### Abstract

This paper proposes a new constrained attitude estimation method for a satellite to reduce the influence of non-Gaussian measurement noise. A conventional constrained filter, the Receding-Horizon Nonlinear Kaiman Filter (RNKF), propagates the state value with a model in the prediction step, and minimizes the cost function with a constraint in the filtering step. The cost function is desired to be a quadratic program problem, whose constraint is linear, in terms of computational complexity. If the RNKF is applied to the attitude estimation problem, the appropriate attitude representation is the quaternion, which does not have a singular point, in the prediction step. However, the quaternion does not define a quadratic program in the filtering step because the quaternion needs to satisfy a single constraint of a unit norm. Therefore, this paper proposes the Receding-Horizon Unscented Kaiman Filter (RUKF) as an improvement of the RNKF to deal with appropriate attitude representation in each step. In the RUKF. the attitude is represented by the Rodrigues parameter in the filtering step owing to the Unscented Transformation. The Rodrigues parameter is an attitude representation with no constraint. It was confirmed from Monte Carlo simulation that the RUKF with a constraint is more accurate than the Extended Kaiman Filter.

Original language | English |
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Title of host publication | Proceedings of the International Astronautical Congress, IAC |

Publisher | International Astronautical Federation, IAF |

Pages | 4963-4970 |

Number of pages | 8 |

Volume | 7 |

ISBN (Print) | 9781634399869 |

Publication status | Published - 2014 |

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

### Other

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

City | Toronto |

Period | 14/9/29 → 14/10/3 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Proceedings of the International Astronautical Congress, IAC*(Vol. 7, pp. 4963-4970). International Astronautical Federation, IAF.

**Receding-horizon unscented Kalman filter for satellite attitude estimation.** / Hirasawa, Ryo; Nakajima, Yuta; Takahashi, Masaki.

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

*Proceedings of the International Astronautical Congress, IAC.*vol. 7, International Astronautical Federation, IAF, pp. 4963-4970, 65th International Astronautical Congress 2014: Our World Needs Space, IAC 2014, Toronto, Canada, 14/9/29.

}

TY - GEN

T1 - Receding-horizon unscented Kalman filter for satellite attitude estimation

AU - Hirasawa, Ryo

AU - Nakajima, Yuta

AU - Takahashi, Masaki

PY - 2014

Y1 - 2014

N2 - This paper proposes a new constrained attitude estimation method for a satellite to reduce the influence of non-Gaussian measurement noise. A conventional constrained filter, the Receding-Horizon Nonlinear Kaiman Filter (RNKF), propagates the state value with a model in the prediction step, and minimizes the cost function with a constraint in the filtering step. The cost function is desired to be a quadratic program problem, whose constraint is linear, in terms of computational complexity. If the RNKF is applied to the attitude estimation problem, the appropriate attitude representation is the quaternion, which does not have a singular point, in the prediction step. However, the quaternion does not define a quadratic program in the filtering step because the quaternion needs to satisfy a single constraint of a unit norm. Therefore, this paper proposes the Receding-Horizon Unscented Kaiman Filter (RUKF) as an improvement of the RNKF to deal with appropriate attitude representation in each step. In the RUKF. the attitude is represented by the Rodrigues parameter in the filtering step owing to the Unscented Transformation. The Rodrigues parameter is an attitude representation with no constraint. It was confirmed from Monte Carlo simulation that the RUKF with a constraint is more accurate than the Extended Kaiman Filter.

AB - This paper proposes a new constrained attitude estimation method for a satellite to reduce the influence of non-Gaussian measurement noise. A conventional constrained filter, the Receding-Horizon Nonlinear Kaiman Filter (RNKF), propagates the state value with a model in the prediction step, and minimizes the cost function with a constraint in the filtering step. The cost function is desired to be a quadratic program problem, whose constraint is linear, in terms of computational complexity. If the RNKF is applied to the attitude estimation problem, the appropriate attitude representation is the quaternion, which does not have a singular point, in the prediction step. However, the quaternion does not define a quadratic program in the filtering step because the quaternion needs to satisfy a single constraint of a unit norm. Therefore, this paper proposes the Receding-Horizon Unscented Kaiman Filter (RUKF) as an improvement of the RNKF to deal with appropriate attitude representation in each step. In the RUKF. the attitude is represented by the Rodrigues parameter in the filtering step owing to the Unscented Transformation. The Rodrigues parameter is an attitude representation with no constraint. It was confirmed from Monte Carlo simulation that the RUKF with a constraint is more accurate than the Extended Kaiman Filter.

UR - http://www.scopus.com/inward/record.url?scp=84937711165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937711165&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781634399869

VL - 7

SP - 4963

EP - 4970

BT - Proceedings of the International Astronautical Congress, IAC

PB - International Astronautical Federation, IAF

ER -