Improvements in computational aspects of interval Kalman filtering enhanced by constraint propagation

Abstract

This paper deals with computational aspects of interval kalman filtering of discrete time linear models with bounded uncertainties on parameters and gaussian measurement noise. In this work, we consider an extension of conventional Kalman filtering to interval linear models [1]. As the expressions for deriving the Kalman filter involve matrix inversion which is known to be a difficult problem. One must hence find a way to implement or avoid this tricky algebraic operation within an interval framework. To solve the interval matrix inversion problem and other problems due to interval calculus, we propose an original approach combining the set inversion algorithm SIVIA and constraint satisfaction propagation. Several contractors are proposed to limit overestimation effects propagating within the interval Kalman filter recursive structure. Thus the description of our approach is followed by an application and we compare the proposed approach with interval kalman filtering developped in [1].

Integrity and Collaboration in Dynamic Sensor Networks

“…A particular focus of this project is on the propagation of imprecision, with the goal of significantly solving the problem of overestimation, which usually occurs with interval mathematics when finding suitable reformulations. The required interval matrix inversions may be addressed by approximations either leading to the loss of some solutions [ 59 ] or to some overestimation effects unless set inversion techniques are used [ 60 ].…”

Integrity – A Topic for Photogrammetry ?

“…A more natural approach could be using interval mathematics that just bound the remaining errors (Jaulin et al, 2001), for GNSS (Schön, 2016, Schön, Kutterer, 2005, Drevelle, Bonnifai, 2009, Dbouk, Schön, 2020, for images (Rohou et al, 2017, Kenmogne et al, 2018, for car navigation (Wörner et al, 2016). A state propagation via Kalman filtering is described in (Xiong et al, 2013, Chen et al, 1997. A final decision about the adequate modeling strategy is complicated.…”