Numerical-analytical optimization of orientation algorithms on a spherical model of angular motion of a rigid body

The problem of numerical-analytical optimization of three algorithms for determining orientation quaternions due to refinement of coefficients in the structure of algorithms is considered. Of them, two algorithms use the orientation vector as an "intermediate parameter". The coefficients are refined on the basis of computer modeling and the minimization of the error of the accumulated computational drift using the analytical reference model of the spherical motion of a rigid body as a model rotational motion in a sequence of Krylov angles that change over time according to a linear law. For this, the test motion model is supplemented by modeling ideal information from the outputs of the angular velocity sensors in the form of quasi-coordinates using analytical formulas for the apparent rotation vector. It is shown that the accumulated error of computational drift on the proposed reference model of rotary motion has a linear law of growth with time for all algorithms under consideration. As a result of the numerical experiment, new values ​​of the coefficients in the structures of the algorithms were obtained, which minimize the error of the accumulated drift and improve the characteristics of the trend of this error. The carried out optimization leads to a decrease by an order of magnitude of the maximum error value and a change in the linearly growing nature of the dependence of the calculation drift error on time to an oscillatory one. The results of the computational experiment are given.