Least squares method applied to astrometric plate reduction
Abstract
The polynomial transformation formulas between the measured (x, y) and standard coordinates (X, Y) give the normal equations by application of the least squares method. In order to check the formulas a number of test stars were chosen, treated as comets or asteroids, and compared with catalog values. The same was done with the reference stars. The arithmetical means of the differences for the two groups of stars are set out in ordinate to get a graph of the internal (reference stars) and external (test stars) error versus number of reference stars (abscissa); at the junction of the two curves the optimal number of reference stars was obtained. These graphs give an idea of the accuracy of the calculations for a given instrument and a chosen formula. Computations related to the mean square error also give valuable information. The polynomial formula of the third degree gave good results, when applied to artificial cloud plates taken by a 500 mm focus distance camera.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1975
 Bibcode:
 1975STIN...7530506D
 Keywords:

 Astrometry;
 Data Reduction;
 Least Squares Method;
 Photographic Plates;
 Artificial Clouds;
 Astronomical Catalogs;
 Astronomical Photography;
 Coordinate Transformations;
 Graphs (Charts);
 Reference Stars;
 Star Trackers;
 Instrumentation and Photography