Design of fault-tolerant interval functions based on their large-sample properties

Abstract

This work is concerned with the design of sensor fusion methods using the fault-tolerant interval functions proposed by K. Marzullo and U. Schmid. A trade-off exists between the precision of the interval functions and their tolerance to invalid input intervals. The study shows how the performances of the interval functions in terms of expected length and variance can be estimated from their asymptotic properties for large data samples. Under certain conditions, the limits of the fault- tolerant interval functions are proven to belong to the class of M-estimators, and to be asymptotically normal when the number of input intervals grows to infinity. The precision of the interval functions is predicted by the approximation of the actual functions by linear functionals that are easier to handle. The relevance of the asymptotic properties of the interval functions for finite input sets is tested on a simulated example.