Parameter estimation in the presence of bounded data uncertainties

SIAM Journal on Matrix Analysis and Applications

Volumn 19, Issue 1, 1998, Pages 235-252

  Chandrasekaran, S ^a   Golub, G H ^b   Gu, M ^c   Sayed, A H ^c  

^a University of California at Santa Barbara   (United States)

^b Stanford University ^*  (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Least squares estimation; Modeling errors; Regularized least squares; Ridge regression; Robust estimation; Secular equation; Total least squares

Indexed keywords

EID: 0032340223     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479896301674     Document Type: Article

References (15)

1. L. E. GHAOUI AND H. LEBRET, Robust solutions to least-squares problems with uncertain data, SIAM J. Matrix Anal. Appl., 18 (1997). pp. 1035-1064.
2. G. H. GOLUB, Some modified matrix eigenvalue problems, SIAM Rev., 15 (1973), pp. 318-344.
3. G. H. GOLUB AND C. F. VAN LOAN, An analysis of the total least squares problem, SIAM J. Numer. Anal., 17 (1980), pp. 883-893.
4. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1997.
5. G. H. GOLUB AND U. VON MATT, Generalized Cross-Validation for Large Scale Problems, Tech. report SCCM-96-06, Computer Science Department, Stanford University, Stanford, CA, 1996.
6. B. HASSIBI, A. H. SAYED, AND T. KAILATH, Linear estimation in Krein spaces - Part I: Theory, IEEE Trans. Automat. Control, 41 (1996), pp. 18-33.
7. S. V. HUFFEL AND J. VANDEWALLE, The Total Least Squares Problem: Computational Aspects and Analysis, SIAM, Philadelphia, PA, 1991.
8. S. M. KAY, Fundamentals of Statistical Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1993.
9. P. KHARGONEKAR AND K. M. NAGPAL, Filtering and smoothing in an H∞ - setting, IEEE Trans. Automat. Control, AC-36 (1991), pp. 151-166.
10. C. L. LAWSON AND R. J. HANSON, Solving Least-Squares Problems. SIAM, Philadelphia, PA, 1995. Revised republication of work first published by Prentice-Hall, Englewood Cliffs, NJ, 1974.
11. L. LJUNG AND T. SÖDERSTRÖM, Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983.
12. A. H. SAYED, B. HASSIBI, AND T. KAILATH, Fundamental inertia conditions for the minimization of quadratic forms in indefinite metric spaces, in Recent Developments in Operator Theory and Its Applications, Oper. Theory Adv. Appl. 87, Birkhäuser, Basel, 1996, pp. 309-347.
13. L. L. SCHARF, Statistical Signal Processing: Detection, Estimation and Time Series Analysis, Addison-Wesley, Reading, MA, 1991.
14. U. SHAKED AND Y. THEODOR, H∞ - optimal estimation: A tutorial, in Proc. IEEE Conference on Decision and Control, Tucson, AZ, December 1992, IEEE Computer Society Press, Los Alamitos, CA, pp. 2278-2286.
15. S. CHANDRASEKARAN, G. GOLUB, M. GU, AND A. H. SAYED. Parameter estimation in the presence of bounded modeling errors. IEEE Signal Processing Letters, 4 (1997), pp. 195-197.