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Revisiting the DSST Standalone Orbit Propagator

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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 truncated models for the short-periodic motion. The 1997 update included the short-periodic terms due to tesseral linear combinations and lunar-solar point masses, 50 x 50 geopotential, and J2000 coordinates. However, the 1997 version did not demonstrate the expected improved accuracy. Three projects undertaken by the authors since 2010 have led to the discovery of additional bugs in the DSST Standalone which are now resolved.
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Revisiting the DSST Standalone Orbit
Propagator
Paul J. Cefola
1
, Zachary Folcik
2
, Romain Di-Costanzo
3
,
Nicolas Bernard
3
, Srinivas Setty
4
and Juan Félix San Juan
5
1
Department of Mechanical and Aerospace Engineering
State University of New York at Buffalo
Amherst, NY, USA
2
Arlington, MA, USA
3
CS Communications & Systemes
31506 Toulouse Cedex 5, France
4
Deutsches Zentrum fur Luft- und Raumfahrt (DLR),
German Space Operations Center (GSOC)
5
Universidad de La Rioja, Logrono, Spain
Paper AAS 14-411
AAS/AIAA Space Flight
Mechanics Meeting
Santa Fe, New Mexico 26-30 January 2014
AAS Publications Office, P.O. Box 28130, San Diego, CA 92198
Rev 8
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REVISITING THE DSST STANDALONE ORBIT PROPAGATOR
Paul J. Cefola,
*
Zachary Folcik,
Romain Di-Costanzo,
Nicolas Bernard,
§
Srinivas Setty
**
, and Juan Félix San Juan
††
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 mo-
tion but truncated models for the short-periodic motion. The 1997 up-
date included the short-periodic terms due to tesseral linear combinations
and lunar-solar point masses, 50 x 50 geopotential, and J2000 coordi-
nates. However, the 1997 version did not demonstrate the expected im-
proved accuracy. Three projects undertaken by the authors since 2010
have led to the discovery of additional bugs which are now resolved.
*
Adjunct Professor, Department of Mechanical and Aerospace Engineering, State University of New York at Buf-
falo, Amherst, NY, USA, paulcefo@buffalo.edu; also Consultant in Aerospace Systems, Spaceflight Mechanics,
and Astrodynamics, Vineyard Haven, MA, USA.
53 Maynard Street, Arlington, MA, USA, zjfolcik@mit.edu; Zachary Folcik is currently Technical Staff at the
MIT Lincoln Laboratory
‡‡
CS Communications & Systemes, 5 rue Brindejonc des Moulinais, 31506 Toulouse Cedex 5 (France),
Email: romain.di-costanzo@c-s.fr
§
CS Communications & Systemes, 5 rue Brindejonc des Moulinais, 31506 Toulouse Cedex 5 (France),
Email: nicolas.bernard@c-s.fr
**
Ph.D Student, Space Situational Awareness, Deutsches Zentrum fur Lüft- and Raumfahrt (DLR), Ger-
man Space Operations Center (GSOC), ncher Str. 20, 82234 Wessling, Germany, Email:
Srinivas.Setty@dlr.de
††
Professor,
Department of Mathematics and Computation,
Universidad de La Rioja, Logroño, Spain, Email:
juanfelix.sanjuan@unirioja.es
(Preprint) AAS 14-411
Rev 8
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INTRODUCTION
Development of the DSST started in the mid 1970’s at the Computer Sciences Corporation in
Maryland with focus on the mean element motion due to conservative perturbations
geopotential and lunar-solar point masses. This development employed the GTDS orbit determi-
nation system as the host environment. Development later continued at the Charles Stark Draper
Laboratory in Cambridge, Massachusetts. All of these developments employed the non-singular
equinoctial elements.
The Draper development initially focused on the following areas:
Numerical averaging concepts for the mean element motion due to the non-
conservative perturbations – atmospheric drag and solar radiation pressure
Coupling between oblateness and atmospheric drag
Analytical short-periodic motion models for the zonal harmonics, tesseral m-
dailies, tesseral linear combination terms, lunar-solar point masses, and J2-
secular/tesseral m-daily coupling
Interpolation strategies for evaluating the mean elements and the short periodic
Fourier coefficients at times off their respective integration grids
Refinement of tesseral resonance models including consideration of the Hansen
coefficients
Semi-analytical theory for the partial derivatives of the perturbed motion
Weighted least squares concept to directly estimate precise mean elements from
tracking data
Kalman Filter concepts to recursively estimate precise mean elements directly
from tracking data
The initial development of the Draper Semi-analytical Satellite Theory discussed above used
the IBM mainframe GTDS orbit determination system as the development environment. Howev-
er, users external to the Draper Laboratory wanted access to the Semi-analytical Satellite Theory
without the ‘overhead’ of GTDS. In this context, ‘overhead’ related to the learning curve associ-
ated with GTDS.
The DSST Standalone was developed in 1983-84 to provide better access to the DSST (Ref.
1). This version of the Standalone included complete models for the mean element motion (based
on the Mean of 1950.0 integration and the 21 x 21 geopotential conventions then employed in
GTDS) and a portion of the short-periodic models (zonal harmonic and tesseral m-daily terms).
