Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements.

Matthias Ellmer, Torsten Mayer-Gürr

Research output: Contribution to conferencePosterResearch

Abstract

Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability.

When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer.

Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy.

We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.
Original languageEnglish
Publication statusPublished - 2016
EventEGU General Assembly 2016 - Wien, Austria
Duration: 17 Apr 201622 Apr 2016
http://meetingorganizer.copernicus.org/EGU2016/EGU2016-13356-1.pdf

Conference

ConferenceEGU General Assembly 2016
CountryAustria
CityWien
Period17/04/1622/04/16
Internet address

Fingerprint

Encke method
orbits
gravitation
GRACE mission
formulations
numerical stability
evaluation
accelerometers

Fields of Expertise

  • Sustainable Systems

Cite this

Ellmer, M., & Mayer-Gürr, T. (2016). Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements.. Poster session presented at EGU General Assembly 2016, Wien, Austria.

Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements. / Ellmer, Matthias; Mayer-Gürr, Torsten.

2016. Poster session presented at EGU General Assembly 2016, Wien, Austria.

Research output: Contribution to conferencePosterResearch

Ellmer M, Mayer-Gürr T. Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements.. 2016. Poster session presented at EGU General Assembly 2016, Wien, Austria.
Ellmer, Matthias ; Mayer-Gürr, Torsten. / Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements. Poster session presented at EGU General Assembly 2016, Wien, Austria.
@conference{553c15355a494663a68e4774889233a8,
title = "Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements.",
abstract = "Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability.When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer.Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy.We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.",
author = "Matthias Ellmer and Torsten Mayer-G{\"u}rr",
year = "2016",
language = "English",
note = "EGU General Assembly 2016 ; Conference date: 17-04-2016 Through 22-04-2016",
url = "http://meetingorganizer.copernicus.org/EGU2016/EGU2016-13356-1.pdf",

}

TY - CONF

T1 - Numerically stable approach for high-precision orbit integration using Encke's method and equinoctial elements.

AU - Ellmer, Matthias

AU - Mayer-Gürr, Torsten

PY - 2016

Y1 - 2016

N2 - Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability.When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer.Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy.We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.

AB - Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability.When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer.Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy.We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.

M3 - Poster

ER -