Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 48, Issue 10, Pages 2866-2874Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2017.2751558
Keywords
Data fitting; Jacobian approximation; parameter estimation; separable nonlinear least squares problems; variable projection (VP)
Categories
Funding
- National Nature Science Foundation of China [61673155, 61673405, 61203106]
- Macao Science and Technology Development Fund [097/2015/A3, 067/2014/A]
- Research Committee of the University of Macau [MYRG2015-00148-FST]
Ask authors/readers for more resources
For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available