A recursive algorithm for nonlinear least-squares problems

被引：0
作者：
A. Alessandri
M. Cuneo
S. Pagnan
M. Sanguineti
机构：
[1] University of Genoa,Department of Production Engineering, Thermoenergetics, and Mathematical Models (DIPTEM)
[2] ISSIA-CNR National Research Council of Italy,Institute of Intelligent Systems for Automation
[3] University of Genoa,Department of Communications, Computer and System Sciences (DIST)
来源：
Computational Optimization and Applications | 2007年 / 38卷
关键词：
Nonlinear programming; Nonlinear least squares; Extended Kalman filter; Recursive optimization; Batch algorithms;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown.
引用
收藏
页码：195 / 216
页数：21
相关论文
共 50 条
[41]   SEPARABLE NONLINEAR LEAST-SQUARES WITH MULTIPLE RIGHT-HAND SIDES [J].
KAUFMAN, L ;
SYLVESTER, G .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1992, 13 (01) :68-89
[42]   Least-Squares Approximations in Geometric Buildup for Solving Distance Geometry Problems [J].
Luo, Xin-long ;
Wu, Zhi-jun .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 149 (03) :580-598
[43]   Least-Squares Approximations in Geometric Buildup for Solving Distance Geometry Problems [J].
Xin-long Luo ;
Zhi-jun Wu .
Journal of Optimization Theory and Applications, 2011, 149 :580-598
[44]   Scaled nonlinear conjugate gradient methods for nonlinear least squares problems [J].
R. Dehghani ;
N. Mahdavi-Amiri .
Numerical Algorithms, 2019, 82 :1-20
[45]   A globally convergent method for nonlinear least-squares problems based on the Gauss-Newton model with spectral correction [J].
Goncalves, Douglas S. ;
Santos, Sandra A. .
BULLETIN OF COMPUTATIONAL APPLIED MATHEMATICS, 2016, 4 (02) :7-26
[46]   Scaled nonlinear conjugate gradient methods for nonlinear least squares problems [J].
Dehghani, R. ;
Mahdavi-Amiri, N. .
NUMERICAL ALGORITHMS, 2019, 82 (01) :1-20
[47]   The application of nonlinear least-squares estimation algorithms in atmospheric density model calibration [J].
Zhang, Houzhe ;
Gu, Defeng ;
Duan, Xiaojun ;
Shao, Kai ;
Wei, Chunbo .
AIRCRAFT ENGINEERING AND AEROSPACE TECHNOLOGY, 2020, 92 (07) :993-1000
[48]   ANALYSIS OF PHOTOACOUSTIC WAVE-FORMS USING THE NONLINEAR LEAST-SQUARES METHOD [J].
SMALL, JR ;
LIBERTINI, LJ ;
SMALL, EW .
BIOPHYSICAL CHEMISTRY, 1992, 42 (01) :29-48
[49]   Scalable subspace methods for derivative-free nonlinear least-squares optimization [J].
Coralia Cartis ;
Lindon Roberts .
Mathematical Programming, 2023, 199 :461-524
[50]   Least-squares fitting Gompertz curve [J].
Jukic, D ;
Kralik, G ;
Scitovski, R .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 169 (02) :359-375
12345