Calibration error analysis of inertially stabilized platforms using quaternions and octonions in rotation decomposition

Abstract

In the calibration process of the inertially stabilized platforms with a high-precision turntable and an autocollimator, significant calibration errors can result from the axis misalignments between the inertially stabilized platforms and the turntable. Based on the relationship between spatial rotations and quaternions or octonions, this article proposes a representation using octonions to realize the decomposition of the rotation axis in two perpendicular axes and subsequently derives the calibration error model. The test results demonstrated that the error is significantly improved after compensation. The azimuth variance is reduced from 0.1379(°)² to 0.0492(°)², which offers a more accurate set of data for further compensation based on the error model of the platform itself.