Parameter estimation in exponential models by linear and nonlinear fitting methods

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

doi:10.1631/FITEE.1601683

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Parameter estimation in exponential models by linear and nonlinear fitting methods

Regular Papers | Updated：2022-05-19

- Parameter estimation in exponential models by linear and nonlinear fitting methods
- 采用线性和非线性拟合方法进行指数模型参数估计
- Frontiers of Information Technology & Electronic Engineering Vol. 18, Issue 3, Pages: 434-444(2017)
- Affiliations：
  
  1School of Digital Media & Design, Hangzhou Dianzi University, Hangzhou 310018, China
  2Ocean College, Zhejiang University, Zhoushan 316021, China
  3State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China
  4State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
- Author bio：
  
  E-mail:yangping@hdu.edu.cn
  E-mail:huih@zju.edu.cn
- Funds：
- DOI：10.1631/FITEE.1601683
  CLC： O433.1
- Received：03 November 2016，
  
  Accepted：16 February 2017，
  
  Published：2017-03
- Accepted：
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Ping YANG, Chao-peng WU, Yi-lu GUO, et al. Parameter estimation in exponential models by linear and nonlinear fitting methods[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(3): 434-444.
DOI：

Ping YANG, Chao-peng WU, Yi-lu GUO, et al. Parameter estimation in exponential models by linear and nonlinear fitting methods[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(3): 434-444. DOI： 10.1631/FITEE.1601683.

摘要

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。

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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