Estimation of constrained parameters with guaranteed MSE improvement

IEEE Transactions on Signal Processing

Volumn 55, Issue 4, 2007, Pages 1264-1274

  Benavoli, Alessio ^a   Chisci, Luigi ^a   Farina, Alfonso ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b SELEX SISTEMI INTEGRATI   (Italy)

Author keywords

Constrained estimators; Dominating estimators; Least squares methods; Linear estimation; Parameter estimation; Target tracking

Indexed keywords

COVARIANCE MATRIX; GAUSSIAN DISTRIBUTION; LEAST SQUARES APPROXIMATIONS; LINEAR EQUATIONS; MEAN SQUARE ERROR; PARAMETER ESTIMATION; PROBABILITY; TARGET TRACKING; VECTORS;

CONSTRAINED ESTIMATORS; LINEAR MATRIX; MAXIMUM A POSTERIORI;

SIGNAL PROCESSING;

EID: 34147121416     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.888094     Document Type: Article

References (21)

1. C. Stein, "Inadmissibility of the usual estimator for the mean of a multivariate normal distribution," in Proc. 3rd Berkeley Symp. Math. Statist. Prob., Berkeley, CA, 1956, vol. 1, pp. 197-206.
2. W. James and C. Stein, "Estimation of quadratic loss," in Proc. 4th Berkeley Symp. Math. Statist. Prob., Berkeley, CA, 1961, vol. 1, pp. 361-379.
3. W. E. Strawderman, "Proper Bayes minimax estimators of a multivariate normal mean," Ann. Math. Statist., vol. 42, pp. 385-388, 1971.
4. K. Alam, "A family of admissible minimax estimators of the mean of a multivariate normal distribution," Ann. Statist., vol. 1, pp. 517-525, 1973.
5. J. O. Berger, "Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss," Ann. Statist., vol. 4, no. 1, pp. 223-226, 1976.
6. P. Stoica and B. Ottersten, "The evil of superefficiency," Signal Process., vol. 55, pp. 133-136, 1996.
7. E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed. New York: Springer, 1999.
8. Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Linear minimax regret estimation of deterministic parameters with bounded data uncertainties," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2177-2188, Aug. 2004.
9. Y. C. Eldar, A. Ben-Tal, "Robust mean-squared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process., vol. 53, no. 1, pp. 168-181, Jan. 2005.
10. Z. Ben-Haim and Y. C. Eldar, "Blind minimax estimators: Improving on least-squares estimation," presented at the IEEE Workshop on Statistical Signal Process. (SSP'05), Bordeaux, France, 2005.
11. Z. Ben-Haim and Y. C. Eldar, "Maximum set estimators with bounded estimation error," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3172-3182, Aug. 2005.
12. Y. C. Eldar, "Comparing between estimation approaches. Admissible and dominating linear estimators," IEEE Trans. Signal Process., to be published.
13. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington, DC: Winston & Sons, 1977.
14. A. E. Hoerl and R. W. Kennard, "Ridge regression: Biased estimation for nonorthogonal problems," Technometrics, vol. 12, pp. 55-67, 1970.
15. L. S. Mayer and T. A. Willke, "On biased estimation in linear models," Technometrics, vol. 15, pp. 497-508, 1973.
16. Y. C. Eldar and A. V. Oppenheim, "Covariance shaping least-squares estimation," IEEE Trans. Signal Process., vol. 51, no. 3, pp. 686-697, Mar. 2003.
17. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.
18. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
19. A. Benavoli, L. Chisci, A. Farina, L. Ortenzi, and G. Zappa, "Hard-constrained vs. soft-constrained parameter estimation," IEEE Trans. Aerosp. Electron. Syst., to be published.
20. B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications. Norwood, MA: Artech House, 2004.
21. P. Gahinet, A. Nemirovshi, A. Laub, and M. Chilali, MATLAB LMI Control Toolbox. Natick, MA: MathWorks, Inc., 1995.