The intent was to provide accuracy for LEO orbits of approximately 200 meters. Analytical
models for the lunar-solar short periodic motion were not initially included in the DSST
Standalone because the GTDS implementation of these models was still being tested (Ref. 2).
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The development of the Standalone was supported by the Aerospace Corporation; Aerospace
subsequently modified the Standalone to interface with the CDC computers then employed for
astrodynamic applications at Aerospace (Ref. 3). Also, Aerospace interfaced the DSST
Standalone with the MEANELT and the SATPROP programs which were standards in the
Astrodynamics Department (Refs. 4, 5). At the Draper Laboratory, the time-independent lunar-
solar short periodic model (Ref. 2) was added to the DSST Standalone in the late 1980s and these
updates were shared with the Astrodynamics Department at the Aerospace Corporation. At that
point, the accuracy of the Standalone models was assumed to match that of the GTDS DSST
models.
By 1996, extensive improvements to the DSST had been made in the GTDS environment.
These included the expansion of the geopotential to include 50 x 50 fields, the additional of solid
Earth tide models, and J2000 coordinate systems (Refs. 6, 7). In 1997, an effort to extensively
upgrade the DSST Standalone was undertaken (Ref. 8). This effort included:
50 x 50 geopotential models
Solid Earth tide contributions to the mean element equations of motion
J2000 coordinate systems
Short periodic motion models for the Tesseral Linear Combination terms
Improvements to the maintainability of the source code
To improve the maintainability of the source code, the following issues were addressed:
Conformance to coding standards
Elimination of COMMON blocks and their replacement with structure records
and modules
Preparation for FORTRAN 90
While 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).
The DSST Standalone next received significant consideration in 2008-2009 when develop-
ment of Linux and Windows versions of the DSST Standalone was the goal (Ref. 9). The DSST
Standalone was originally installed at MIT LL on the same SGI-UNIX machine used for GTDS
R&D. The code was maintained under version control on a Linux machine at MIT LL. The Intel
FORTRAN Compiler version 9.1 was used to compile the code. On the Windows side, the code
was implemented under Microsoft Visual Studio and Intel Visual Fortran 11; the port was
straight-forward. Comparison testing of GTDS versus the Linux DSST Standalone was initiated
(see Tables 6 and 7 in Ref. 9). These tests included some short periodic geopotential perturba-
tions but the degree and order of the field was limited to 2 x 2. Some discrepancies in the DSST
Standalone were uncovered. The test protocol for Windows DSST Standalone was to use the
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LLNL SatOrb program (a special perturbations program) to least-squares fit position and velocity
data generated with the Windows DSST Standalone. This latter effort was not completed.
The roadmap of this paper is as follows. In Section 2, we discuss the three demonstration pro-
jects that have contributed to the refinement of the DSST Standalone. Each of the projects has a
test process and discussion of these test processes is emphasized. In Section 3, we discuss the
fixes that have been made to the DSST Standalone and anticipate the impact of these fixes. Sec-
tion 4 gives current numerical results for the comparison of the Orekit java DSST with DSST
Standalone. These results constitute an evolution of the Orekit DSST versus F77 Standalone
DSST comparisons given in February 2013 (Ref. 10). Conclusions and Future Work end the pa-
per.
OPEN SOURCE SOFTWARE SPACE SITUATIONAL AWARENESS
DEMONSTRATION PROJECTS
In 2010, the first author presented a paper with the title Open Source Software Suite for
Space Situational Awareness for and Space Object Catalog Work”
(Ref. 11). This paper
proposed three demonstration tasks:
1. Creation of a Web interface for the DSST Standalone Orbit Propagator
2. Migration of the DSST Standalone Orbit Propagator from Fortran 77 to an Ob-
ject-Oriented software platform
3. Non-invasive encapsulation of the Linux GTDS R&D Orbit Determination sys-
tem
The top level design of the F77 DSST Standalone is given in Figure 1.
In 2011 and 2012, three projects were initiated which address the first two of the three demon-
strations tasks:
1. The DSST Standalone was included on the
Astrody
Tools
Web
Web-Site prototype,
which provided a friendly web interface for DSST (Ref. 12). The
Astrody
Tools
Web
web site was established at the Universidad de La Rioja, Spain. This prototype
has now evolved into a stable platform based on the Drupal open source content
management system (Ref. 13).
2. The DSST was implemented as an orbit propagator in object-oriented java as
part of Orekit open source library for space flight dynamics (Refs. 10 and 14
thru 16).
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3. The accuracy and computation time characteristics of the DSST Standalone rela-
tive to the requirements of space object catalog maintenance are being evaluated
by the Space Situational Awareness (SSA) Group at the DLR GSOC (Refs. 17
and 18).
WEB DSST
Figure 2 shows the encapsulation process followed by the Astro Web Tools team in order to
integrate DSST in the software repository at the Universidad de La Rioja. The DSST Web inter-
face allows registered users to access and execute the original DSST Standalone through an easy-
to-use graphical user web-interface after completing the appropriate form with the initial values
and parameters. We note that the core DSST Standalone code did not require modification; only
its interface required re-engineering.
At University of Rioja, the DSST Standalone operates under the Linux system CentOS. It is
compiled with the Intel Fortran compiler version 11.1.
