Errata: A Unified Mathematical Framework for Strapdown Algorithm Design

Abstract

A unified two-speed mathematical framework is described for strapdown inertial system integration algorithm design that uses a new concept for velocity/position updating. The velocity/position equations are structured using a Jordan-like attitude updating approach; the update equations are designed to provide the exact solution under particular input conditions, and the update inputs are then redefined to provide the correct solution under general motion. For the Jordan approach, the attitude update input is the Euler rotation vector generated by high-speed integration of a rotation vector rate equation; for the new velocity/position updating concept, inputs are velocity/position translation vectors generated by high-speed integration of translation vector rate equations. Exact differential equations are derived for the translation vectors that parallel the exact rotation vector rate equation originally derived by Laning and applied by Bortz in a Jordan-like structure. The new velocity/position concept coupled with the Jordan/Bortz/Laning attitude updating approach provides a unified framework for strapdown integration algorithm design. Continuous-form algorithms are developed within the unified framework based on simplified forms of the exact rotation/translation vector rate equations. Algorithm performance comparisons are presented based on derived analytical error equations under maneuver and vibration motion. A discussion is included on algorithm design approaches for digital integration of the rotation/translation vector rate equations. Simulation studies are described that numerically validate the accuracy of the principal analytical results.