Abstract

The paper develops a method for describing and estimating the state of a multidimensional dynamical object including the numerical-analytical representation of the general solution to the differential equation for the dynamical object and its measurable output, accounting for the domain of admissibility of time values and initial condition and of the uncertainty parameters in the right-hand side of the equation. The required quality of representation is achieved by using the family of previously constructed high-precision reference integral curves (of the needed size) and the principle of smooth dependence of solution and measured cooordinates in the given domain of admissibility for a wide class of dynamical objects. The estimate of method errors is given and the recommendations for the choice of its main parameters are provided.

中文翻译：

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描述和估计多维动态对象的输入和输出参数的数值分析方法：第一部分

摘要

本文提出了一种描述和估计多维动态对象状态的方法，其中包括动态对象及其可测量输出的微分方程的一般解的数值解析表示，并考虑了时间值和初始值的允许范围条件和方程右侧的不确定性参数。通过使用一系列先前构建的（所需大小的）高精度参考积分曲线，以及在宽泛的动态对象的给定容许范围内，对溶液和测得坐标的平滑依赖性原理，可以实现所需的表示质量。 。给出了方法误差的估计，并提供了选择其主要参数的建议。