Evaluation of parity equations for gyro failure detection and isolation

A set of seven unique parity equations (linear dependence relationships) are derived for an octahedron inertial measurement unit (IMU) having six skew-redundant sensing axes. Single and dual axis gyro failure detection and isolation (FDI) algorithms, utilizing the parity equations, are evaluated for a typical earth launch to geosynchronous orbit mission. The IMU implemented with single degree-of-freedom gyros had better FDI characteristics but was relegated in favor of the more cost effective IMU with two degree-of-freedom gyros. A life cycle cost analysis showed that to be more cost effective the latter IMU was required to yield an FDI probability greater than 0.98 with false alarm rate less than 0.001. This capability was verified by Monte Carlo simulation.