## Details

Original language | English |
---|---|

Pages (from-to) | 728-749 |

Number of pages | 22 |

Journal | Advances in space research |

Volume | 63 |

Issue number | 1 |

Publication status | Published - 19 Sept 2018 |

## Abstract

Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, …) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations.

## Keywords

- Asteroidal ring, Evolution strategy, Solar-system ephemeris, Stochastic optimization

## ASJC Scopus subject areas

- Engineering(all)
**Aerospace Engineering**- Physics and Astronomy(all)
**Astronomy and Astrophysics**- Earth and Planetary Sciences(all)
**Geophysics**- Earth and Planetary Sciences(all)
**Atmospheric Science**- Earth and Planetary Sciences(all)
**Space and Planetary Science****Earth and Planetary Sciences(all)**

## Cite this

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- Apa
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- BibTeX
- RIS

**Application of an evolution strategy in planetary ephemeris modeling.**/ Mai, Enrico; Müller, Jürgen; Oberst, Jürgen.

In: Advances in space research, Vol. 63, No. 1, 19.09.2018, p. 728-749.

Research output: Contribution to journal › Article › Research › peer review

*Advances in space research*, vol. 63, no. 1, pp. 728-749. https://doi.org/10.1016/j.asr.2018.09.011

*Advances in space research*,

*63*(1), 728-749. https://doi.org/10.1016/j.asr.2018.09.011

}

TY - JOUR

T1 - Application of an evolution strategy in planetary ephemeris modeling

AU - Mai, Enrico

AU - Müller, Jürgen

AU - Oberst, Jürgen

N1 - Funding information: This research was funded by the German Research Foundation Deutsche Forschungsgemeinschaft (DFG) within the research unit FOR-1503 Space-Time Reference Systems for Monitoring Global Change and for Precise Navigation in Space, as well as within the collaborative research center SFB-1128 geo-Q Relativistic Geodesy and Gravimetry with Quantum Sensors.

PY - 2018/9/19

Y1 - 2018/9/19

N2 - Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, …) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations.

AB - Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, …) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations.

KW - Asteroidal ring

KW - Evolution strategy

KW - Solar-system ephemeris

KW - Stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85053905503&partnerID=8YFLogxK

U2 - 10.1016/j.asr.2018.09.011

DO - 10.1016/j.asr.2018.09.011

M3 - Article

AN - SCOPUS:85053905503

VL - 63

SP - 728

EP - 749

JO - Advances in space research

JF - Advances in space research

SN - 0273-1177

IS - 1

ER -