Table 1 - uploaded by Romain Di-Costanzo

Content may be subject to copyright.

Source publication

The goal of the Draper Semi-analytical Satellite Theory (DSST) Standalone Orbit Propagator is to provide the same algorithms as in the GTDS orbit determination system implementation of the DSST, without GTDS's overhead. However, this goal has not been achieved. The 1984 DSST Standalone included complete models for the mean element motion but trunca...

## Contexts in source publication

**Context 1**

... the 1997 upgrade to the DSST Standalone upgrade touched large portions off the source code, the testing described in Reference 8 only focused on the mean element equations of motion (see Tables 1 and 2 in Ref. 8). ...

**Context 2**

... Low inclination transfer orbit Tables 1 though 4 give the initial conditions for the four test cases. Figures 9 through 14 are the results of comparing Orekit java DSST and F77 DSST Standalone for the LEO case. ...

## Citations

... It is an interesting tool for a fast and accurate orbit propagation, close to current needs. Its development started in the mid-1970s at the Computer Sciences Corporation of Maryland by a team led by Paul J. Cefola [5]. ...

Space objects catalog maintenance demands an accurate and fast Orbit Determination (OD) process to cope with the ever increasing number of observed space objects. The development of new methods, that answer the two previous problems, becomes essential.
Presented as an alternative to numerical and analytical methods, the Draper Semi-analytical Satellite Theory (DSST) is an orbit propagator based on a semi-analytical theory allowing to preserve the accuracy of a numerical method while providing the speed of an analytical method. This propagator allows computing the mean elements and the short-period effects separately. We reproduced this architecture at the OD process level in order to be able to return, as desired, the mean elements or the osculating elements. Two major use cases are thus possible: fast OD for big space objects catalog maintenance and mean elements OD for station keeping needs.
This paper presents the different steps of development of the DSST-OD included in the Orekit open-source library [1]. Integrating an orbit propagator into an OD process can be a difficult process. Computing and validating derivatives is a critical step, especially with the DSST whose equations are very complex. To cope with this constraint, we used the automatic differentiation technique. Automatic differentiation has been developed as a mathematical tool to avoid the calculations of the derivatives of long equations. This is equivalent to calculating the derivatives by applying chain rule without expressing the analytical formulas. Thus, automatic differentiation allows a simpler computation of the derivatives and a simpler validation. Automatic differentiation is also used in Orekit for the propagation of the uncertainties using the Taylor algebra.
Existing OD applications based on semi-analytical theories calculate only the derivatives of the mean elements. However , for higher accuracy or if the force models require further development, adding short-period derivatives improves the results. Therefore, our study implemented the full contribution of the short-period derivatives, for all the force models, in the OD process. Nevertheless, it is still possible to choose between using the mean elements or the osculating elements derivatives for the OD.
This paper will present how the Jacobians of the mean rates and the short-periodic terms are calculated by automatic differentiation into the DSST-specific force models. It will also present the computation of the state transition matrices during propagation. The performance of the DSST-OD is demonstrated under Lageos2 and GPS Orbit Determination conditions.

... The standalone DSST is implemented in FORTRAN 77, with command line executables. The evolution of the standalone version and its working architectural information can be found in Cefola et al. (2014). To improve the accuracy performance of DSST, the available standalone version was enhanced with additional perturbing force models during the current study. ...

Catalog maintenance for Space Situational Awareness (SSA) demands an accurate and computationally lean orbit propagation and orbit determination technique to cope with the ever increasing number of observed space objects. As an alternative to established numerical and analytical methods, we investigate the accuracy and computational load of the Draper Semi-analytical Satellite Theory (DSST). The Standalone version of the DSST was enhanced with additional perturbation models to improve its recovery of short periodic motion. The accuracy of DSST is, for the first time, compared to a numerical propagator with fidelity force models for a comprehensive grid of low, medium, and high altitude orbits with varying eccentricity and different inclinations. Furthermore, the run-time of both propagators is compared as a function of propagation arc, output step size and gravity field order to assess its performance for a full range of relevant use cases. For use in orbit determination, a robust performance of DSST is demonstrated even in the case of sparse observations, which is most sensitive to mismodeled short periodic perturbations. Overall, DSST is shown to exhibit adequate accuracy at favorable computational speed for the full set of orbits that need to be considered in space surveillance. Along with the inherent benefits of a semi-analytical orbit representation, DSST provides an attractive alternative to the more common numerical orbit propagation techniques.