Optimal Linear Attitude Estimator

Daniele Mortari, F. Landis Markley, Puneet Singla
2007 Journal of Guidance Control and Dynamics  
An Optimal Linear Attitude Estimator (OLAE), is presented for the case of a singlepoint real-time estimation of spacecraft attitude using the minimum-element attitude parametrization: Rodrigues (or Gibbs) vector g. The optimality criterion, which does not coincide with the Wahba's constrained criterion, is rigorously quadratic and unconstrained. The singularity, which occurs when the principal angle is π, can easily be avoided by one rotation. The attitude accuracy tests show that the proposed
more » ... that the proposed method provides a precision comparable with those fully complying the Wahba optimality definition. Finally, computational speed tests demonstrate that the proposed method belongs to the class of the fastest optimal attitude estimation algorithms. a The relation of the Cayley parameters G to the Rodrigues vector g is given in Refs. [6, 7] , even though the elements of the Rodrigues vector (Rodrigues parameters) were used by Rodrigues in Ref. [8] to describe rotations in 1840, long before Cayley; and Cayley apparently knew the relation to his transform in 1843.
doi:10.2514/1.29568 fatcat:qluc3ei5mzaq3lddrom2omdcla