Figure 3 illustrates the test processes available for the Web DSST. Basically, the process con-
sists of comparisons between the DSST Standalone executing at the University of Rioja and the
DSST Standalone executing in the USA.
These comparisons are supported by the process originally used to test the Standalone DSST
vs the GTDS DSST which is described in Figure 4.
Referring to Figure 4, the GTDS Cowell orbit propagator can be used to generate ‘truth’ posi-
tion and velocity time history files. These position and velocity files can be used as observation
data in GTDS DSST orbit determination runs, either using the mean element differential correc-
tion (DC) or mean element Kalman Filter estimators. This process is given the name Precise
Conversion of Elements (PCE). If the force models are consistent between GTDS Cowell and
GTDS DSST, we expect the final residuals to be small. We can then compare GTDS DSST with
the DSST Standalone. We can also generate the ‘truth’ position and velocity time histories with
the DSST Standalone. Assuming a preprocessor to transform the DSST Standalone output to an
appropriate format, the GTDS Cowell DC program can process the DSST Standalone output file
as observation data. Again, the final residuals should be small if the force models are compatible.
If the same mean elements are input to the GTDS DSST program and the DSST Standalone
program, then the two programs should produce equivalent mean element time histories and
equivalent Fourier coefficients for the short periodic motion.
Additionally, explicit formulas for the mean element rates and the short periodic formulas in
the DSST were constructed with the Macsyma utility (Refs. 19 and 20). These formulas have
been reproduced with the current open source Maxima utility. The numerical results from such
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explicit formulas can be compared with results from the recursive code in GTDS DSST and the
DSST Standalone.
OREKIT JAVA DSST
Orekit is a library for space flight dynamics. Orekit started in 2002 as a small in-house prod-
uct developed by CS Systèmes d’Information, Toulouse, France. The ORbits Extrapolation KIT
(Orekit) was intended to be a fundamental asset for CS in addition to serving as a basis for cus-
tom systems developed for customers (Ref. 14). The design goals were to write a tool that is easy
to adapt, up to date with respect to recent space flight dynamics models, and still compatible with
older models. Over several years the library matured from a small set of core components to a
full-fledged collection of core classes and associated algorithms: orbits, time, reference frames,
bodies, propagation, attitude, etc. Orekit was first published under the terms of the Apache li-
cense V2 in July 2008. The Apache license is a ‘permissive’ license – the Orekit source code is
published as open-source but distribution of source code for derived works is not mandated (Ref.
15). In early 2011, a public source-forge site was established for Orekit. The Orekit forge pro-
vides public access to activity, bug reports, source code repository, documentation, and down-
loads (Ref. 16). Open governance was established for Orekit in 2012 using a meritocratic model
(Ref. 16). The most prominent application of the meritocratic model is the Apache Software
Foundation (Ref. 21) (Linux also has a very prominent meritocratic model). An initial meeting of
the Orekit Project Management Committee was held in July 2012 (Ref. 22). This meeting led to
an updated Orekit governance charter which is available at Ref. 23.
The wide range of applications of the DSST motivated the inclusion of the DSST in the Orekit
library. The decision to proceed on the development of an Orekit DSST was made in 2011.
Since Orekit employs the java object-oriented programming platform (Refs. 24 and 25), migra-
tion of the DSST to java is necessary for the DSST to be included in Orekit. Migration of the
DSST to an object-oriented programming platform also was identified earlier as a demonstration
task for the Open Source Software Suite for Space Situational Awareness and Space Object Cata-
log project (Ref. 11).
The initial design for the inclusion of the DSST in Orekit was described in (Ref. 10). An
overview is given in Figures 5 and 6. Since February 2013, testing of Orekit DSST has continued
and we report the current results of that testing in this paper.
The options available for testing Orekit DSST are illustrated in Figure 7. The primary ap-
proaches are:
1. Comparison of orbits created with the Orekit numerical integrator with orbits
created with the Orekit DSST
2. Comparison of orbits created with the Orekit java DSST with orbits created with
the F77 DSST Standalone
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The test results given in this paper are based on this second option.
GSOC EVALUATION OF DSST VERSUS SSA REQUIREMENTS
The purpose of the GSOC study is to find an optimal orbit propagation method which is suita-
ble for space object cataloging.
Figure 8 illustrates the test options available. We note the role of the ODEM Special Perturba-
tion Orbit Determination system and particularly the use of the ODEM least squares estimator to
provide position and velocity vectors compatible with the mean elements assumed in the F77
DSST Standalone.
Refs. 17 and 18 provide initial results of this effort for the LEO, MEO, and GEO flight re-
gimes. This effort has been very helpful in identifying areas for refinement of the F77 DSST
Standalone software, particularly the short periodic motion model
FIXES TO THE F77 DSST STANDALONE SOFTWARE, 2011-2013
The following are the routines in the F77 DSST Standalone that were modified to correct
bugs:
READ_EPOT.FOR
NKREAD.FOR
SPTESS.FOR
SETSP.FOR
PTHIRD.FOR
READ_EPOT.FOR was modified to allow the usage of GTDS-style geopotential files with on-
ly one geopotential model.
