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

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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.