Interval Superposition Arithmetic for Guaranteed Parameter Estimation
For researchers in parameter estimation and set-based computing, ISA offers a novel method to address the bottleneck of constructing enclosures for image-sets of factorable functions.
The paper introduces interval superposition arithmetic (ISA) for guaranteed parameter estimation, improving enclosure accuracy and reducing the number of set-membership tests in set-inversion algorithms.
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.