Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007acasn..48..343c&link_type=abstract
Acta Astronomica Sinica, vol. 48, no. 3, p. 343-354
Astronomy and Astrophysics
Astronomy
Celestial Mechanics: Determination Of Orbit, Celestial Mechanics: Numerical Method
Scientific paper
In practical application, the perturbed unit vector method (PUVM1) is widely used to determine the orbit by the observation data related to artificial satellites. Some improvement efforts have been done to this method in this paper. Firstly, based on the model of measurement error and the idea of unit vector method, a new mathematical model MMUVM which is essentially a nonlinear optimization problem is introduced. Using simulation data and observation data, the objective function of MMUVM can be formed and solved respectively. Numerical results show that the mathematical model MMUVM is correct and the direct search method, i.e. the quadratic tri-diagonal interpolation DFO method is practical and effective.Secondly, based on the relationship of the semi-normal equation of PUVM1 and the gradient of MMUVM, it points out that MMUVM is a reasonable generalization of PUVM1 and PUVM1 is essentially a simplification to MMUVM. It is a big residual problem when MMUVM is formed by multi-circle long arc data, on the contrary, it is a little residual one when MMUVM is obtained by short arc data. The optimization problem of MMUVM can be solved by a suitable algorithm. The original PUVM1 algorithm is only suitable for the little residual problem. It can be obtained that PUVM1 may be used to determine the preliminary orbit by short arc data, but can not be used to deal with the job of orbit improvement by multi-circle long arc data. Finally, a discussion is made on the convergence of the iterative scheme which is used to solve the semi-normal equation of PUVM1. The corresponding numerical examples are also presented to point out that the iterative scheme of PUVM1 is convergent conditionally. It means that even if there is a reasonable solution to the semi-normal equation of PUVM1, it may be also divergent using the iterative scheme of PUVM1 in some cases.
Chen Wei-Sheng
Lu Ben-Ku
Ma Jing-Yuan
No associations
LandOfFree
The mathematical model of unit vector method and the iterative method for its simplification does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The mathematical model of unit vector method and the iterative method for its simplification, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The mathematical model of unit vector method and the iterative method for its simplification will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1028640