke, and E. Deprettere, “Parallel and adaptive high resolution direction finding,” in Proc. SPIE: Advanced Signal Processing Algorithms, Architectures and Implementations III, F. Luk, Ed., 1992, pp. 219–230.
71. M. D. Zoltowski and D. Stavrinides, “Sensor array signal processing via a Procrustus rotations based eigenanalysis of the ESPRIT data pencil,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 832–861, June 1989.
72. Y. Hua and T. K. Sarkar, “On SVD for estimating generalized eigenvalues of singular matrix pencil in noise,” IEEE Trans. Signal Processing, vol. 39, pp. 892–900, Apr. 1991.
73. Y. T. Chan and R. P. Langford, “Spectral estimation via the high-order Yule-Walker equations,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 689–698, Oct. 1982.
74. P. Stoica, R. L. Moses, T. Söderström, and J. Li, “Optimal high-order Yule-Walker estimation of sinusoidal frequencies,” IEEE Trans. Signal Processing, vol. 39, pp. 1360–1368, June 1991.
75. V. M. Adamjan, D. Z. Arov, and M. G. Krein, “Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem,” Mat. USSR Sbornik, vol. 15, no. 1, pp. 31–73, 1971.
76. M. Bouvet and H. Clergeot, “Eigen- and singular value decomposition techniques for the solution of harmonic retrieval problems,” in SVD and Signal Processing, E. F. Deprettere, Ed. Amsterdam, The Netherlands: North-Holland, 1988.
77. V. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. Roy. Astron. Soc., vol. 33, pp. 347–366, 1973.
78. R. Kumaresan and D. W. Tufts, “Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 833–840, Dec. 1982.
79. D. W. Tufts and R. Kumaresan, “Estimation of frequencies of multiple sinusoids: Making Linear Prediction perform like Maximum Likelihood,” Proc. IEEE, vol. 70, pp. 975–989, Sept. 1982.
80. R. Kumaresan, “On the zeros of the Linear Prediction-error filter for deterministic signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 217–220, Feb. 1983.
81. B. Porat and B. Friedlander, “On the accuracy of the Kumarsean-Tufts method for estimating complex damped exponentials,” IEEE Trans. Acoust., Speech, Signal Processing, voi. ASSP-35, pp. 231–235, Feb. 1987.
82. F. Li, R. J. Vaccaro, and D. W. Tufts, “Min-Norm Linear Prediction for arbitrary sensor arrays,” in Proc. IEEE ICASSP (Glasgow), May 1989, pp. 2613–2616.
83. D. W. Tufts, R. J. Vaccaro, and A. C. Kot, “Analysis of estimation of signal parameters by Linear Prediction at high SNR using matrix approximations,” in Proc. IEEE ICASSP (Glasgow), May 1989, pp. 2194–2197.
84. E. M. Dowling and R. D. DeGroat, “The equivalence of the Total Least Squares and Minimum Norm methods,” IEEE Trans. Signal Processing, vol. 39, pp. 1891–1892, Aug. 1991.
85. G. Cybenko, “Locations of zeros of predictor polynomials,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, no. 1, pp. 235–237, 1982.
86. A.Bultheel, “Recursive rational approximation,” Ph.D.dissertation, Catholic University Louvain, Louvain, Belgium, 1979.
87. K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems,” Int. J. Contr., vol. 39, no. 6, pp. 1115–1193, 1984.
88. Y. V. Genin and S. Y. Kung, “A two-variable approach to the model reduction problem with Hankel norm criterion,” IEEE Trans. Circuits Syst., vol. CAS-28, 912–924, Sept. 1981.
89. Ph. Delsarte, Y. Genin, and Y. Kamp, “On the role of the Nevanlinna-Pick problem in circuit theory and design,” Circuit Theory Appl., vol. 9, pp. 177–187, 1981.
90. M. H. Gutknecht, J. O. Smith, and L. N. Trefethen, “The Carathéodory-Fejér method for recursive digital filter design,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 1417–1426, Dec. 1983.
91. P. M. Dewilde and E. F. Deprettere, “Singular value decomposition: an introduction,” in SVD and Signal Processing, E. F. Deprettere, Ed. Amsterdam, The Netherlands: North-Holland, 1988, pp. 3–41.
92. L. M. Silverman and M. Bettayeb, “Optimal approximation of linear systems,” in Proc. 1980 Joint Autom. Control Conf., 1980.
