In this paper, we present a new uncertainty propagation algorithm based on interval arithmetic, and its applications for space surveillance. Using validated simulation, the goal is to explore the benefits of a set-based approach of estimation and data association for satellite tracking. The presented algorithm capitalises on the position measures of a satellite to improve its estimation and reduce uncertainties on its trajectory. Our approach also contributes to data association by computing the precision required for a measure to belong to a given track with confidence-levels. This paper illustrates the contributions of this new algorithm with several scenarios of orbit determination and satellite tracking and their numerical simulations.