The Kalman Filter Uncertainty Concept in the Possibility Domain

The Kalman filter (KF) is one of the most important and common optimal recursive data processing algorithms in many applications characterized by linear dynamical behavior and affected by random zero-mean white Gaussian noise. However, when measurement processes are considered, inaccuracy is not only due to noise but also to several contributions to uncertainty that can be due to both random and uncompensated systematic effects. Therefore, when the KF is used on experimental data, all uncertainty contributions should be considered. While several proposals are available in the literature to modify the KF in order to consider different probability distributions and systematic effects, represented both in probability and possibility domains, they are not fully compliant with the uncertainty concept adopted in metrology. The aim of this paper is, hence, to reformulate the KF theory within the possibility domain in compliance with the measurement uncertainty concept, in order to be able to consider both the random and systematic contributions to uncertainty (regardless of their distribution) that may affect the measurement process. An experimental setup is considered and the results obtained under different assumptions are reported.