As a type of differential equations with high-order derivatives of uncertain processes, high-order uncertain differential equations are widely applied to modelling dynamic systems in uncertain environment, which usually involve unknown parameters to be estimated. Since observations are always discrete in practice, based on these discrete observations of solution processes, we propose moment estimations for unknown parameters by Euler method approximation of high-order uncertain differential equations. Matching sample moments with corresponding population moments, a system of equations whose solution is the moment estimation of the set of unknown parameters is derived. Finally, some examples illustrate our method in detail.

高阶不确定微分方程作为一类具有不确定过程高阶导数的微分方程，被广泛应用于不确定环境下的动态系统建模，这些动态系统通常涉及待估计的未知参数。由于观测在实践中总是离散的，基于求解过程的这些离散观测，我们提出了通过高阶不确定微分方程的欧拉法逼近未知参数的矩估计。将样本矩与对应的总体矩匹配，导出了一个方程组，其解是一组未知参数的矩估计。最后，一些例子详细说明了我们的方法。