NKREAD.FOR is the routine for reading the Newcomb operator file. The Newcomb opera-
tors are used to initialize the Hansen coefficient recursions for both the tesseral resonance and the
tesseral linear combination short-periodic terms.
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SPTESS.FOR is the driver for the DSST tesseral linear combination short periodic terms. The
bug in this routine allowed it to turn off the tesseral resonance terms in the mean element equa-
tions of motion.
SETSP.FOR is the routine that allows convenient selection of moderate or high accuracy con-
figurations for the DSST for the various flight regimes
PTHIRD.FOR primarily is the driver for the third-body mean element rates. However, it is al-
so used in the calculation of the constant terms in the third-body short-periodic expansion in the
eccentric longitude. The bug in PTHIRD.FOR was associated with the constant terms and disa-
bled the third-body short periodic models in the DSST Standalone.
Interestingly, the bugs in SPTESS.FOR and PTHIRD.FOR both seem are associated with the
effort to remove traditional common blocks from the DSST Standalone.
NUMERICAL TEST CASES
We employ four test cases in this paper:
LEO Sun-synchronous orbit
GPS 12 hr orbit
SIRIUS 24 hr elliptical orbit at critical inclination
Low inclination transfer orbit
Tables 1 though 4 give the initial conditions for the four test cases.
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Table 1: LEO Sun-synchronous Test Case
Mean Keplerian Element
Epoch 2013 July 23, 3 hr 3 min 5.97 sec UTC
Semi-major Axis
7198.4832626
km
Eccentricity
0.00012750114
Inclination
98.6894245
deg
Right Ascension of the Ascending Node
263.17707959
deg
Argument of Perigee
56.9237741458
deg
Mean Anomaly
303.21338071
deg
TOD Coordinate System
50 x 50 geopotential
Third-body point masses
Atmosphere Drag
Harris-Priester density
Table 2: GPS 12 hr Test Case
Mean Keplerian Element
Epoch 1996 January 1, 1 hr 0 min 0.0 sec UTC
Semi-major Axis
26560.271744
km
Eccentricity
0.00089794449
Inclination
54.905215982
deg
Right Ascension of the Ascending Node
336.831733455
deg
Argument of Perigee
5.54483916534
deg
Mean Anomaly
354.376050766
deg
TOD Coordinate System
8 x 8 geopotential
Third-body point masses
Solar Radiation Pressure
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Table 3: SIRIUS 24 hr Elliptical Orbit (Critical Inclination) Test Case
Mean Keplerian Element
Epoch 2000 July 3, 0 hr 0 min 0.0 sec UTC
Semi-major Axis
42163.393
km
Eccentricity
0.2684
Inclination
63.435
deg
Right Ascension of the Ascending Node
285.0
deg
Argument of Perigee
270.0
deg
Mean Anomaly
344.0
deg
TOD Coordinate System
8 x 8 geopotential
Third-body point masses
Table 4: Low Inclination Transfer Orbit Test Case
Mean Keplerian Element
Epoch 1996 January 1, 1 hr 0 min 0.0 sec UTC
Semi-major Axis
27348.233234545
km
Eccentricity
0.5236375082382266024377202553175
9
Inclination
5.99985975232
deg
Right Ascension of the Ascending
Node
1.50307478738
deg
Argument of Perigee
177.993508218
deg
Mean Anomaly
162.1050405
deg
TOD Coordinate System
5 x 5 geopotential
Third-body point masses
Solar Radiation Pressure
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Figures 9 through 14 are the results of comparing Orekit java DSST and F77 DSST
Standalone for the LEO case. The mean equinoctial element histories and differences are given.
Figures 15 through 25 are the results of comparing Orekit java DSST and F77 DSST
Standalone for the GPS case. Both mean Keplerian and mean equinoctial element histories and
differences are given. The interval is 17500 days in length.
Figures 26 through 31 are the results of comparing Orekit java DSST and F77 DSST
Standalone for the SIRIUS case. The mean Keplerian element histories and differences are given.
Figures 32 through 34 are the results of comparing Orekit java DSST and F77 DSST
Standalone for the low inclination transfer orbit case. The mean Keplerian element histories and
differences are given.
In all the cases, the difference between the Orekit java DSST and the F77 DSST Standalone is
very small relative to the element motion over the time interval considered.
CONCLUSION
In the interval from 2011 through 2013, three projects were initiated which together have un-
covered several bugs in the F77 Standalone implementation of the DSST satellite theory.
1. The DSST Standalone was included on the
Astrody
Tools
Web
Web-Site prototype es-
tablished at the Universidad de La Rioja, Spain.
2. The DSST was implemented as an orbit propagator in object-oriented java as
part of Orekit open source library for space flight dynamics
3. The accuracy and computation time characteristics of the DSST Standalone rela-
tive to the requirements of space object catalog maintenance are being evaluated
by the Space Situational Awareness Group at the DLR GSOC.
While each of these projects has its own set of goals and tests, the test cases results taken to-
gether have led to significant overall improvement of the DSST F77 software and a better under-
standing of the associated documentation.
