用决策理论的非参数方法确定非平稳随机过程的特征

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Bulat-Batyr Yesmagambetov
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引用次数: 0

摘要

本文致力于处理随机过程的方法。在随机过程是宽带和非平稳的情况下,这项任务变得特别相关;然后,随机过程的测量可以与对其概率特征的评估相关联。通常,一个非平稳宽带随机过程是由一个具有关于分布函数类型的先验不确定性的单一实现来表示的。这种随机过程发生在以实时速度传输信息的信息和测量通信系统中(例如,航天器上的无线电遥测系统)。在这种情况下,使用传统数理统计方法,例如最大似然方法来确定概率特征是不可能的。此外,航天器的星载计算系统在质量尺寸特性和能量消耗的限制条件下运行。因此,有必要应用加速方法来处理测量的随机过程。本文讨论了一种基于决策理论的非参数方法处理非平稳宽带随机过程的方法。考虑了使用非参数Kendall统计量将观测区间划分为平稳区间的算法,以及使用有序统计量估计平稳区间上的概率特征的方法。本文介绍了使用Mathcad程序进行统计建模的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Determination of the Characteristics of Non-Stationary Random Processes by Non-Parametric Methods of Decision Theory
This article is devoted to methods of processing random processes. This task becomes particularly relevant in cases where the random process is broadband and non-stationary; then, the measurement of a random process can be associated with an assessment of its probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation with a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real-time pace (for example, radio telemetry systems in spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods, to determine probability characteristics in this case is not possible. In addition, the on-board computing systems of spacecraft operate under conditions of restrictions on mass-dimensional characteristics and energy consumption. Therefore, there is a need to apply accelerated methods of processing measured random processes. This article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall’s statistics is considered, as are methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. This article presents the results of statistical modeling using the Mathcad program.
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来源期刊
Computation
Computation Mathematics-Applied Mathematics
CiteScore
3.50
自引率
4.50%
发文量
201
审稿时长
8 weeks
期刊介绍: Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.
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