Formal parametric kinematic model of conical type of angular motion of a rigid body and its application to precision analysis and optimization of orientation algorithms

The paper is devoted to the problem of developing orientation algorithms and increasing the accuracy of orientation determination in strapdown inertial systems of orientation of moving objects by using new analytical models of angular motion and improving existing algorithms for determining orientation quaternions. The problem of numerical-analytical optimization of two algorithms for determining the orientation quaternion is considered by refining the coefficients in the structure of the algorithms, which use the rotation vector as an “intermediate parameter”. The refinement of the coefficients in the algorithms is based on computer modeling and software-numerical minimization of the error of the accumulated computational drift using as a model test motion an analytical reference model of the angular motion of a rigid body, which is based on a formal parametric kinematic model of the coning type. For this, the test motion 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 seeming turn vector. It was experimentally obtained that the error of the accumulated computational drift on the parametric reference model of the coning type has a linear law of growth with time for all non-optimized algorithms considered. As a result of the numerical experiment, new values ​​of coefficients in the structures of algorithms were obtained that minimize the error of the accumulated drift and improve the characteristics of the trend of this error without worsening the error of the quaternion norm. The optimization carried out for one of the algorithms leads to a decrease in the maximum module of the error of the accumulated drift and a change in the linearly increasing nature of the dependence of the error of the computational drift on time to an oscillatory nature without a tendency to grow with time. The results of the conducted computational experiment are presented.