# Why would someone use Modified Rodrigues Parameters over Quaternions for spacecraft attitude estimation? And vice versa?

I see quite some papers on spacecraft attitude determination and control, that rely on quaternions. While some others rely on MRPs. The advantage that I see so far is that... for quaternions, the projection of the set and shadow set on the hyperplane of projection (which lies outside the hypersphere and is tangent to the surface of the sphere) goes to infinity at phi = 180 degrees. While for MRPs the projection plane lies inside the unit sphere. If the projection of one of the set lies outside the unit sphere, then the other set's projection always lies inside. At 360 deg, when the projection of one of the set goes to infinity, the projection of the other set lies perfectly stable inside the hypersphere. Thus if one blows up, with MRPs, one can easily switch to the other set of parameters. While for quaternions both of the projections blow up at the same time.

My question: Does this mean that MRPs are always advantageous over quaternions for spacecraft attitude determination and control? Since we are avoiding this discontinuity with MRPs. Please, correct me if I am wrong in any of the above reasoning.

Thanks :)

• Slightly related: What are quaternions and how are they used to represent spacecraft dynamics? the answer may be of interest, though not an answer to your question. – uhoh Nov 6 '18 at 12:48
• Welcome to Space, nice first question. It won't matter at all to spacecraft computers, as either form must be calculated as a series of multiplication and addition instructions. So, it's a matter of preference for the humans developing the mathematics. – DrSheldon Nov 6 '18 at 14:00
• Thanks uhoh and Dr Sheldon for your replies. Dr Sheldon, apparently not all coordinate system representations are unique or global. Shouldn't this non global and non uniqueness condition be an issue for reference tracking via feedback control? References: imgur.com/a/NPZ0i7V and imgur.com/a/zMLWfNv – Watch This Nov 7 '18 at 9:09