Interval Superposition Arithmetic for Guaranteed Parameter Estimation

Abstract

The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks in GPE algorithms is the construction of enclosures for the image-set of factorable functions. In this paper, we introduce a novel set-based computing method called interval superposition arithmetics (ISA) for the construction of enclosures of such image sets and its use in GPE algorithms. The main benefits of using ISA in the context of GPE lie in the improvement of enclosure accuracy and in the implied reduction of number set-membership tests of the set-inversion algorithm.