A Method for Nonlinear Least Squares With Structured Residuals

IEEE Transactions on Automatic Control

Volumn 51, Issue 10, 2006, Pages 1704-1708

  Shaw, Steven R ^a   Laughman, Christopher R ^b  

^a Montana State University   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Nonlinear least squares; optimization; system identification

Indexed keywords

EID: 85008053906     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.2006.883036     Document Type: Article

References (15)

1. G. A. F. Seber and C. J. Wild, Nonlinear Regression, ser. Probability and Mathematical Statistics. New York: Wiley, 1989.
2. W. H. Press, S. A. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1992.
3. J. J. More, The Levenburg-Marquardt Algorithm: Implementation and Theory, ser. Lecture Notes in Mathematics. New York: Springer-Verlag, 1977, pp. 105–116.
4. J. Dennis, Jr., D. Gay, and R. Welsch, “An adaptive nonlinear least-squares algorithm,” ACM Trans. Math. Software, vol. 7, no. 3, pp. 348–368, Sep. 1981.
5. G. Golub and V. Pereyra, “Separable nonlinear least squares: The variable projection method and its applications,” Inverse Prob., vol. 19, pp. R1-R26, 2003.
6. D. Bertsekas, “A new class of incremental gradient methods for least squares problems,” SIAM J. Optim., vol. 7, no. 4, pp. 913–926, Nov. 1997.
7. G. Simon, R. Pintelon, L. Sujbert, and J. Schoukens, “An efficient nonlinear least square multisine fitting algorithm,” IEEE Trans. Instrum. Measure., vol. 51, no. 4, pp. 750–755, Aug. 2002.
8. A. Routray, A. K. Pradhan, and K. P. Rao, “A novel Kalman filter for frequency estimation of distorted signals in power systems,” IEEE Trans. Instrum. Measure., vol. 51, no. 3, pp. 469–479, Jun. 2002.
9. J. Q. Zhang, Z. Xinmin, S. Jinwei, and H. Xiao, “Sinewave fit algorithm based on total least-squares method,” in IEEE Instrumentation and Measurement Technology Conf, Brussels, Belgium, Jun. 1996, pp. 1436–1440.
10. N. Gianquinto and A. Trotta, “Fast and accurate ADC testing via an enhanced sine wave fitting algorithm,” IEEE Trans. Instrum. Measure., vol. 46, no. 4, pp. 1020–1024, Aug. 1997.
11. J. J. More, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” ACM Trans. Math. Software, vol. 7, no. 1, pp. 17–41, March 1981.
12. B. Averick and J. J. More, User Guide for the Minpack-2 Test Problem Collection Argonne National Laboratory, Argonne, IL, Tech. Rep. 157, Oct. 1991.
13. J. J. More, B. S. Garbow, and K. E. Hillstrom, User Guide for MINPACK-1 Argonne National Laboratory, Argonne, IL, Tech. Rep. ANL-80-74, Aug. 1980.
14. S. H. Strogatz, Nonlinear Dynamics and Chaos. Boulder, CO: Westview Press, 2000.
15. K. Radhakrishnan and A. C. Hindmarsh, Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations Lawrence Livermore National Laboratory, Livermore, CA, Tech. Rep. UCRL-ID-113855 1993.