高精度参数估计问题

对高精度参数的估计问题进行了研究.在观测数据无误差的情况下,将微分方程组转化为线性方程组,利用矩阵的奇异值分解给出了参数的最优解.在有观测数据误差的情况下,采用高斯-牛顿迭代法进行求解,给出了改进的高斯-牛顿法和阻尼最小二乘算法;通过灰色估计法给出了模型的初始解,通过微分方程数值解法计算模型迭代过程中误差和偏导数.最后,通过对迭代过程中的状态变量引入误差项,导出了基于总体最小二乘的高斯-牛顿迭代法,从系统的角度解决了观测时间有误差下的参数估计问题.

A High Precision Parameter Estimation Problem

The methods of a high definition parameter estimation problem in different conditions are discussed.When the observations have no errors,we convert the differentiation equations to linear equations,then the parameters are estimated by the singular value decomposition of the coefficient matrix.When the observations have errors,the Gaussian-Newton method is given,with the modified Gaussian-Newton method and damping least square method as an improvement.The initial value is obtained through gray estimation and the differential coefficients of the parameters are approximated by a numerical mean.At last,when the observation time has errors,a total least square Gaussian-Newton method is developed by introducing errors into the state variables of the system.Emulation experiments showed that our method can get a high definition solution for the given nonlinear parameter estimation problem.