### Abstract

A discrete-time attitude state estimation scheme that uses a global representation of the configuration space for rigid body attitude motion, is presented. This estimation scheme uses discrete-time state measurements of inertially known vectors along with rate gyro measurements of the angular velocity, to obtain state estimates in the filtering stage. Additionally, a set of sigma points is obtained from the unscented transform based on exponential coordinates, with re-sampling centered at the current state estimate at each measurement instant. The state estimates along with sampled sigma points are propagated between measurement instants, using a discrete-time attitude state observer that is almost globally finite-time stable. The propagated sigma points and state estimate are enclosed by a minimum volume ellipsoid at the measurement instant. It is assumed that all states are measured at a constant measurement sample rate and that state measurement errors are bounded by an ellipsoidal bound. The update stage of the filter consists of finding the minimum volume enclosing ellipsoid that contains the propagated sigma points and the measurement uncertainty bound. This updated ellipsoid provides the filtered uncertainty bound and its center provides the updated state estimate. A new set of sigma points is selected from this ellipsoid and the propagation and update steps are repeated between measurement instants. Numerical simulation results confirm the analytically obtained stability properties of the attitude state observer. Numerical results also show that state estimate errors are bounded in the presence of bounded measurement noise and bounded disturbance torque.

Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4698-4703 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

State | Published - Dec 27 2016 |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |

### Other

Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization

### Cite this

*2016 IEEE 55th Conference on Decision and Control, CDC 2016*(pp. 4698-4703). [7798985] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798985

**Unscented state estimation for rigid body attitude motion with a finite-time stable observer.** / Bohn, Jan J.; Sanyal, Amit; Butcher, Eric A.

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

*2016 IEEE 55th Conference on Decision and Control, CDC 2016.*, 7798985, Institute of Electrical and Electronics Engineers Inc., pp. 4698-4703, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798985

}

TY - GEN

T1 - Unscented state estimation for rigid body attitude motion with a finite-time stable observer

AU - Bohn, Jan J.

AU - Sanyal, Amit

AU - Butcher, Eric A.

PY - 2016/12/27

Y1 - 2016/12/27

N2 - A discrete-time attitude state estimation scheme that uses a global representation of the configuration space for rigid body attitude motion, is presented. This estimation scheme uses discrete-time state measurements of inertially known vectors along with rate gyro measurements of the angular velocity, to obtain state estimates in the filtering stage. Additionally, a set of sigma points is obtained from the unscented transform based on exponential coordinates, with re-sampling centered at the current state estimate at each measurement instant. The state estimates along with sampled sigma points are propagated between measurement instants, using a discrete-time attitude state observer that is almost globally finite-time stable. The propagated sigma points and state estimate are enclosed by a minimum volume ellipsoid at the measurement instant. It is assumed that all states are measured at a constant measurement sample rate and that state measurement errors are bounded by an ellipsoidal bound. The update stage of the filter consists of finding the minimum volume enclosing ellipsoid that contains the propagated sigma points and the measurement uncertainty bound. This updated ellipsoid provides the filtered uncertainty bound and its center provides the updated state estimate. A new set of sigma points is selected from this ellipsoid and the propagation and update steps are repeated between measurement instants. Numerical simulation results confirm the analytically obtained stability properties of the attitude state observer. Numerical results also show that state estimate errors are bounded in the presence of bounded measurement noise and bounded disturbance torque.

AB - A discrete-time attitude state estimation scheme that uses a global representation of the configuration space for rigid body attitude motion, is presented. This estimation scheme uses discrete-time state measurements of inertially known vectors along with rate gyro measurements of the angular velocity, to obtain state estimates in the filtering stage. Additionally, a set of sigma points is obtained from the unscented transform based on exponential coordinates, with re-sampling centered at the current state estimate at each measurement instant. The state estimates along with sampled sigma points are propagated between measurement instants, using a discrete-time attitude state observer that is almost globally finite-time stable. The propagated sigma points and state estimate are enclosed by a minimum volume ellipsoid at the measurement instant. It is assumed that all states are measured at a constant measurement sample rate and that state measurement errors are bounded by an ellipsoidal bound. The update stage of the filter consists of finding the minimum volume enclosing ellipsoid that contains the propagated sigma points and the measurement uncertainty bound. This updated ellipsoid provides the filtered uncertainty bound and its center provides the updated state estimate. A new set of sigma points is selected from this ellipsoid and the propagation and update steps are repeated between measurement instants. Numerical simulation results confirm the analytically obtained stability properties of the attitude state observer. Numerical results also show that state estimate errors are bounded in the presence of bounded measurement noise and bounded disturbance torque.

UR - http://www.scopus.com/inward/record.url?scp=85010756185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010756185&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7798985

DO - 10.1109/CDC.2016.7798985

M3 - Conference contribution

AN - SCOPUS:85010756185

SP - 4698

EP - 4703

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -