Determination of the Most Probable Elements of a Satellite Orbit from Incomplete Systems of Elements
Normal equations are ill-conditioned if the observations embrace a small arc of the satellite orbit. In order to avoid the great scattering of the results in this case some elements are to be fixed. Then the non-fixed elements, determined with small random errors, form an incomplete system of elements which is not sufficient to calculate satellite coordinates definitely. When computing the orbit a number of such incomplete systems refered to different time intervals may be obtained. In this case there arises a problem of determining the most probable set of elements which is sufficient for the satellite coordinates to be found. This problem has been solved by the method of maximum likelihood in general form which allows to use the formulae for determining both elements and disturbing parameters such as the coefficients of the earth potential, air drag coefficients and so on.
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