MATHEMATICAL MODEL FOR SOLVING THE NAVIGATION PROBLEM AND ANGULAR ORIENTATION SPACECRAFT
Currently, there is an increased interest in the creation of strapdown inertial navigation systems (SINS), which make up the information core of modern airborne systems for the orientation and navigation of spacecraft (SC). An urgent problem arises, which is associated with the development of high-precision algorithms for estimating and filtering data from the sensors of the SC motion parameters, the mathematical model of the SINS, calculating its errors and analyzing the effect of errors on the characteristics of the navigation system and orientation of the SC. A mathematical model is proposed for solving the problem of navigation and angular orientation of a small SC equipped with electromagnetic control elements, taking into account the filtering of “noisy” magnetometer data. The requirements are set for the accuracy of the angular orientation and stabilization of the SC in the mode of maintaining the triaxial orientation of the SC in the orbital coordinate system (OCS) and for the duration of the damping mode of the angular velocities obtained by the SC during separation from the launch vehicle (LV), and the mode of the initial construction of the triaxial orientation of the SC in OCS. The mathematical model includes: a model of the motion of the center of mass of the SC in the osculating elements of the orbit with specified parameters, a model of the angular motion of the SC around the center of mass, a model of the Earth’s magnetic field (EMF) and a model of filtering magnetometer data. As an arithm for filtering data from a magnetometer on the components of the magnetic induction vector of the EMF, a one-parameter algorithm of exponential smoothing (exponential moving average) is used, which belongs to the class of first-order filters with an infinite impulse response. The results of numerical simulation of the dynamic processes of navigation and the angular orientation of the SC after separation from the LV taking into account the filtering of magnetometer data by the method of exponential smoothing using mathematical models are presented, and the accuracy of the angular orientation and stabilization of the SC is estimated.
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