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

真实的流程具有高度复杂性的特点，需要智能系统来辅助决策。这些过程往往受到其他不确定性的影响，其表现形式是不精确的已知参数，影响变量和动态，从而阻碍可靠的决策自动化。不确定性，即有限的信息具有不同的形状和来源，在许多建模和设计过程中无处不在，充分考虑这种不确定性是必要的--但到目前为止还没有得到充分的研究。过滤器允许对系统的时变、内部和不一定可观测的变量进行推断。他们的知识往往是知情决策过程的基本先决条件。然而，现有的过滤技术通常严重依赖精确的--即概率--错误描述，这种描述通常只能很好地解释统计上可评估的不确定性，并且在严重缺乏知识的情况下不能被证明是合理的。需要新的、直观的、数值上易于实现的方法和工具，以便能够更真实地量化和处理状态估计中的不确定性，例如，在仅有有限信息的早期设计阶段，或者在数据稀疏的不可访问系统中。在这个项目中，将开发具有解析和精确或近似数值解的新的滤波器设计方法，并能够在实时应用中实现有效的实施。为此，可能性理论将被用来作为一个通用的工具来量化许多类型的不确定性。动态过滤方法通常可以归结为几个重复的任务，即预测，测量，更新和重采样在基于粒子的过滤器的情况下。这些步骤现在将在可能性理论的框架内进行制定和分析，从而可以使用现有的理论解决方案，如可能性不确定性传播或证据统计。特别是，重点是将不同的方法非平凡地组合成普遍适用的滤波器设计方法，除了封闭的解析解之外，这还使得能够进行有效的数值实现，以保证实时适用性-这是滤波器实际使用的主要前提。所开发的方法可以例如在早期设计阶段使用，当系统的完整描述还不可用时，或者当稀疏的数据阻碍精确的统计建模时，从而缩小现有理论和现代滤波器的实际要求之间的差距。

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.