FUTURE WORK
The following tasks are to be addressed in the future:
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1. Extension of the Web interface for the DSST Standalone Orbit Propagator to in-
clude Orbit Determination processing
2. Inclusion of the DSST short-periodic motion models in the Orekit java DSST li-
brary
3. Extension of the DSST short-periodic motion models included in the F77
Standalone DSST
4. Activating the DSST partial derivative models in the F77 Standalone DSST
5. Development of procedures for applying complex spacecraft geometrical and
material models in the DSST non-conservative forces
6. Non-invasive encapsulation of the Linux GTDS R&D Orbit Determination sys-
tem
7. Development of approaches for applying heterogeneous parallel computing ca-
pabilities (CPU, GPU, and FPGA) in the Linux GTDS R&D Orbit Determination
system
The Web interface for DSST-based orbit determination requires consideration of the estima-
tor(s) to be employed, improvements to Web DSST necessary to process data, the observation
modeling, and the observation database.
The short-periodic motion models in the DSST are more complicated (particularly the closed-
form zonal harmonic and lunar-solar point mass terms) than the analogous mean element equa-
tions of motion models. We expect to be able to apply knowledge gained from the existing java
implementation of the DSST.
We intend to extend the F77 Standalone DSST short periodic models to include:
a. J2-squared terms
b. J2 secular/tesseral m-daily coupling terms
c. Lunar-solar point mass weak-time-dependent (WTD) terms
d. Additional SPSHPER options to provide high accuracy options for LEO-
eccentric, MEO, GEO, and HEO orbits
It is also our intent to reconsider the numerical integration method to be used with the DSST.
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The overall intent is to improve the capability of the F77 Standalone to process observation
data in multiple orbital regimes.
The partial derivative capability was included in the original DSST Standalone (1984) but this
capability is not visible with the current orbit_propagator_services architecture. The partial
derivative capability needs to be activated in order to allow the F77 DSST Standalone to support
orbit determination.
The work of Dr. Bent Fritsche (Ref. 26) is typical of the complex spacecraft geometrical and
material models that we would like to investigate in the DSST context.
For the non-invasive encapsulation of the Linux GTDS R&D Orbit Determination system, we
would like to investigate the LCML and LEGEND concepts developed at MIT (Ref. 27).
We would like to investigate the role of software tools such as OpenACC in the application of
heterogeneous parallel computing capabilities to legacy software such as the Linux GTDS R&D
Orbit Determination system (Ref. 28).
ACKNOWLEDGMENTS
The authors would like to acknowledge the support and encouragement of Mr. Luc
Maisonobe, Mr. Pascal Parraud, Dr. Petr Bazavan, and Mr. Nicolas Frouvelle of CS Communica-
tions & Systèmes, Toulouse, France and Dr. Oliver Montenbruck and Dr. Hauke Fiedler at the
DLR/GSOC, Wessling, Germany.
The authors would like to acknowledge the original developers of the DSST Satellite Theory
and its implementation in Fortran 77 including Mr. Wayne McClain, Mr. Leo Early, Dr. Ron
Proulx, Dr. Mark Slutsky, Dr. David Carter, and Mr. Rick Metzinger, all at the Draper Laborato-
ry, Cambridge, MA. The authors also acknowledge the efforts of Prof. Don Danielson at the Na-
vy Postgraduate School, Monterey, CA, in preparing a single integrated document describing the
as-built DSST. The authors also acknowledge the several MIT Aeronautics and Astronautics De-
partment graduate students who participated in the development, test, evaluation, and application
of the Semi-analytical Satellite Theory at the Draper Laboratory.
The work of Zachary Folcik is sponsored by the Department of the Air Force under contract
FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of
the author and are not necessarily endorsed by the United States Government.
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REFERENCES
1. Leo W. Early, A Portable Orbit Generator using Semi-analytical Satellite Theory,
AIAA preprint 86-2164, presented to AIAA/AAS Astrodynamics Conference, Williams-
burg, VA, August 1986.
2. M. Slutsky, The First-Order Short-Periodic Motion of An Artificial Satellite Due to
Third-Body Perturbations: Numerical Evaluation, AAS paper 83-393, AAS/AIAA
Astrodynamics Specialist Conference, Lake Placid, NY, August 1983.
3. G. B. Green, Semi-Analytic Propagator Alterations, Aerospace Corporation Interoffice
Correspondence, August 1985.
4. R. G. Hopkins, Description of the Astrodynamics Department MEANELT
Stationkeeping and Orbit Propagation Capabilities, Aerospace Corporation, Aerospace
Technical Memorandum #86(9975)-23, January 1986.
5. R. G. Hopkins, A User’s Guide to Program MEANELT, Aerospace Corporation, Aero-
space Technical Memorandum #87(9975)-62, September 1987.
6. Daniel John Fonte, Jr., Implementing a 50 x 50 Gravity Field Model in an Orbit Deter-
mination System, Master of Science Thesis, Department of Aeronautics and Astro-
nautics, MIT, June 1993 (CSDL-T- 1169).
7. Scott Shannon Carter, Precision Orbit Determination from GPS Receiver Navigation
Solutions, Master of Science Thesis, Department of Aeronautics and Astronautics, MIT,
June 1996 (CSDL-T- 1260).
8. Joseph G. Neelon, Paul J. Cefola, and Ronald J. Proulx, Current Development of the
Draper Semi-analytical Satellite Theory Standalone Orbit Propagator Package, AAS
paper 97-731, AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, ID, August
1997.
