On the covariance singularity of quaternion estimators Academic Article uri icon


  • 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 fllter. The analytical results are demonstrated via a simulation study using the recently introduced quaternion particle fllter and the additive quaternion extended Kalman fllter.

publication date

  • January 1, 2007