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Parameter estimation in exponential models by linear and nonlinear fitting methods

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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.

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Authors and Affiliations

  1. School of Digital Media & Design, Hangzhou Dianzi University, Hangzhou, 310018, China

    Ping Yang & Qiang Wang

  2. Ocean College, Zhejiang University, Zhoushan, 316021, China

    Chao-peng Wu, Yi-lu Guo, Hong-bo Liu, Hui Huang, Hang-zhou Wang, Shu-yue Zhan & Hong Song

  3. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou, 310012, China

    Bang-yi Tao

  4. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, 130033, China

    Quan-quan Mu

Authors
  1. Ping Yang
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  2. Chao-peng Wu
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  3. Yi-lu Guo
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  4. Hong-bo Liu
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  5. Hui Huang
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  6. Hang-zhou Wang
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  7. Shu-yue Zhan
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  8. Bang-yi Tao
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  9. Quan-quan Mu
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  10. Qiang Wang
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  11. Hong Song
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Corresponding authors

Correspondence to Ping Yang or Hui Huang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 61605038 and 11304278), the National High-Tech R&D Program (863) of China (No. 2014AA093400), and the Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics (No. SOED1606)

ORCID: Hui HUANG, http://orcid.org/0000-0003-1204-3684

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Yang, P., Wu, Cp., Guo, Yl. et al. Parameter estimation in exponential models by linear and nonlinear fitting methods. J. Zhejiang Univ. - Sci. C 18, 434–444 (2017). https://doi.org/10.1631/FITEE.1601683

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  • DOI: https://doi.org/10.1631/FITEE.1601683

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