Parameter estimation is a critical problem in the wide applications of uncertain differential equations. The method of moments is employed for the first time as an approach for estimating the parameters in uncertain differential equations. Based on the difference form of an uncertain differential equation, a function of the parameters is proved to follow a standard normal uncertainty distribution. Setting the empirical moments of the functions of the parameters and the observed data equal to the moments of the standard normal uncertainty distribution, a system of equations about the parameters is obtained whose solutions are the estimates of the parameters. Analytic examples and numerical examples are given to illustrate the proposed method of moments.

中文翻译：

---

不确定微分方程中的参数估计

在不确定微分方程的广泛应用中，参数估计是一个关键问题。矩量法首次被用作估算不确定微分方程参数的方法。基于不确定微分方程的差分形式，证明了参数的函数遵循标准正态不确定性分布。将参数函数的经验矩和观察到的数据设置为等于标准正态不确定性分布的矩，就可以得到关于参数的方程组，其解是参数的估计。给出了解析例子和数值例子来说明所提出的力矩方法。