Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

Details Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

Jul 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010acasn..51..285p&link_type=abstract

Acta Astronomica Sinica, vol. 51, no. 3, p.285-298

Astronomy and Astrophysics

Astronomy

Celestial Mechanics: Orbit Calculation And Determination, Method: Numerical

Scientific paper

The traditional LSE (least square estimation) method for orbit determination will not be optimal if the error of observational data of orbit determination does not obey Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method for orbit determination is presented to deal with the non-Gaussian distribution cases because of the adaptability of p-norm distribution. Through estimating the parameter p, the results can be more reasonable. The corresponding character of Lp estimation is analyzed. It is proved that the traditional Lp estimation method is not a robust method. So a stable Lp estimation based on data depth weighting is put forward to deal with the model error and outlier. In orbit determination process, the outlier of observational data and coarse model error can be quantitatively described. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the common Lp estimation and the break down point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is more perfect. Finally, taking the Space Based Space Surveillance System as an example to make simulation experiments, the results show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space based observation platform, LSE will not be optimal even though the observational data obeys Gaussian distribution and the orbit determination precision by the self-adaptive stable Lp estimation method is much higher than that by the common LSE method.

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