On Processing Heterogeneous Sources of Limited Data for Uncertainty Quantification in a Possibilistic Framework

Abstract

This contribution aims at highlighting the use of possibility theory in uncertainty quantification for engineering problems by inferring distributions from different sources of limited data and combining the gained knowledge to serve as a basis for subsequent decisions. The mathematical framework of possibility theory offers the ability to infer information in the form of concrete mathematical expressions from data in the narrow sense, while also proving convenient for the simultaneous or subsequent incorporation of other sources of information through transformation, conjunction and propagation of possibilistic distributions, while continuously resting on a solid mathematical foundation that guarantees the conservative validity of the result.In a robot localization scenario carried out in a lab environment, only a few noisy measurements from a UWB (ultra-wideband) sensor setup as well as some additional knowledge such as room dimensions and sensor characteristics are available. The impact of progressively adding and combining information from these data sources is analyzed, showcasing the advantages and opportunities of possibility theory for processing heterogeneous sources of limited data for uncertainty quantification, while also discussing practical limitations of the current state of the framework.