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## Citations

... This corresponds to a revisit time of 17 d. The orbit was propagated for 1 year with a numerical propagator based on the Orekit space flight dynamics library (Maisonobe et al., 2018). ...

ALTIUS (Atmospheric Limb Tracker for the Investigation of the Upcoming Stratosphere) is the upcoming stratospheric ozone monitoring limb sounder from ESA's Earth Watch programme. Measuring in the ultraviolet–visible–near-infrared (UV–VIS–NIR) spectral regions, ALTIUS will retrieve vertical profiles of ozone, aerosol extinction coefficients, nitrogen dioxide and other trace gases from the upper troposphere to the mesosphere. In order to maximize the geographical coverage, the instrument will observe limb-scattered solar light during daytime (i.e. bright limb observations), solar occultations at the terminator and stellar/lunar/planetary occultations during nighttime. This paper evaluates the constraint of ALTIUS ozone profiles on modelled stratospheric ozone by means of an observing system simulation experiment (OSSE). In this effort, a reference atmosphere has been built and used to generate ALTIUS ozone profiles, along with an instrument simulator. These profiles are then assimilated to provide ozone analyses. A good agreement is found between the analyses and the reference atmosphere in the stratosphere and in the extra-tropical upper troposphere. In the tropical upper troposphere, although providing significant information in the analyses, the assimilation of ozone profiles does not completely eliminate the bias with respect to the reference atmosphere. The impacts of the different modes of observations have also been evaluated, showing that all of them are necessary to constrain ozone during polar winters where solar/stellar occultations are the most important during the polar night and bright limb data are the most important during the development of the ozone hole in the polar spring.

... This method prevents the complex task to establish and validate all model derivatives. State transition matrix terms are computed directly from model evolution equations, instead of creating a new differential equation to integrate as it is done in Orekit numerical or semi-analytical orbit determination [5] [6]. Moreover, automatic differentiation is used to create SGP4/SDP4 compliant TLEs from a state vector. ...

Earth orbital space suffers from the ever increasing count of space objects, including operational satellites and space debris. Space system operations rely on the management of vast catalogs of objects to avoid any damaging collision. NORAD (North American Aerospace Defense Command) and NASA (National Aeronautics and Space Administration) both maintain a database for a large quantity of orbiting objects. Data are stored as Two Line Elements (TLE) and used along with specific analytical propagation models. Operation centers need Orbit Determination methods to accurately compute conjunctions and collision probabilities. With more and more flying objects, computations must be fast enough to ensure satellite safety. Mixing Orbit Determination and TLE analytical propagation models appears to be an effective way to grant security in space. This paper presents an open-source solution for an Orbit Determination method based on TLE propagation models. The method was implemented and validated inside the Orekit space mechanic library. It was then confronted with a classical numerical Orbit Determination on a GNSS test case.

... The first one is a Batch Least Squares algorithm and the other one is a Kalman Filter. The architecture as well as the operating principle of these algorithms in Orekit, are exposed by Maisonobe et al [11]. ...

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.

This article proposes a method to decentralize the navigation burden and improve the fault tolerance for a spacecraft constellation. The constellation body reference system is introduced, which is the perifocal frame of one satellite in the constellation. The structure of the proposed navigation method is constructed to enable each spacecraft to estimate its own orbit in this body reference system. This step is essentially the relative orbit determination (OD) based on inter-satellite range measurements. Thereafter, the approach to transfer an orbit from the constellation body reference system to an inertial reference system is developed. The essential requirements on absolute measurements to realize the coordinate transfer are presented. By dividing the absolute OD into relative OD and coordinate transfer, each navigation subsystem operated in a spacecraft can be independent with others, and the absolute measurements collected by any spacecraft can contribute to the absolute OD of the whole constellation. The proposed method applies to constellations in any geometric configuration. A Walker constellation is taken as an example for numerical simulations. The results show that the proposed method has a lower computation burden compared to an integrated navigation system. With the same type of absolute measurements, the proposed method has higher accuracy and convergence velocity than conventional decentralized algorithms. When a spacecraft occurs with fault, the orbit results of other spacecraft are not affected using the proposed method, which is beyond the ability of conventional methods.

ALTIUS (Atmospheric Limb Tracker for the Investigation of the Upcoming Stratosphere) is the upcoming stratospheric ozone monitoring limb sounder from ESA's Earth Watch programme. Measuring in the ultraviolet-visible-near infrared spectral regions, ALTIUS will retrieve vertical profiles of ozone, aerosol extinction coefficients, nitrogen dioxide and other trace gases from the upper troposphere to the mesosphere. In order to maximize the geographical coverage, the instrument will observe limb- scattered solar light during daytime, solar occultation at the terminator and stellar/lunar/planetary occultations during nighttime. This paper evaluates the constraint of ALTIUS ozone profiles on modelled stratospheric ozone by the means of an Observing System Simulation Experiment (OSSE). In this effort, a reference atmosphere has been built and used to generate ALTIUS ozone profiles, along with an instrument simulator. These profiles are then assimilated to provide ozone analyses. A good agreement is found between the analyses and the reference atmosphere in the stratosphere and in the extra-tropical upper troposphere. In the tropical upper troposphere, although providing a significant weight in the analyses, the assimilation of ozone profiles does not allow to completely eliminate the bias with the reference atmosphere. The weight of the different modes of observations have also been evaluated, showing that all of them are necessary to constrain ozone during polar winters where solar/stellar occultations are the most important during the polar night and limb data are the most important during the development of the ozone hole in the polar spring.