An analytic solution to Wahbaʼs problem

Authors:  Yaguang Yang, Zhiqiang Zhou

Abstract:
All spacecraft attitude estimation methods are based on Wahba’s optimization problem. This problem can be reduced to finding the largest eigenvalue and the corresponding eigenvector for Davenport’s K-matrix. Several iterative algorithms, such as QUEST and FOMA, were proposed, aiming at reducing the computational cost. But their computational time is unpredictable because the iteration number is not fixed and the solution is not accurate in theory. Recently, an analytical solution, ESOQ was suggested. The advantages of analytical solutions are that their computational time is fixed and the solution should be accurate in theory if there is no numerical error. In this paper, we propose a different analytical solution to Wahba’s problem. We use simple and easy to be verified examples to show that this method is numerically more stable than ESOQ, potentially faster than QUEST and FOMA. We also use extensive simulation test to support this claim.

Keywords:
Attitude estimation
Analytical solution
Spacecraft

Published in: Aerospace Science and Technology  (Volumes 30, issue 1, October 2013)

Publisher: Elsevier

ISSN Information: 1270-9638

An analytic solution to Wahbaʼs problem

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