9. Paul J. Cefola, Donald Phillion, and K. S. Kim, Improving Access to the Semi-Analytical
Satellite Theory, AAS paper 09-341, AAS/AIAA Astrodynamics Specialist Conference,
Pittsburgh, PA, August 2009.
10. Paul J. Cefola, Barry Bentley, Luc Maisonobe, Pascal Parraud, Romain Di-Costanzo and
Zachary Folcik, Verification of the Orekit Java Implementation of the Draper Semi-
Analytical Satellite Theory, AAS paper 13-398, AAS/AIAA Space Flight Mechanics
Meeting, Lihue,Kauai, Hawaii, 10-14 February 2013.
11. Cefola, Paul J., Brian Weeden, and Creon Levit, Open Source Software Suite for Space
Situational Awareness and Space Object Catalog Work, presented at the International
Conference on Astrodynamic Tools and Techniques (ICATT), ESA/ESAC, Madrid,
Spain, 3-6 May 2010
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15
12. San-Juan, J. F., Lara, M., López, R., López, L. M., Weeden, B. and Cefola, P. J., Using
the DSST Semi-Analytical Orbit. Propagator Package via the
NondyWebTools/AstrodyWebTools, Proceedings of 62
nd
International Astronautical
Congress, Cape Town, SA. 2011.
13. San-Juan, J. F., Lara, M., López, R., López, L. M., Weeden, B. and Cefola, P. J.,
Allocationof DSST in the new implementation of , Proceedings of the
AMOS Advanced Maui Optical and Space Surveillance Technologies Conference, Maui,
Hawaii, USA. September 2012.
14. Pommier-Maurussanet, V., and Mainsonobe, L., Orekit: an Open-source Library for
Operational Flight Dynamics Applications, presented at the International Conference on
Astrodynamic Tools and Techniques (ICATT), ESA/ESAC, Madrid, Spain, 3-6 May
2010.
15. Mainsonobe, L., Cefola, P. J., Frouvelle, N., Herbiniere, S., Laffront, F.-X., Lizy-Destrez,
S., and Neidhart, T., Open Governance of the Orekit Space Flight Dynamics Library,
presented at the International Conference on Astrodynamic Tools and Techniques
(ICATT). ESA/ESTEC, Noordwijk, The Netherlands, 29 May-1 June 2012.
16. Orekit forge, https://www.orekit.org/forge/projects/orekit
17. Srinivas J. Setty, Paul J. Cefola, Oliver Montenbruck, and Hauke Fiedler, Investigating
the Suitability of Analytical and Semi-Analytical Satellite Theories for Space Object
Catalogue Maintenance in Geosynchronous Regime, AAS paper 13-769, AAS/AIAA
Astrodynamics Specialist Conference, Hilton Head, South Carolina, August 2013.
18. Srinivas J. Setty, Paul J. Cefola, Oliver Montenbruck, and Hauke Fiedler, Prediction Ac-
curacies of Draper Semi-analytical Satellite Theory in LEO, MEO and Regime for
Space Object Catalogue Maintenance, AAS paper 14-319, to be presented at the
AAS/AIAA Spaceflight Mechanics Meeting, Santa Fe, New Mexico, 26 -30 January
2014.
19. Zeis E. G., A Computerized Algebraic Utility for the Construction of Nonsingular Sat-
ellite Theories, Master of Science Thesis, Department of Aeronautics and Astronautics,
MIT, September 1978.
20. Kaniecki, J. P., Short Periodic Variations in the First Order Semianalytical Satellite
Theory, Master of Science Thesis, Department of Aeronautics and Astronautics, MIT,
August 1979.
21. Apache meritocracy, http://www.apache.org/foundation/how-it-works.html#meritocracy
22. Minutes of first Orekit Project Management Committee (PMC) meeting,
https://www.orekit.org/forge/attachments/318/PMC_meeting_050712.pdf
23. OREKIT governance charter,
https://www.orekit.org/forge/attachments/317/OREKIT_Governance.pdf
Rev 8
16
24. Maisonobe, Luc, Using Java for numerical computation: a space flight dynamics oper-
ational example, presented at the Data Systems in Aerospace Conference (DASIA 2010),
Budapest, Hungary, 1-4 June 2010.
25. Roberts, Eric S., The Art & Science of Java -- An Introduction to Computer Science,
Addison Wesley (Pearson), Boston, MA, 2008
26. Fritsche, B., and H. Klinkrad, Accurate Prediction of Non-gravitational Forces for Pre-
cise Orbit Determination, Part I Principles of the Computation of Coefficients of Force
and Torque, AIAA preprint 2004-5461, presented at the AIAA/AAS Astrodynamics
Specialist Conference, Providence, RI (August 2004).
27. Evangelinos, C., Lermusiaux, P. F. J., Geiger, S. K., Chang, R. C., and Patrikalakis, N.
M., (2006) Web-enabled Configuration and Control of Legacy Codes: An Application
to Ocean Modeling, Ocean Modeling, 13, 197-220.
