A general theory for inertial navigator error modeling

Abstract

This paper presents a general theory for the development of error equations for an inertial navigator. A large space of possibilities is presented, based on how one defines the error parameters. For attitude, rotation vector parameterizations of the errors are introduced that are based on the difference between true can computed versions of each coordinate frame. Since these definitions are valid for large error angles, one can obtain general nonlinear equations for the psi- and phi-angle differential equations. These definitions are applicable to any mechanization and to either strapdown or platform navigators. This allows the development of general nonlinear formulas for the error dynamics, as well as new linear formulas using a different parameterization of the errors. There are two commonly used choices for the errors in position and velocity [1]; the more commonly used choice is to form the error as that of the true variable in the true frame less the computed variable in the computed frame. The alternate approach is one in which the error is the true variable less the computed variable, with both errors coordinatized in the computed frame. This latter approach gives new error equations not previously considered in the literature. Transformations between the new error parameterizations and the traditional ones are presented.