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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

Cited: 0

Clicked: 6349

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Hui Huang

http://orcid.org/0000-0003-1204-3684

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

http://doi.org/10.1631/FITEE.1601683


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


Share this article to: More <<< Previous Article|

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",
volume="18",
number="3",
pages="434-444",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1601683"
}

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A1 - Shu-yue Zhan
A1 - Bang-yi Tao
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Abstract: 
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.

采用线性和非线性拟合方法进行指数模型参数估计

概要:本文探讨了通过线性和非线性拟合方法估计指数模型中的未知参数。基于多元函数极值定理及泰勒级数展开,从理论上证明了:在实验测量数据中包含噪声的情况下,通过线性拟合方法所得到的参数估计值并不能保证指数模型的残差平方和达到最小。通过数值仿真对线性和非线性拟合方法的结果进行了对比,仿真结果显示:线性方法只能获得未知参数的次优估计,但非线性方法给出更准确的结果。利用水下图像和成像距离数据对水体光谱衰减系数进行了估计,结果证实非线性拟合方法能够对参数估计准确度有明显的提升。

关键词:指数模型;参数估计;线性最小二乘法;非线性拟合

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Adi, N.S., 2015. Characterisation of the light environment and biophysical parameters of seagrass using remote sensing. PhD Thesis, The University of Queensland, Brisbane, Australia, p.23-38.

[2]Åhlén, J., Bengtsson, E., Sundgren, D., 2006. Evaluation of underwater spectral data for color correction applications. Proc. 5th WSEAS Int. Conf. on Circuits, Systems, Electronics, Control & Signal Processing, p.321-326.

[3]Bardaji, R., Sánchez, A.M., Simon, C., et al., 2016. Estimating the underwater diffuse attenuation coefficient with a low-cost instrument: the KdUINO DIY buoy. Sensors, 16(3):373-387.

[4]Floudas, C.A., Pardalos, P.M., 2001. Encyclopedia of Optimization. Kluwer Academic Publishers, Norwell, p.1129-1134.

[5]Guo, Y.L., Song, H., Liu, H.B., et al., 2016. Model-based restoration of underwater spectral images captured with narrowband filters. Opt. Expr., 24(12):13101-13120.

[6]Hartley, H.O., 1961. The modified Gauss-Newton method for the fitting of nonlinear regression functions by least squares. Technometrics, 3(2):269-280.

[7]He, Q.R., Li, L.P., 2015. Algorithm study on reducing frequency measurement variance of acousto-optic spectrum analyzer. Infrar. Laser Eng., 44(5):1564-1568 (in Chinese).

[8]Kaeli, J.W., Singh, H., Murphy, C., et al., 2011. Improving color correction for underwater image surveys. Proc. IEEE/MTS Oceans, p.805-810.

[9]Lai, J.S., Yang, B., Lin, D.M., et al., 2013. The allometry of coarse root biomass: log-transformed linear regression or nonlinear regression. PLoS One, 8(10):e77007.

[10]Levenberg, K., 1944. A method for the solution of certain non-linear problems in least squares. Q. Appl. Math., 2:164-168.

[11]Lieb, S.G., 1997. Simplex method of nonlinear least-squares: a logical complementary method to linear least-square analysis of data. J. Chem. Educat., 74(8):1008-1011.

[12]Liu, C.Q., Ma, J.S., Shao, X.L., et al., 2013. Detection of Gaussian beam distribution of light intensity. Opt. Instrum., 35(6):69-73 (in Chinese).

[13]Marquardt, D.W., 1963. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11(2):431-441.

[14]Mascaro, J., Litton, C.M., Hughes, R.F., et al., 2011. Minimizing bias in biomass allometry: model selection and log-transformation of data. Biotropica, 43(6):649-653.

[15]Novković, D., Nadderd, L., Kandić, A., et al., 2006. Testing the exponential decay law of gold 198Au. Nucl. Instrum. Methods Phys. Res. Sect. A, 566(2):477-480.

[16]Peterson, P., Baker, E., McGaw, B., 2010. International Encyclopedia of Education. Elsevier Science, Oxford, p.339-346.

[17]Schechner, Y.Y., Karpel, N., 2004. Clear underwater vision. Proc. IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, p.536-543.

[18]Semkow, T.M., 2007. Exponential decay law and nuclear statistics. In: Semkow, T.M., Pommé, S., Jerome, S., et al. (Eds.), Applied Modeling and Computations in Nuclear Science. ACS, Washington DC.

[19]Simon, A., Shanmugam, P., 2016. Estimation of the spectral diffuse attenuation coefficient of downwelling irradiance in inland and coastal waters from hyperspectral remote sensing data: validation with experimental data. Int. J. Appl. Earth Observ. Geoinform., 49:117-125.

[20]Swinehart, D.F., 1962. The Beer-Lambert law. J. Chem. Educat., 39(7):333-335.

[21]Vickery, P.J., 2005. Simple empirical models for estimating the increase in the central pressure of tropical cyclones after landfall along the coastline of the United States. J. Appl. Meteorol., 44:1807-1826.

[22]Wei, J.W., Lee, Z.P., 2013. Model of the attenuation coefficient of daily photosynthetically available radiation in the upper ocean. Methods Oceanogr., 8:56-74.

[23]Xiao, X., White, E.P., Hooten, M.B., et al., 2011. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology, 92(10):1887-1894.

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