On Precision Bound of Distributed Fault-Tolerant Sensor Fusion Algorithms

Sensors have limited precision and accuracy. They extract data from the physical environment, which contains noise. The goal of sensor fusion is to make the final decision robust, minimizing the influence of noise and system errors. One problem that has not been adequately addressed is establishing the bounds of fusion result precision. Precision is the maximum range of disagreement that can be introduced by one or more faulty inputs. This definition of precision is consistent both with Lamport's Byzantine Generals problem and the mini-max criteria commonly found in game theory. This article considers the precision bounds of several fault-tolerant information fusion approaches, including Byzantine agreement, Marzullo's interval-based approach, and the Brooks-Iyengar fusion algorithm. We derive precision bounds for these fusion algorithms. The analysis provides insight into the limits imposed by fault tolerance and guidance for applying fusion approaches to applications.