28. Wolfe, Michael, (Introduction to GPU Computing with OpenACC, November 2012
(http://www.pgroup.com/lit/presentations/sc12_tutorial_openacc_intro.pdf )
17
Figure 1. Fortran 77 DSST Standalone Program Top Level Design
Figure 2. DSST encapsulation in the
Astrody
Tools
Web
Web-Site
18
Figure 3. Test Process for the DSST encapsulation in the
Astrody
Tools
Web
Web-Site
Figure 4. Test Process for the F77 DSST Standalone
19
Figure 5. Design of Flight Dynamics Applications using the Orekit Library
Figure 6. Orekit DSST Propagator Class Diagram
20
Figure 7. Test Processes for the Orekit java DSST
Figure 8. Test Processes for the GSOC Evaluation of DSST for SSA
21
Figure 9 DSST Mean Semi-major axis Histories and Difference for the LEO orbit over 7500
days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
Figure 10 DSST Mean Equinoctial Element h Histories and Difference for the LEO orbit over
7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
22
Figure 11 DSST Mean Equinoctial Element k Histories and Difference for the LEO orbit over
7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
Figure 12 DSST Mean Equinoctial Element p Histories and Difference for the LEO orbit over
7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
23
Figure 13 DSST Mean Equinoctial Element q Histories and Difference for the LEO orbit over
7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
Figure 14 DSST Mean Mean Longitude λ
λλ
λ Histories and Difference for the LEO orbit over 7500
days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)
24
Figure 15 DSST Mean Semi-major axis Histories and Difference for the GPS orbit over 17500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 16 DSST Mean Eccentricity Histories and Difference for the GPS orbit over 17500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
25
Figure 17 DSST Mean Inclination Histories and Difference for the GPS orbit over 17500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 18 DSST Mean RAAN Histories and Difference for the GPS orbit over 17500 days
(Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
26
Figure 19 DSST Mean Argument of Perigee Histories and Difference for the GPS orbit over
17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 20 DSST Mean Mean Anomaly Histories and Difference for the GPS orbit over 17500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
27
Figure 21 DSST Mean Equinoctial Element h Histories and Difference for the GPS orbit over
17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 22 DSST Mean Equinoctial Element k Histories and Difference for the GPS orbit over
17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
28
Figure 23 DSST Mean Equinoctial Element p Histories and Difference for the GPS orbit over
17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 24 DSST Mean Equinoctial Element q Histories and Difference for the GPS orbit over
17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
29
Figure 25 DSST Mean Mean Longitude λ
λλ
λ Histories and Difference for the GPS orbit over 17500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)
Figure 26 DSST Mean Semi-major axis Histories and Difference for the SIRIUS 24 hr orbit
over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
30
Figure 27 DSST Mean Eccentricity Histories and Difference for the SIRIUS 24 hr orbit over
7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
Figure 28 DSST Mean Inclination Histories and Difference for the SIRIUS 24 hr orbit over
7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
31
Figure 29 DSST Mean RAAN Histories and Difference for the SIRIUS 24 hr orbit over 7500
days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
Figure 30 DSST Mean Argument of Perigee Histories and Difference for the SIRIUS 24 hr or-
bit over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
32
Figure 31 DSST Mean Mean Anomaly Histories and Difference for the SIRIUS 24 hr orbit
over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)
Figure 32 DSST Mean Semi-major Axis Histories and Difference for low inclination 12.5 hr
transfer orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point
masses, solar radiation pressure)
33
Figure 33 DSST Mean Eccentricity Histories and Difference for low inclination 12.5 hr transfer
orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point masses,
solar radiation pressure)
Figure 34 DSST Mean Inclination Histories and Difference for low inclination 12.5 hr transfer
orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point masses,
solar radiation pressure)
... 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]. ...
Conference Paper
Full-text available
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. ...
Article
Full-text available
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.
Article
Full-text available
Early development of the Draper Semianalytical Satellite Theory (DSST) was motivated by the goal of a nonsingular, semianalytical theory that combined the best characteristics of existing Numerical and Semianalytical Satellite Theories. By early 1983, the Draper Goddard Trajectory Determination System (GTDS) implementation of the DSST included the major physical models: higher order geopotential (21 times; 21), atmospheric drag, lunar-solar point masses, and solar radiation pressure. To provide greater access to the DSST, a Standalone version which operated separately from GTDS was constructed. GTDS and the Standalone each developed through incremental changes, but in different directions. Currently, an effort is in progress to improve the accuracy and maintainability of the Standalone. The improvements include new models for the coordinate system reference (J2000), geopotential (50 × 50), and solid Earth tides, and modifications to the short-periodic model. The most recent application of this Standalone is the Automated Station-Keeping Simulator (ASKS) tool for satellite constellations.