93. H. Ozbay, “Computing the singular values and vectors of a Hankel operator,” in SVD and Signal Processing, II: Algorithms, Analysis and Applications, R. J. Vaccaro, Ed. New York: Elsevier, 1991, pp. 455–469.
94. S. Y. Kung and D. W. Lin,” A state-space formulation for optimal Hankel-normapproximations, IEEE Trans. Automat.Contr., vol. AC-26, pp. 942–946, Aug. 1981.
95. J. A. Ball, I. Gohberg, and L. Rodman, Interpolation ofRational Matrix Functions, vol. OT 45 of Operator Theory:Advances and Applications. Basel, Switzerland: Birkhäuser Verlag, 1990.
96. P. M. Dewilde and A. J. van der Veen, On the Hankel-norm approximation of upper-triangular operators and matrices, Integral Equations and Operator Theory, vol. 17, no.1, pp. 1–45, 1993.
97. M. Viberg and B. Ottersten, Sensor array processing based on subspace fitting, IEEE Trans. Signal Processing, vol. 39, pp.1110-1121, May 1991.
98. P.Stoica and A.Nehorai, MUSIC, Maximum Likelihood and CramCr-Rao bound, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 720–741, May 1989.
99. P.Stoica and K. C. Shaman, Maximum Likelihood methods for direction-of-arrival estimation, IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1132–1 143, July 1990.
100. D. W. Tufts and R. Kumaresan, Improved spectral resolution 11, in Proc. IEEE ICASSP (Denver, CO), Apr. 1980, pp.592-597.
101. R. Kumaresan, L. L. Scharf, and A. K. Shaw, An algorithm for pole-zero modeling and spectral analysis, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 637–640, June 1986.
102. J. F. Bohme, Estimation of spectral parameters of correlated signals in wavefields, Signal Processing, vol. 11, pp. 329–337, Dec. 1986.
103. M. Wax, Detection and estimation of superimposed signals, Ph.D. dissertation, Stanford University, Stanford, CA, 1985.
104. Y. Bresler and A. Macovski, Exact Maximum Likelihood parameter estimation of superimposed exponential signals in noise, IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-34, pp. 1081–1089, Oct. 1986.
105. J. A. Cadzow, A highresolution direction-of-arrival algorithm for narrow-bandcoherent and incoherent sources, IEEE Trans.Acoust., Speech, Signal Processing, vol. 36, pp. 965–979, July 1988.
106. A. Swindlehurst, B. Ottersten, R. Roy, and T. Kailath, Multiple invariance ESPRIT, IEEE Trans. Signal Processing, vol. 40, pp. 867–881, Apr. 1992.
107. R. Roy, B. Ottersten, A. L. Swindlehurst, and T. Kailath, Multiple invariance ESPRIT, in Proc. 22-nd Asilomar Conf.Sign., Syst., Computing, 1988, pp. 583–587.
108. A. Swindlehurst and T. Kailath, Azimuth/elevation direction finding using regular array geometries, IEEE Trans. Aerosp.Electron. Syst., vol. 29, pp.145-156, Jan. 1993.
109. G. Bienvenue and L. Kopp, Optimality of high resolution array processing using the eigensystem approach, IEEE Trans.Acoust., Speech, Signal Processing, vol. ASSP-31, no. 5. pp.1235-1 247, 1983.
110. A. J. Barabell, Improving the resolution performance of eigenstructure-based direction finding algorithms, in Proc.IEEE ICASSP, 1983, pp. 336–339.
111. M. Kaveh and A. J. Barabell, The statistical performance of the MUSIC and minimum-norm algorithms in resolving plane waves in noise, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 331–341, Apr. 1986. (Corrections in vol. ASSP-34, no. 6, 1986.)
112. D. V. Bhaskar Rao and K. V. S. Hari, Performance analysis of root-MUSIC, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 1939–1949, Dec. 1989.
113. B. Ottersten, M. Viberg, and T. Kailath, Analysis of subspacefitting and ML techniques for parameter estimation from sensor array data, IEEE Trans. Signal Processing, vol.40, pp.590-600, Mar.1992.
114. P. Stoica and A. Nehorai, Performance study of conditional and unconditional direction-of-arrival estimation, IEEE Trans.Acoust., Speech, Signal Processing, vol. 38, pp. 1783–1795, Oct.1990.
115. B. Ottersten, M. Viberg, P. Stoica, and A. Nehorai, Exact and large sample MLtechniques for parameter estimation and detection in array processing, in Radar Array Processing, S. Haykin, Ed.New York: Springer-Verlag, 1991, ch. 4.
