### Abstract

Space Situational Awareness (SSA) has been recognized to be important for the safe space activities including these problems. As low-thrust propulsion technology becomes increasingly popular, SSA for low-thrust spacecraft may become an area of increasing interest. More frequently use of low-thrust propulsion to place satellites in orbit create more opportunities for collisions and radio frequency interference as these spacecraft travel slowly through altitude ranges. The purpose of this paper is to develop a method for estimation of the mean orbital elements for low-thrust spacecraft. To overcome the instability of the estimation problem with low-thrust acceleration, we estimate the mean elements instead of osculating elements. By use of the averaging technique, Hudson and Scheeres (2009) proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only finite number of Fourier coefficients of the thrust acceleration appear because of the orthogonality of the trigonometric function. Based on the nonlinear state equation representation for the extended state variable which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from observation data of mean orbital elements. Moreover, the mapping from mean to osculating elements is derived which can be replaced by a measurement equation. Proposed method is demonstrated through numerical simulations

Original language | English |
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Title of host publication | 65th International Astronautical Congress 2014, IAC 2014: Our World Needs Space |

Publisher | International Astronautical Federation, IAF |

Pages | 4645-4655 |

Number of pages | 11 |

Volume | 7 |

ISBN (Electronic) | 9781634399869 |

Publication status | Published - 2014 |

Event | 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014 - Toronto, Canada Duration: Sep 29 2014 → Oct 3 2014 |

### Other

Other | 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014 |
---|---|

Country | Canada |

City | Toronto |

Period | 9/29/14 → 10/3/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Space and Planetary Science
- Aerospace Engineering
- Astronomy and Astrophysics

### Cite this

*65th International Astronautical Congress 2014, IAC 2014: Our World Needs Space*(Vol. 7, pp. 4645-4655). International Astronautical Federation, IAF.

**Estimation of mean orbital elements with unknown low-thrust acceleration.** / Bando, Mai; Date, Naoki; Hokamoto, Shinji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*65th International Astronautical Congress 2014, IAC 2014: Our World Needs Space.*vol. 7, International Astronautical Federation, IAF, pp. 4645-4655, 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014, Toronto, Canada, 9/29/14.

}

TY - GEN

T1 - Estimation of mean orbital elements with unknown low-thrust acceleration

AU - Bando, Mai

AU - Date, Naoki

AU - Hokamoto, Shinji

PY - 2014

Y1 - 2014

N2 - Space Situational Awareness (SSA) has been recognized to be important for the safe space activities including these problems. As low-thrust propulsion technology becomes increasingly popular, SSA for low-thrust spacecraft may become an area of increasing interest. More frequently use of low-thrust propulsion to place satellites in orbit create more opportunities for collisions and radio frequency interference as these spacecraft travel slowly through altitude ranges. The purpose of this paper is to develop a method for estimation of the mean orbital elements for low-thrust spacecraft. To overcome the instability of the estimation problem with low-thrust acceleration, we estimate the mean elements instead of osculating elements. By use of the averaging technique, Hudson and Scheeres (2009) proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only finite number of Fourier coefficients of the thrust acceleration appear because of the orthogonality of the trigonometric function. Based on the nonlinear state equation representation for the extended state variable which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from observation data of mean orbital elements. Moreover, the mapping from mean to osculating elements is derived which can be replaced by a measurement equation. Proposed method is demonstrated through numerical simulations

AB - Space Situational Awareness (SSA) has been recognized to be important for the safe space activities including these problems. As low-thrust propulsion technology becomes increasingly popular, SSA for low-thrust spacecraft may become an area of increasing interest. More frequently use of low-thrust propulsion to place satellites in orbit create more opportunities for collisions and radio frequency interference as these spacecraft travel slowly through altitude ranges. The purpose of this paper is to develop a method for estimation of the mean orbital elements for low-thrust spacecraft. To overcome the instability of the estimation problem with low-thrust acceleration, we estimate the mean elements instead of osculating elements. By use of the averaging technique, Hudson and Scheeres (2009) proposed an analytical model of secular variations of orbital elements under thrust acceleration. The resulting averaged equation has a nice property in which only finite number of Fourier coefficients of the thrust acceleration appear because of the orthogonality of the trigonometric function. Based on the nonlinear state equation representation for the extended state variable which include not only orbital elements but also unknown Fourier coefficients, mean orbital elements and thrust history are estimated from observation data of mean orbital elements. Moreover, the mapping from mean to osculating elements is derived which can be replaced by a measurement equation. Proposed method is demonstrated through numerical simulations

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M3 - Conference contribution

VL - 7

SP - 4645

EP - 4655

BT - 65th International Astronautical Congress 2014, IAC 2014: Our World Needs Space

PB - International Astronautical Federation, IAF

ER -