Walf@ZWO the principle of goto is reference the nearest position which has been alignment
That is not how you use alignment stars. All stars need to be used to satisfy the degree of freedom of the equations (solving for "the unknowsns"). If you have more stars, just use the metod of Least Squares to avearge out the measurement variances.
The way you do it properly is to measure the positions of the alignment stars, and then establish a mathematical model for the mount from all of the stars. You can then go to any target by using the coordinate system of the model.
Toshimi Taki had described it in a 1989 "Sky And Telescope" issue, and repeated it here in case your local library does not have an old issue of the Sky And Telescope magazine (or like me, had already thrown the old copies away):
http://takitoshimi.starfree.jp/aim/aim.htm
Notice for example that he incorporates cone error of the mount into his "Equations for Mount with Fabrication Error." But you don't need to specifically measure the cone erro -- the matrix parameters will falll out from the alignment stars.
Something like this should take less than a second on a modern microprocessor. But you need to use double precision arithmetic.
(If you read Japanese, you can look at Reference 2 and 3 in the above link, for how it is done in Alt-Azimuth mounts, or refer to the next link below.)
For more detailed mathematics, you can also refer to Taki-san's other white paper:
http://takitoshimi.starfree.jp/matrix/matrix_method_rev_e.pdf
where he also describes "Compensation of Mounting Fabrication Errors" in section 5.3 of the paper. That is followed in Section 5.4 with "Equations for Pointing Telescope."
For a German mount, depending on how precise the mount is machined, you may need a model for each side of a Meridian flip.
Taki-san's useful web site is found here:
http://takitoshimi.starfree.jp/index.htm
Chen
