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Verification of the Orekit Java implementation of the Draper semi-analytical satellite theory
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Verification of the java Orekit implementation of the Draper Semi-analytical Satellite Theory (DSST) is discussed. The Orekit library for space flight dynamics has been published under the open-source Apache license V2. The DSST is unique among analytical and semi-analytical satellite theories due to the scope of the included force models. However, the DSST has not been readily accessible to the wider Astrodynamics research community. Implementation of the DSST in the Orekit library is a comprehensive task because it involves the migration of the DSST to the object-oriented java language and to a different functional decomposition strategy. The resolution of the code and documentation anomalies discovered during the verification process is the important product of this project.
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... 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 paper. ...
... 16 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. ...
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 which are now resolved.
... A more rigorous way to extract mean elements would be to use a semi-analytical propagator (like DSST (McClain, 1992;Cefola et al., 2013;Bernard et al., 2015;Cazabonne and Cefola, 2021)) as it separates the periodic terms from the mean parameters naturally. A fitting on the mean elements is still needed, though, as for convenience polynomial models are desired for Mean (or Apparent) Local Solar Time and inclination. ...
Traditional station-keeping for Earth observation satellites with chemical thrusters generally involves maneuvers every couple months that are able to change significantly the semi-major axis and the inclination. These strategies do not scale down to very low thrust level (a few hundreds of μN) electrical thrusters. This paper presents both in-plane and out-of-plane strategies that spread corrections over very long arcs and discretize them to tiny maneuvers every couple orbits, taking into account mission-constraints on maneuvers locations. These strategies scale up to medium thrust strategies, filling the gap between propulsion technologies. The out-of-plane strategy although features a new no-deadband property and controls the full orbital momentum. All strategies allow control very close to the reference (a few hundreds meters in osculating parameters) and very low cost.
... During its development, Orekit DSST has been conscientiously validated against the original FORTRAN version. 22,23,24 The current version of Orekit DSST provides a lot of features which are summarized in Table 1. Partial derivatives computed for both mean elements and shortperiodic terms using automatic differentiation ...
Space agencies generally use numerical methods to meet their orbit determination needs. Due to the ever increasing number of space objects, the development of new orbit determination methods becomes essential. DSST is an orbit propagator based on a semi-analytical theory. It combines the accuracy of numerical propagation and the speed of analytical propagation. The paper presents an open-source DSST orbit determination application included in the Orekit library. Accuracy of the DSST orbit determination is demonstrated by comparison with a numerical method. Both the satellite's state vector estimation and the measurement residuals are used as comparison metrics.
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.
Orekit is a library for space flight dynamics. It was released under an open-source license in 2008 and has since gained widespread recognition. It has already been used operationally, it has been selected as the basis of new generation systems in agencies, it has been used for several studies and ground systems developments by various industrial actors, and it is used for training purposes at universities.
The project has gone through several phases, becoming more and more open at each step. During the first phase, Orekit started as a closed-source product. During the second phase (2008), Orekit switched to a permissive open-source license (Apache License V2) in 2008. The Orekit third phase started in early 2011. The third phase included a collaborative site, with direct public visibility of the development version control
system, issue tracker, mailing lists, blog and wiki. The third phase culminated in late 2011 when the
first external committer was nominated and gained write access to the source code
repository.
The Orekit project is now entering its fourth phase, with a completely open governance
model, involving representatives from different space field actors in a Project Management
Committee (PMC). The Orekit governance model follows the Apache Software Foundation meritocracy. This model is based on several roles (user, contributor, committer, Project Management Committee
member and PMC chair).
This paper explains the various roles and the rights that are bound to them. Everyone can go through the various roles. The rules to get access to the various roles are explained in the paper. They are based on merit
previously earned within the project. Merit is gained through contributions and involvement. The first PMC of the Orekit project is officially set up as the 5 th ICATT conference is taking place. It is composed of people with
different affiliations in order to meet the needs of the widest possible range of users. There are
representatives of spacecraft manufacturers, academics (both European and US), satellite
operators, software industry and independent experts. Representatives of space agencies are
expected to join the PMC soon. This PMC will be in charge of defining the roadmap for the future evolution of the Orekit project. The rules for evolution of the PMC are explained in the paper.
The role of the PMC is mainly to define global orientation. The technical low level decisions are still taken by the members of the development list where everyone can contribute to discussions, regardless of affiliation and whether they are or not members of the PMC. Orekit is a community oriented project.
