A method to deal with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) to nonlinearly map uncertainties from the observation space to the state space. When a minimum set of observations is available, DA is used to expand the solution of the IOD problem in Taylor series with respect to measurement errors. When more observations are available, high order inversion tools are exploited to obtain full state pseudo-observations at a common epoch. The mean and covariance of these pseudo-observations are nonlinearly computed by evaluating the expectation of high order Taylor polynomials. Finally, a linear scheme is employed to update the current knowledge of the orbit. Angles-only observations are considered and simplified Keplerian dynamics adopted to ease the explanation. Three test cases of orbit determination of artificial satellites in different orbital regimes are presented to discuss the feature and performances of the proposed methodology.

Dealing with uncertainties in angles-only initial orbit determination

ARMELLIN, ROBERTO;DI LIZIA, PIERLUIGI;
2016

Abstract

A method to deal with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) to nonlinearly map uncertainties from the observation space to the state space. When a minimum set of observations is available, DA is used to expand the solution of the IOD problem in Taylor series with respect to measurement errors. When more observations are available, high order inversion tools are exploited to obtain full state pseudo-observations at a common epoch. The mean and covariance of these pseudo-observations are nonlinearly computed by evaluating the expectation of high order Taylor polynomials. Finally, a linear scheme is employed to update the current knowledge of the orbit. Angles-only observations are considered and simplified Keplerian dynamics adopted to ease the explanation. Three test cases of orbit determination of artificial satellites in different orbital regimes are presented to discuss the feature and performances of the proposed methodology.
Differential algebra (DA); Initial orbit determination (IOD); Optical observations; Uncertainties mapping; Astronomy and Astrophysics; Space and Planetary Science
File in questo prodotto:
File Dimensione Formato  
ARMER02-16.pdf

Accesso riservato

Descrizione: Paper
: Publisher’s version
Dimensione 817.72 kB
Formato Adobe PDF
817.72 kB Adobe PDF   Visualizza/Apri
ARMER_OA_02-16.pdf

embargo fino al 04/05/2017

Descrizione: Paper Open Access
: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 498.09 kB
Formato Adobe PDF
498.09 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/990894
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 9
social impact