Talk:Wahba's problem
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There is lots to do for this article. Starting with:
- Description of the common solutions to the problem (e.g. q-method, QUEST, ...)
- Links to Wahba's original 1965 paper
- Academic sources for the the solutions listed
- A history of the method (i.e. development of the method) and notable missions using solutions to Wahba's problem for attitude determination
- Relation to the Orthogonal Procrustes problem.
- Shuster's generalised Wahba's problem for both vector an attitude observations.
And, of course, much much more.
-- Damien d (talk) 13:05, 6 June 2011 (UTC)
The correct formula for Markley's solution for R is given as U*diag([1,1,det(U)det(V)])*V' (see equation (18) of the referenced paper, R is A_{opt} in his notation). This article recently had U and V transposed.
-- Mark T.
Applications to soft body physics simulation
[edit]I wanted to share some informal notes I wrote up while studying this problem in the context of developing this soft body physics engine. I can't claim that these notes are themselves suitable to use as a direct source, but they do contain many references and links to research papers that make direct contact with the original problem.
In particular, Davenport's Q-method seems to be the most robust known solution to the problem. It effectively sums tensor products of each transformed sample point to build a symmetric 4x4 matrix. This matrix acts to scale unit quaternions in proportion to how well the rotation each quaternion represents matches the current measured cloud of arbitrary samples. In turn this means that the eigenvector corresponding to the largest eigenvalue can be interpreted as the quaternion that best describes the rigid rotation of the undeformed system.
Because much of the early research in this domain needed to run on more limited hardware (early satellites doing star tracking with limited power and computational abilities), many other methods (I think QUEST is the big one) were derived that offered solutions that were more approximate but faster to compute. Even for modern real time simulation, certain approximate solutions seem to work well enough for a lot of people. My personal experience has been that these methods are not sufficiently stable or robust enough to avoid edge cases that introduce energy, but it is just that: personal experience.
I'd be happy to answer questions and/or share other resources I might know about upon request since I have spent a lot of time on this problem. I am just hesitant to add much to the article directly because so much of my knowledge is independent research. In particular, I believe that the insights derived in the context of geometric algebra are novel, and I would not feel qualified to translate the original algebraic derivations that try to minimize a more abstract loss function. As a final point of reference I can link to this Stack Exchange post where I tried to get assistance in understanding the derivation before I made the connection to GA. I hope some of this is helpful in fleshing out the article!