The Orekit library is a space flight dynamics library developed since 2002 by CS. It was operationally used during the Jules Verne ATV mission. Since 2008, the library is freely available as an open-source product under the terms of the business-friendly Apache V2.0 license. Given the small size of the market and the still high need for advanced tailored solutions for space systems, the service based business model for added value is much more suited than the license based business model or its new version, the Software As a Service. There are several business models that can be used for economically sound open-source systems. Some are well suited for the space field and will be explained. Some are not adapted and the reasons for this will also been explained. Open-source is an approach that proved efficient in mainstream software industry. It does not always need a very large community as was once thought, but still needs some involvement. The return on investment increases for all contributors as the project expands and the risks decrease at the same time as more and more people use it. The model is attractive for both public entities, academics, industry and SMEs, bringing something to each one of them. It also increases the yield of public funding. OREKIT is an example of a successful open-source project initiated by private industry and operationally during ATV rendezvous. Since its inception, the OREKIT library was aimed both towards quick development for simple use cases and towards fine tuning for expert users. In order to fulfill the first goal, the programming interface provides high level features like attitude modes, automatic discrete events handling within propagation (ground station visibilities, eclipses, maneuver start/stop, altitude crossing, user defined event …), transparent handling of leap seconds, automatic transforms between all frames, transparent use of Earth Orientation Parameters and much more. In order to fulfill the second goal, several physical models are provided for many concepts (orbits, propagators, frames, events, attitudes, time scales, ephemerides …) and all of them can be extended naturally to add user specific models or change the behavior of the provided ones. Since many models offer similar user interfaces, it is possible to build applications that can be used both in a mission analysis configuration with fast models and in an operational configuration with accurate models with a single switch. The presentation will provide both a business view and a technical view of OREKIT. It will explain the benefits of open-source and business models. It will present an overview of the library features and available physical models. A focus on a few innovative concepts will be made, like for example discrete events, time scale handling, slave and master propagation modes, management of time-dependent frames, models switching or transparent handling of complex models that need lots of configuration data. Some examples of how the tool can be used in different operational contexts will be given. The roadmap for the future of the tool will be presented.
Description of the MethodApplications of the Derivative-Expansion Method
The Two-Variable Expansion ProcedureGeneralized Method
Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
On time scales of interest for mission planning of GNSS satellites, the qualitative motion of the semimajor axis and the node evolves primarily from resonances with the Earth’s gravitational field. The relevant dynamics of GPS orbits, which are in deep 2 to 1 resonance, is modeled with an integrable intermediary that depends only on one angle, the stroboscopic mean node, plus a two degrees of freedom perturbation that is factored by the eccentricity. Results are compared with long-term runs of the GTDS DSST showing very good agreement.
There is a common suspicion that formal covariances do not represent a realistic measure of orbital uncertainties. By devising metrics for measuring the representations of orbit error, we assess under what circumstances such lore is justified as well as the root cause of the discrepancy between the mathematics of orbital uncertainty and its practical implementation. We offer a scheme by which formal covariances may be adapted to be an accurate measure of orbital uncertainties and show how that adaptation performs against both simulated and real space-object data. We also apply these covariance adaptation methods to the process of observation association using many simulated and real data test cases. We demonstrate that covariance-informed observation association can be reliable, even in the case when only two tracks are available. Satellite breakup and collision event catalog maintenance could benefit from the automation made possible with these association methods.
To achieve maximum benefit from the altimetric data collected by the French-aAmerican TOPEX/POSEIDON spacecraft, radial orbit accuracy of 10 cm or better is required. This unprecedented requirement led the French Space Agency Centre National d'Etudes Spatiales (CNES) to develop a new high-accuracy tracking system, Doppler orbitography and radiopositioning integrated by satellite (DORIS), and a new precision orbit production facility, the Service d'Orbitographie DORIS. A global effort produced new models and a new orbit determination strategies. The result of these efforts has been assessed after 1 year of operation. The original goal has clearly been met, and the TOPEX/POSEIDON orbits produced by NASA and CNES agree beter than the 5 cm root mean square (RMS) level in the radial direction. At this level of accuracy, traditional techniques cannot correctly describe the actual orbit error, and some new procedures are proposed.
New power series representations in the eccentricity and a related parameter are developed for the Hansen coefficients. The coefficients of the power series are easily obtained with simple recurrence relations generated from a partial differential equation. In many cases, the new series representations offer significant improvement in convergence for moderate to larger eccentricities. Rational approximations for the new representations are also investigated.