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 paramete...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.展开更多
A modeling method is proposed for a dynamic fast steering mirror(FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coup...A modeling method is proposed for a dynamic fast steering mirror(FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.展开更多
基金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)the Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics(No.SOED1606)
文摘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.
基金supported by the National Natural Science Foundation of China(No.11304278)the National High-Tech R&D Program(863)of China(No.2014AA093400)
文摘A modeling method is proposed for a dynamic fast steering mirror(FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.
