Analytical-numerical modeling of the process of solid body orientation in quaternions through a sequence of Euler angles for accurate analysis of orientation algorithms in SINS

Abstract

Two concepts for constructing analytical angular test motions of a rigid body for testing orientation algorithms when designing strapdown orientation systems are considered. The first concept is based on representing the orientation quaternion in a sequence of three Euler angles. The second concept is based on a formalized representation of the quaternion as a superposition of trigonometric functions of linear arguments and does not have a clear visual interpretation through the angles of elementary rotations. Analytical expressions for the model angular velocity can be obtained from the inverted kinematic equation in quaternions. The general case of linear Krylov and Euler angles is considered, as well as the case when one of the angles does not change over time. Analytical-numerical modeling of the angular motion of a rigid body and an assessment of the accuracy of the algorithm for determining the quaternion based on fourth- and fifth-order expansions with preliminary application of the Miller algorithm were carried out. For this purpose, the test movement model is supplemented by modeling ideal information from the outputs of angular velocity sensors in the form of quasi-coordinates using analytical formulas for the apparent rotation vector. It is shown that fifth-order formulas provide an improved estimate of the accumulated computational drift compared to fourth-order formulas. 
 Keywords: Euler angles, orientation vector, quaternion, reference model, test motion, quasi-coordinates, Miller orientation algorithm, numerical-analytical modeling, accumulated drift.