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Comparative analysis of classical and approximate approaches of a covariance matrices errors calculations for parameters estimations of space objects orbit evolution forecast

Keywords:

I.K. Kostin, A.A. Rozhkov


Results of revaluation of error covariance matrices for different methods used for orbit parameters of space object moving prediction were compared. Results got by means of classical method using linear transformation of input covariance matrix using matrix of partial derivatives of forecasting parameters by it\'s initial values were used as a reference. An alternative method was to use an elementary formula that associates evolution of discrepancy of time of revolution from start till n-th revolution forecast with discrepancy of period of rotation and it\'s reduction discrepancy. The simplicity and clear physical meaning of such a formula result to it\'s prevalence in applied calculations. Coefficients for this linear formula were clearly detected from it\'s physical meaning but have mathematical meaning as partial derivatives of transformation function. Changing these coefficients to the calculated values of corresponded partial derivatives we\'ve got another alternative method for covariance matrices forecast. Results got by means of this second method provides far better fitness to the reference results than the first alternative method results. In passing the possibility of simplified precise calculation of required partial derivatives was found. Thus the second alternative method investigated here becomes a compromise between tedious referenced method and simple but less accurate first alternative method.
References:
  1. Rao S.R. Linejjnye statisticheskie metody i ikh primenenija. M.: Nauka. 1968.
May 29, 2020

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