Optimum Skewed Redundant Inertial Navigators

The problem of proper placement of the inertial sensors to optimize system performance is important to system designers. This is especially true of redundant strapdown systems that employ more sensors than the conventional, mutually orthogonal sets of three. In systems designed for a free fall environment and with no preferred direction, such as for spacecraft attitude reference, the sensor input axes should divide the three-space equally, and can thus be viewed as being normal to the faces of regular polyhedra.' In Earth-bound inertial navigators, the effect of gravity-dependent sensor errors and the generally reduced effect of azimuth errors on navigation accuracy significantly alter the situation. Both effects tend to decrease sensor elevation angles in an optimized system. Formulas are derived and curves are drawn for optimum sensor elevation and azimuth angles vs a 0-sensitive sensor error parameter, and a mission relative azimuth error parameter. Tetrad, pentad, and hexad arrays are analyzed, affording a dramatic improvement in accuracy as well as autonomous fault isolation and/or detection capability.