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CLC number: O433.1

On-line Access: 2017-03-10

Received: 2016-11-03

Revision Accepted: 2017-02-16

Crosschecked: 2017-02-28

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Citations:  Bibtex RefMan EndNote GB/T7714


Hui Huang


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Frontiers of Information Technology & Electronic Engineering  2017 Vol.18 No.3 P.434-444


Parameter estimation in exponential models by linear and nonlinear fitting methods

Author(s):  Ping Yang, Chao-peng Wu, Yi-lu Guo, Hong-bo Liu, Hui Huang, Hang-zhou Wang, Shu-yue Zhan, Bang-yi Tao, Quan-quan Mu, Qiang Wang, Hong Song

Affiliation(s):  School of Digital Media & Design, Hangzhou Dianzi University, Hangzhou 310018, China; more

Corresponding email(s):   yangping@hdu.edu.cn, huih@zju.edu.cn

Key Words:  Exponential model, Parameter estimation, Linear least squares, Nonlinear fitting

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Ping Yang, Chao-peng Wu, Yi-lu Guo, Hong-bo Liu, Hui Huang, Hang-zhou Wang, Shu-yue Zhan, Bang-yi Tao, Quan-quan Mu, Qiang Wang, Hong Song. Parameter estimation in exponential models by linear and nonlinear fitting methods[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(3): 434-444.

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author="Ping Yang, Chao-peng Wu, Yi-lu Guo, Hong-bo Liu, Hui Huang, Hang-zhou Wang, Shu-yue Zhan, Bang-yi Tao, Quan-quan Mu, Qiang Wang, Hong Song",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

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%T Parameter estimation in exponential models by linear and nonlinear fitting methods
%A Ping Yang
%A Chao-peng Wu
%A Yi-lu Guo
%A Hong-bo Liu
%A Hui Huang
%A Hang-zhou Wang
%A Shu-yue Zhan
%A Bang-yi Tao
%A Quan-quan Mu
%A Qiang Wang
%A Hong Song
%J Frontiers of Information Technology & Electronic Engineering
%V 18
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%P 434-444
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%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1601683

T1 - Parameter estimation in exponential models by linear and nonlinear fitting methods
A1 - Ping Yang
A1 - Chao-peng Wu
A1 - Yi-lu Guo
A1 - Hong-bo Liu
A1 - Hui Huang
A1 - Hang-zhou Wang
A1 - Shu-yue Zhan
A1 - Bang-yi Tao
A1 - Quan-quan Mu
A1 - Qiang Wang
A1 - Hong Song
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
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SP - 434
EP - 444
%@ 2095-9184
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1601683

Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.




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