A Derivation of the Nonlinear Platform Orientation Error Equations for an INS: With an Introduction to Rotating Coordinate Frames

摘要

This report documents a derivation of the nonlinear platform orientation error equations for a local level inertial navigation system (INS). These differential equations govern the Euler angles that relate the actual orientation of the INS platform axes to the ideal orientation of these axes. The derivation deals with specific coordinate representations from the outset, by explicitly including the time-dependent transformations that relate the particular coordinate frames involved in the problem. Thus, the elements of the required angular velocity vectors are obtained in a very natural fashion, and the resulting equations incorporate the transformations needed to ensure computational consistency. A tutorial description of this approach to problems involving rotating coordinate frames is included in this report. (Author)