Karlsruhe Institute of Technology
On-line fault-detection in uncertain measurement and estimation systems is of particular interest in many applications. In certain systems based on the Kalman filter, this test can be performed by checking whether hyper-ellipsoids overlap. This test can be applied to detecting failure in the system itself or in the sensors used to determine the system state. To facilitate the practical application of such tests, the authors describe a simple condition for overlap of two ellipsoids and propose an efficient algorithmic implementation for testing this condition. There are applications in many other areas, such as collision avoidance or computer graphics.