Conference Paper
Full-text available
Currently, the number of space debris particles is about 33,500, out of which approximately 1100 are in geosynchronous orbits, which are tracked and whose orbital data are provided from US Space surveillance network, with instances of colliding and increasing the number of space debris. To further not exacerbate this situation, it is important to track and maintain a catalogue of these objects. To determine orbits of tracked objects and to propagate them in time, to correlate for not having duplicates in a catalogue, and to predict the close encounters of the satellites with tracked objects, it is important to have computationally efficient ephemeris propagators. For the purpose the well-known flavors of Simplified General perturbation theories for deep space(SDP4/SDP8), Kamel’s theory – a dedicated geosynchronous satellite perturbation theory formulated in equinoctial elements, and draper semi-analytical satellite theory – which makes use of generalized method for averaging, are examined for their best possible fit with numerically generated orbits and also for their computational loads. These propagators are selected in order to gain the understanding of behavior of different analytical formulations and semi-analytical propagation techniques. Previous studies on analytical and semi-analytical propagator have claimed that they are computationally lean and much faster than the numerical propagators, if any of the above mentioned propagator meets the requirements specified by Space Situational Awareness demands, it will considerably reduce the computational burden on the system. If cross-track and along-track accuracies are within the limits, then they can also be used for the purpose of collision predictions, which usually require high number of function calls in determining the close encounters. Simplified General Perturbation - 4 (SGP4) theory was developed based on Brower’s theory for the purpose of propagating Low-altitude satellites, further it was extended to be used for deep space satellites (SDP4) which includes solar and lunar perturbations which constitutes to the accuracies of objects in orbits with mean motion greater than half a day. Further SGP8 was developed by Hoots then extended to SDP8 similar to SDP4. Kamel’s theory uses a set of non-singular canonical orbital elements, i.e. equinoctial elements, to express the perturbations of a geosynchronous satellite’s orbit under the action of Earth’s and third bodies’ gravity field. The Earth's triaxiality effect is represented by zonal and tesseral harmonics up to J33 coefficients. Solar motion is described by an elliptic orbit expansion and lunar motion is represented by the Hill-Brown theory with coefficients up to 10-3 rad. DSST is a mean element orbit propagator based upon the generalized method of averaging. DSST was developed by P. Cefola with his colleagues at Draper Laboratory and Computer Sciences Corporation, Maryland, with the mathematical development relying on recursive series to model conservative perturbations and numerical quadrature in modeling non-conservative effects. Geosynchronous objects are defined by European Space Agency’s DISCOS catalogue as objects which lie between the following limits • Mean motion between 0.9 to 1.1 revolution per sidereal day (0.9≤n≤1.1) • Eccentricity smaller than 0.2 (0≤e≤0.2) • Inclination smaller than 70˚ (0˚≤i≤70˚) For all the orbits within these ranges, speed and accuracies of the selected analytical and semi-analytical theories’ are determined. Analytical and semi-analytically generated orbits are fitted with SP theory orbit for the arc lengths of few days. Details of which are elaborated in the paper.
Article
Thesis. 1979. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Article
Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Article
Earlier work on the first-order short-periodic motion due to third body point mass gravitational attraction is extended. Simplified analytical expressions for the partial derivatives of the short-periodic generating function with respect to the equinoctial elements h and k are developed. A software implementation is performed and used to produce numerical results defining the performance characteristics of this short-periodic model for three different satellite orbital regimes. The accuracy of this model equals or exceeds that obtained with the Green model.
Article
The Kepler problem treats the earth as if it is a spherical body of uniform density. In actuality, the earth's shape deviates from a sphere in terms of latitude (described by zonal harmonics), longitude (sectorial harmonics), and combinations of both latitude and longitude (tesseral harmonics). Operational Orbit Determination (OD) systems in the 1960's focused on the effects of the first few zonal harmonics since (1) they represented the dominant terms of the geopotential perturbation, (2) they were well known, and (3) the use of a limited number of harmonics greatly simplified the perturbation theory used. The demand for increasingly accurate modeling of a satellite's motion, combined with an increase in knowledge of the geopotential and an advancement in computer technology, led to the inclusion of tesseral harmonics. The Draper Laboratory version of the Goddard Trajectory Determination System (R&D GTDS), one operational OD system, can currently implement up to a 2lx2l gravity field model in its Cowell and Semianalytic Satellite Theory (SST) orbit generators. This thesis investigates the extension of R&D GTDS to include a 50x50 gravity field model in the Cowell and SST orbit generators. This extension would require code modifications in the following environments to support the various operational versions of R&D GTDS: IBM, VAX, Sun Workstation, and Silicon Graphics.
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For modern interdisciplinary ocean prediction and assimilation systems, a significant part of the complexity facing users is the very large number of possible setups and parameters, both at build-time and at run-time, especially for the core physical, biological and acoustical ocean predictive models. The configuration of these modeling systems for both local as well as remote execution can be a daunting and error-prone task in the absence of a graphical user interface (GUI) and of software that automatically controls the adequacy and compatibility of options and parameters. We propose to encapsulate the configurability and requirements of ocean prediction codes using an eXtensible Markup Language (XML) based description, thereby creating new computer-readable manuals for the executable binaries. These manuals allow us to generate a GUI, check for correctness of compilation and input parameters, and finally drive execution of the prediction system components, all in an automated and transparent manner. This web-enabled configuration and automated control software has been developed (it is currently in “beta” form) and exemplified for components of the interdisciplinary Harvard ocean prediction system (HOPS) and for the uncertainty prediction components of the error subspace statistical estimation (ESSE) system. Importantly, the approach is general and applies to other existing ocean modeling applications and to other “legacy” codes.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1996. Includes bibliographical references (p. 499-509). by Scott Shannon Carter. M.S.