1. School of Digital Media & Design, Hangzhou Dianzi University, Hangzhou 310018, China 2. Ocean College, Zhejiang University, Zhoushan 316021, China 3. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China 4. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
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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