Guaranteed Approach for Orbit Determination with Limited Error Measurements

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Guaranteed Approach for Orbit Determination with Limited Error Measurements

Khutorovsky, Zakhary N. / Samotokhin, Alexander S. / Alfriend, Kyle T.

A nonstatistical statement of the orbit determination of a near-Earth space object in Earth orbit with certain limitations on the measurement errors is considered. The optimization criterion and the algorithms satisfying the limited error criterion are given. As distinguished from the traditionally used least-squares method, the interpolated algorithms are adapted to the measurement errors and always provide a guaranteed error range of the estimated parameters. The central algorithms, optimal in measurement errors in the minimax statement, have robust properties with regard to such errors. The projective robust-interpolated algorithms are independent of the measurement error upper limit. Computational schemes are given for the most practically interesting central and projective algorithms. The accuracy characteristics of such algorithms are given for different distributions of measurement errors using a mathematical simulation for typical situations occurring in the maintenance of a space objects catalog. It is demonstrated that the errors in the orbit determination of a space object using this nonstatistical approach may be less than the least-squares method errors.