Modeling of predicting the stochastic motion of near-Earth objects of space debris based on differential-Taylor transformations

The paper proposes a method for solving the problem of predicting the motion of a near-Earth object of space debris using a stochastic dynamic model. The model of the motion of a space debris object is specified by an ordinary stochastic differential equation, which takes into account the probabilistic nature of the initial conditions and variations in the atmospheric density. Prediction is carried out by the method of numerical integration which is developed on the basis of the multidimensional Pukhov’s differential-Taylor transformations. The initial and final data of stochastic prediction are the mathematical expectation and the correlation matrix of errors in determining the position of the space debris object. Applying of multidimensional differential-Taylor transformations makes it possible to reduce the methodical complexity of integrating of solving of an ordinary stochastic differential equation that describes the motion of a space debris object.