Performance analysis of fault detection systems based on analytically redundant linear time-invariant dynamics

In the aircraft industry, it is common to use physically redundant components to ensure that the overall system meets the necessary safety requirements. For systems where physical redundancy is impractical (e.g, Unmanned Aerial Vehicles), analytical redundancy can be used to reduce the number of components needed. However, it is more difficult to certify the safety of an analytically redundant system. This paper presents a performance analysis framework that applies to both physically and analytically redundant sensor systems with linear time-invariant dynamics and additive faults. The framework is used to compare and certify the performance of two air-data sensor examples - one with physically redundant altitude sensors, and another that exploits the analytical relationship between altitude, airspeed, and flight path angle. In both examples, a threshold fault detection scheme is used.