A method to improve accuracy of definition and promptness of forecasting of spacecraft motion parameters

Abstract

The subject of the presented paper is the methods used to define spacecraft motion parameters. The goal of the paper is to develop approaches to improve accuracy of definition and promptness of forecasting of motion parameters. The tasks are 1) to determine the aspects influencing the result accuracy at defining initial conditions of the spacecraft motion, 2) to reveal the drawbacks of traditional methods and 3) to suggest some possible ways that can be used to improve accuracy and promptness at defining the spacecraft motion parameters. During the research it is revealed that the result accuracy at defining the initial conditions of the spacecraft motion is influenced by three aspects – a random component caused by presence of random errors in trajectory measurements, a dynamic component due to dynamic errors of the used model of the spacecraft motion and the error defined by the size of convergence region of the minimization method that is used to solve the multi-point boundary problem. To receive the least inaccuracy at defining the spacecraft motion parameters it is necessary to process some optimal quantity of measuring information which should ensure sufficient compensation of random errors and at the same time prevent the dynamic error from influencing considerably. At it it should be taken into account that the amount of the measured information should not be less than it is necessary to ensure convergence of the algorithm used to define those motion parameters. The main results are as follows. For solving the task of increasing accuracy of spacecraft motion parameters definition the paper suggests a new method based on minimization with definition of initial approximation region. The suggested method implements a non-local approach to minimization of the goal function, which ensures better as compared to traditional methods convergence. To increase the promptness of spacecraft motion forecasting it is suggested to use the mathematical apparatus of differential transformations. It allows decreasing the computational expenditures 3 to 4 times as compared to the regular ballistic and navigational algorithms while the given accuracy is preserved. On the basis of the performed research the following conclusions can be made. To increase the accuracy of the spacecraft motion parameters definition it is necessary to optimize the required number of measurement orbit passes, for that it is appropriate to use the Nelder-Mead search method. At implementing the advanced coordinate methods of the spacecraft control, to increase the promptness of the spacecraft motion forecasting, it is necessary to considerably decrease the computational expenditures for the motion parameters definition. To achieve that it is reasonable to use the mathematical apparatus of the differential transformations.