116. A. Swindlehurst, R. Roy, B. Ottersten, and T. Kailath, A subspace fitting approach for identification of linear state space models, submitted to IEEE Trans. Automat.Contr., 1993.
117. P. Stoica and A. Nehorai, “MUSIC, Maximum Likelihood, and Cramér-Rao bound: Further results and comparisons,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 2140–2150, Dec. 1990.
118. B. Ottersten, M. Viberg, and T. Kailath, “Performance analysis of the Total Least Squares ESPRIT algorithm,” IEEE Trans. Signal Processing, vol. 39, pp. 1122–1135, May 1991.
119. H. Krim, P. Forster, and J. G. Proakis, “Operator approach to performance analysis of root-MUSIC and root-Min-Norm,” IEEE Trans. Signal Processing, vol. 40, pp. 1687–1696, July 1992.
120. P. Stoica and T. Söderström, “Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies,” IEEE Trans. Signal Processing, vol. 39, pp. 1836–1847, Aug. 1991.
121. F. Li and R. J. Vaccaro, “Performance analysis of state-space realization (TAM) and ESPRIT algorithms for DO A estimation,” IEEE Trans. Antennas Propagat., vol. 39, pp. 418–423, Mar. 1991.
122. W. J. Bangs, “Array processing with generalized beamformers,” Ph.D. dissertation, Yale University, New Haven, CT, 1971.
123. K. M. Wong, R. S. Walker, and G. Niezgoda, “Effects of random sensor motion on bearing estimation by the MUSIC algorithm,” Proc. Inst. Elec. Eng., vol. 135, pt. F, pp. 233–250, June 1988.
124. B. Friedlander, “A sensitivity analysis of the MUSIC algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1740–1751, Oct. 1990.
125. A. L. Swindlehurst and T. Kailath, “A performance analysis of subspace-based methods in the precence of model errors —Part 1: The MUSIC algorithm,’IEEE Trans. Signal Processing, vol. 40, pp. 1758–1774, July 1992.
126. F. Li, R. Vaccaro, and D. Tufts, “Unified performance analysis of subspace-based estimation algorithms,” in Proc. IEEE ICASSP (Albuquerque, NM), 1990, vol. 5, pp. 2575–2578.
127. A. Swindlehurst and T. Kailath, “On the sensitivity of the ES-PRIT algorithm to non-identical subarrays,” Sadhana, Academy Proc. in Eng. Sciences, vol. 15, 197–212, Nov. 1990.
128. B. Friedlander, “Sensitivity of the Maximum Likelihood direction finding algorithm,” IEEE Trans. Aerosp. Electron. Syst., vol. 26, 953–968, Nov. 1990.
129. F. Li and R. Vaccaro, “Statistical comparison of subspace based DO A estimation algorithms in the presence of sensor errors,” in Proc. 5th Acoust., Speech, Signal Processing Spectral Estimation Workshop (Rochester, NY), Oct. 1990, pp. 327–331.
130. A. Swindlehurst and T. Kailath, “An analysis of subspace fitting algorithms in the presence of sensor errors,” in Proc. IEEE ICASSP (Albuquerque, NM), 1990, vol. 5, 2647–2650.
131. A. Swindlehurst, “Robust algorithms for direction-finding in the presence of model errors,” in Proc. 5th Acoust., Speech, Signal Processing Workshop on Spectral Estimation and Modeling (Rochester, NY), Oct. 1990, pp.362–366.
132. A. Swindlehurst and T. Kailath, “A performance analysis of subspace-based methods in the presence of model errors—Part 2: Multidimensional algorithms,” IEEE Trans. Signal Processing, vol. 41, pp. 2882–2890, Sept. 1993.
133. Y. Hua and T. K. Sarkar, “Perturbation analysis of TK method for harmonic retrieval problems,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 228–240, Feb. 1988.
134. A. J. van der Veen and E. F. Deprettere, “Parallel VLSI matrix pencil algorithm for high resolution direction finding,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 39, pp. 383–394, Feb. 1991.
135. T. F. Chan, “Rank revealing QR factorizations,” Lin. Alg. Appl., vol. 88/89, 67–82, 1987.
136. C. H. Bischof and G. M. Schroff, “On updating signal sub-spaces,” IEEE Trans. Signal Processing, vol. 40, pp. 96–105, Jan. 1992.
137. G. W. Stewart, “An updating algorithm for subspace tracking,” IEEE Trans. Signal Processing, vol. 40, pp. 1535–1541, June 1992.