Development of Possibilistic Filter Design Methods for State Estimation in Dynamical Systems under Uncertainty

不确定性下动态系统状态估计的可能性滤波器设计方法的发展

• 批准号: 319924547
• 负责人: Professor Dr.-Ing. Michael Hanss
• 金额: --
• 依托单位: Institut für Technische und Numerische Mechanik (ITM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/319924547?language=en
• 关键词: Development; Possibilistic; Filter; Design; Methods

Real processes are characterized by a high degree of complexity, and intelligent systems are needed in order to aid decision-making. These processes are often subject to additional uncertainties, which manifest themselves in the form of imprecisely known parameters, influencing variables and dynamics and thus impede a reliable automation of decision-making. Uncertainty, i.e. limited knowledge where the available information is of different shape and origin, is omnipresent in many modeling and design processes, and an adequate consideration of this uncertainty is necessary - but has so far been insufficiently investigated.Filters allow inference about time-variant, internal and not necessarily observable variables of a system. Their knowledge is frequently an essential prerequisite for informed decision-making processes. However, existing filtering techniques typically rely heavily on precise - i.e. probabilistic - error descriptions which usually only account well for statistically assessable uncertainty and cannot be justified in cases of a severe lack of knowledge. New, intuitive and numerically easy-to-implement methods and tools are needed, enabling a more faithful quantification and processing of uncertainties in state estimation, e.g. in early-stage design phases when only limited information is available or in inaccessible systems where data is sparse.In this project, novel filter design methods are to be developed which possess both analytical and exact or approximative numerical solutions and enable validated implementations in real-time applications. To this end, possibility theory will be used as a versatile tool for quantifying many types of uncertainty.Dynamic filtering methods can typically be reduced to a few recurring tasks, namely prediction, measurement, update and resampling in the case of particle-based filters. These steps are now to be formulated and analyzed within the framework of possibility theory, whereby existing theoretical solutions, such as possibilistic uncertainty propagation or evidential statistics, can be used. In particular, the focus is on the non-trivial assembly of the different methods into a universally applicable filter design methods, which, in addition to a closed analytical solution, also enable efficient numerical implementations that guarantee real-time applicability - a major prerequisite for the practical use of filters.The developed methods can be used e.g. in early stage design phases, when a complete description of the system is not yet available or when sparse data prevent a precise statistical modeling, thus closing a gap between existing theory and the practical requirements for modern filters.

真实的过程的特点是高度复杂，需要智能系统来辅助决策。这些过程常常受到额外的不确定性的影响，这些不确定性以不精确的已知参数的形式表现出来，影响变量和动态，从而阻碍了决策的可靠自动化。不确定性，即有限的知识，其中可用的信息是不同的形状和来源，是无处不在的许多建模和设计过程中，并充分考虑这种不确定性是必要的-但迄今为止还没有得到充分的调查。过滤器允许有关时变的，内部的，不一定是可观察的变量的系统的推断。他们的知识往往是知情决策进程的一个基本先决条件。然而，现有的过滤技术通常严重依赖于精确的-即概率-错误的描述，通常只占统计评估的不确定性，并不能证明在严重缺乏知识的情况下。需要新的、直观的和易于数字实现的方法和工具，以便更忠实地量化和处理状态估计中的不确定性，例如在早期设计阶段，只有有限的信息可用，或者在数据稀疏的不可访问系统中。一种新的滤波器设计方法是要开发拥有解析和精确或近似的数值解，并使验证实施在实时应用中。为此，可能性理论将被用作量化许多类型的不确定性的通用工具。动态过滤方法通常可以简化为几个重复的任务，即预测，测量，更新和基于粒子的过滤器。这些步骤，现在制定和分析的框架内的可能性理论，从而现有的理论解决方案，如可能性不确定性传播或证据统计，可以使用。特别是，重点是将不同的方法组装成一个普遍适用的滤波器设计方法，除了封闭的解析解外，还可以实现有效的数值实现，保证实时适用性-这是滤波器实际使用的主要先决条件。所开发的方法可以用于例如早期设计阶段，当系统的完整描述还不可用时，或者当稀疏数据阻止精确的统计建模时，从而缩小了现有理论与现代滤波器的实际要求之间的差距。