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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.
The problem of high-precision parameter estimation is studied.Under the condition of no error of observation data, the differential equations are converted into linear equations and the optimal solutions of the parameters are given by using the singular value decomposition of the matrix.With the error of observed data , The Gauss-Newton iterative method is used to solve the problem. The improved Gauss-Newton method and the damping least squares method are given. The initial solution of the model is given by the gray estimation method. The iterative process of the model is calculated by the numerical solution of the differential equation In the end, by introducing the error term into the state variables in the iterative process, the Gauss-Newton iterative method based on global least squares is derived, which solves the parameter estimation problem under the error of observation time systematically.