TY - GEN
T1 - On the covariance singularity of quaternion estimators
AU - Carmi, Avishy
AU - Oshman, Yaakov
N1 - Funding Information:
The experimental data used in this study is the output of WILS II JIP which was organized and operated by KRISO. The project was participated and funded by Daewoo Shipbuilding and Marine Engineering, Samsung Heavy Industry, Hanjin Heavy Industry, Korean Register of Shipping, American Bureau of Shipping, Lloyd Register, Bureau Veritas, Germanischer Lloyd, Class NK, Seoul National University and Maritime Ocean Engineering Research Institute. Authors would like to thank their support for this study.
PY - 2007/1/1
Y1 - 2007/1/1
N2 - The asymptotic behavior of the estimation error covariance of quaternion estimators is mathematically examined. It is proved that the condition number of the asymptotic covariance matrix is of the order of the inverse of its largest eigenvalue, so that this matrix becomes asymptotically ill-conditioned as its trace tends to zero. Nevertheless, it is proved that the aforementioned asymptotic behavior cannot be captured by low-order Taylor approximations of the covariance, such as the one computed by the extended Kalman filter. The analytical results are demonstrated via a simulation study using the recently introduced quaternion particle filter and the additive quaternion extended Kalman filter.
AB - The asymptotic behavior of the estimation error covariance of quaternion estimators is mathematically examined. It is proved that the condition number of the asymptotic covariance matrix is of the order of the inverse of its largest eigenvalue, so that this matrix becomes asymptotically ill-conditioned as its trace tends to zero. Nevertheless, it is proved that the aforementioned asymptotic behavior cannot be captured by low-order Taylor approximations of the covariance, such as the one computed by the extended Kalman filter. The analytical results are demonstrated via a simulation study using the recently introduced quaternion particle filter and the additive quaternion extended Kalman filter.
UR - http://www.scopus.com/inward/record.url?scp=37249055928&partnerID=8YFLogxK
U2 - 10.2514/6.2007-6814
DO - 10.2514/6.2007-6814
M3 - Conference contribution
AN - SCOPUS:37249055928
SN - 1563479044
SN - 9781563479045
T3 - Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2007
SP - 4648
EP - 4665
BT - Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2007
PB - American Institute of Aeronautics and Astronautics Inc.
T2 - AIAA Guidance, Navigation, and Control Conference 2007
Y2 - 20 August 2007 through 23 August 2007
ER -