A Comparative Study of Trignometric Parallax Reduction Techniques
Abstract
A comparative study of reduction techniques of trigonometric parallaxes from measurements of photographic plates is presented. The rigorous noniterative technique is the most mathematically elegant and is the only one which produces the exact covariance matrix of the unknowns. The normal plate constant technique is reduced from the rigorous noniterative method if it is assumed that the covariance matrix is diagonal, the reference star parallaxes are small and can be considered zero, and the central star data is not used to determine the plate constants; the method uses simplified calculations but some accuracy is lost because of the assumptions required. The iterative plate constant technique has the advantage of including data which the other methods cannot use with only a moderate increase in the amount of calculations. It is concluded that the choice of method depends on the results desired beyond the central star parallax, so that the normal plate constant solution is simplest for reducing one star's parallax and the full rigorous method should be used if a most complete error estimate and the full covariance matrix of the results are required.
 Publication:

IAU Colloq. 48: Modern Astrometry
 Pub Date:
 1978
 Bibcode:
 1978moas.coll..355R
 Keywords:

 Astronomical Coordinates;
 Parallax;
 Photographic Plates;
 Trigonometry;
 Astrometry;
 Matrices (Mathematics);
 Tables (Data);
 Astronomy