Abstract

The well-known methods of supporting integral curves and generalized invariant unbiased estimation are used to find numerical-analytical representations of the solution to an equation describing a dynamical system and its measured output and to compute optimal values of continuous linear functionals (numerical characteristics) of measured parameters based on incorrect data involving both a fluctuation error and a singular disturbance. A two-step method is developed for this purpose. Numerical-analytical representations depending continuously on all parameters of the system are formed at the first stage, and numerical characteristics of the system that are invariant under the singular disturbance are estimated at the second stage. The method ensures the maximum possible decomposition of the numerical procedures involved; moreover, it does not require traditional linearization or initial guess choice and does not involve the computation of spectral coefficients in finite linear combinations (with given basis functions) describing the integral curves, measured parameters, and the singular disturbance. The random and systematic errors are analyzed, an illustrative example is given, and recommendations on practical application of the results are made.

中文翻译：

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支撑积分曲线和广义不变无偏估计在多维动力系统研究中的应用

摘要

使用众所周知的支持积分曲线和广义不变无偏估计的方法来找到描述动力学系统及其测得输出的方程的解的数值解析表示，并计算连续线性函数（数值特征）的最佳值基于涉及波动误差和奇异干扰的不正确数据来测量参数。为此，开发了一种两步方法。在第一阶段形成连续依赖于系统所有参数的数值分析表示，在第二阶段估计在奇异扰动下不变的系统数值特征。该方法可确保最大程度地分解所涉及的数字过程。此外，它不需要传统的线性化或初始猜测选择，并且不需要涉及描述积分曲线，测量参数和奇异干扰的有限线性组合（具有给定的基函数）中的频谱系数计算。分析了随机误差和系统误差，给出了一个说明性的例子，并对结果的实际应用提出了建议。