Resilient multidimensional sensor fusion using measurement history

This work considers the problem of performing resilient sensor fusion using past sensor measurements. In particular, we consider a system with n sensors measuring the same physical variable where some sensors might be attacked or faulty. We consider a setup in which each sensor provides the controller with a set of possible values for the true value. Here, more precise sensors provide smaller sets. Since a lot of modern sensors provide multidimensional measurements (e.g. position in three dimensions), the sets considered in this work are multidimensional polyhedra. Given the assumption that some sensors can be attacked or faulty, the paper provides a sensor fusion algorithm that obtains a fusion polyhedron which is guaranteed to contain the true value and is minimal in size. A bound on the volume of the fusion polyhedron is also proved based on the number of faulty or attacked sensors. In addition, we incorporate system dynamics in order to utilize past measurements and further reduce the size of the fusion polyhedron. We describe several ways of mapping previous measurements to current time and compare them, under different assumptions, using the volume of the fusion polyhedron. Finally, we illustrate the implementation of the best of these methods and show its effectiveness using a case study with sensor values from a real robot.