### Abstract

Range-ambiguous spacecraft relative orbits based on linear dynamics for elliptic chief orbits were studied for the purpose of sequential relative orbit estimation with range-only measurements. Using a geometric solution of the Tschauner-Hempel equation (“Rendezvous zu einem in elliptischer Bahn umlaufenden Ziel,” Acta Astronautica, Vol. 11, No. 2, 1965, pp. 104-109), the mirror range-ambiguous relative orbits, which were shown to have the same size as the true relative orbit for a circular chief reference orbit, are also shown to exist for elliptic chief orbits. However, it is found that deformed range-ambiguous relative orbits, which do not have the same size as the true relative orbit for the circular case, do not analytically exist for nonvanishing chief orbit eccentricity, although they persist in Kalman filtering simulations. This persistence is explained analytically through a perturbation analysis using the variation of the geometric quantities associated with range-ambiguous relative orbits. Furthermore, by altering the relative orbit configuration and model used in the filter, it is shown that the inclusion of chief orbit eccentricity and dynamic model nonlinearities in the filter model can help resist the tendency of an extended Kalman filter to converge to the range-ambiguous relative orbits.

Original language | English (US) |
---|---|

Pages (from-to) | 708-724 |

Number of pages | 17 |

Journal | Journal of Spacecraft and Rockets |

Volume | 56 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Journal of Spacecraft and Rockets*,

*56*(3), 708-724. https://doi.org/10.2514/1.A34083

**Ambiguous orbits in elliptic chief spacecraft relative orbit estimation with range-only measurements.** / Wang, Jingwei; Butcher, Eric; Alan Lovell, T.

Research output: Contribution to journal › Article

*Journal of Spacecraft and Rockets*, vol. 56, no. 3, pp. 708-724. https://doi.org/10.2514/1.A34083

}

TY - JOUR

T1 - Ambiguous orbits in elliptic chief spacecraft relative orbit estimation with range-only measurements

AU - Wang, Jingwei

AU - Butcher, Eric

AU - Alan Lovell, T.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Range-ambiguous spacecraft relative orbits based on linear dynamics for elliptic chief orbits were studied for the purpose of sequential relative orbit estimation with range-only measurements. Using a geometric solution of the Tschauner-Hempel equation (“Rendezvous zu einem in elliptischer Bahn umlaufenden Ziel,” Acta Astronautica, Vol. 11, No. 2, 1965, pp. 104-109), the mirror range-ambiguous relative orbits, which were shown to have the same size as the true relative orbit for a circular chief reference orbit, are also shown to exist for elliptic chief orbits. However, it is found that deformed range-ambiguous relative orbits, which do not have the same size as the true relative orbit for the circular case, do not analytically exist for nonvanishing chief orbit eccentricity, although they persist in Kalman filtering simulations. This persistence is explained analytically through a perturbation analysis using the variation of the geometric quantities associated with range-ambiguous relative orbits. Furthermore, by altering the relative orbit configuration and model used in the filter, it is shown that the inclusion of chief orbit eccentricity and dynamic model nonlinearities in the filter model can help resist the tendency of an extended Kalman filter to converge to the range-ambiguous relative orbits.

AB - Range-ambiguous spacecraft relative orbits based on linear dynamics for elliptic chief orbits were studied for the purpose of sequential relative orbit estimation with range-only measurements. Using a geometric solution of the Tschauner-Hempel equation (“Rendezvous zu einem in elliptischer Bahn umlaufenden Ziel,” Acta Astronautica, Vol. 11, No. 2, 1965, pp. 104-109), the mirror range-ambiguous relative orbits, which were shown to have the same size as the true relative orbit for a circular chief reference orbit, are also shown to exist for elliptic chief orbits. However, it is found that deformed range-ambiguous relative orbits, which do not have the same size as the true relative orbit for the circular case, do not analytically exist for nonvanishing chief orbit eccentricity, although they persist in Kalman filtering simulations. This persistence is explained analytically through a perturbation analysis using the variation of the geometric quantities associated with range-ambiguous relative orbits. Furthermore, by altering the relative orbit configuration and model used in the filter, it is shown that the inclusion of chief orbit eccentricity and dynamic model nonlinearities in the filter model can help resist the tendency of an extended Kalman filter to converge to the range-ambiguous relative orbits.

UR - http://www.scopus.com/inward/record.url?scp=85066298438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066298438&partnerID=8YFLogxK

U2 - 10.2514/1.A34083

DO - 10.2514/1.A34083

M3 - Article

AN - SCOPUS:85066298438

VL - 56

SP - 708

EP - 724

JO - Journal of Spacecraft and Rockets

JF - Journal of Spacecraft and Rockets

SN - 0022-4650

IS - 3

ER -