Abstract

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-ot-freedoni 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. HE requirement for high reliability and low life-cycle cost in a production program involving many vehicles makes the selection of a skew-redundant strapdown inertial measurement unit (IMU) an attractive choice. Gimbaled orthogonal platform systems which provide single-point failure protection require triple modular redundancy (TMR) implementation with a significant penalty in size, weight, power, and production cost. The decision to go skewed is complicated somewhat by the need to provide a highly effective instrument failure detection and isolation (FDI) algorithm. A TMR system can simply vote each set of three independent redundant axes and thereby avoid the need for special algorithms for failure detection and isolation. Soft failures are, by definition, undetectable with built-in test equipment (BITE). They gradually degrade IMU performance and, if undetected, may cause end-of-mission (EOM) accuracy specifications to be violated. The effectiveness of an FDI algorithm is measured by how likely it is to detect and correctly isolate (cover) a soft failure before it has a chance to jeopardize mission success. At the same time the algorithm must not have a high probability for false alarm (i.e., inadvertently causing the removal of a good instrument). Several different types of FDI algorithms have been developed and/or evaluated by numerous authors.J'3 One of the most attractive, from the point of view of ease of implementation in an airborne digital computer (ADC), is the parity equation algorithm. This paper presents results of an analysis of parity equation efficacy for two strapped-down skewed IMU's. A. Description of Skewed IMU's Figure 1 illustrates the IMU type discussed in the paper. This is the so-called octahedron configuration. The body frame is shown as XNB, YNB, ZNB with the instrument input axes labeled numerically 1 through 6. Each axis contains a gyro and an accelerometer. Complimentary axes in the octahedron IMU (i.e., 1 and 2, 3 and 4, and 5 and 6) make angles of 90 deg with each other and are symmetrically placed with respect to the body system. That is to say, instruments 1 and 2 both are inclined 45 deg with respect to the ZNB body axis, 3 and 4, 45 deg with respect

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