An algorithm for the statistically rigorous and noniterative computation of trigonometric parallaxes
Abstract
A noniterative algorithm is developed for the statistically rigorous computation of parallaxes from measurements on photographic plates using the initial equations of the central overlap method. For this, it is assumed that no reference star positions and/or proper motions (from a catalogue) are used and that the proper motions of the reference stars are subjected to the condition that they are random except for a systematic component due to solar motion and differential galactic rotation. It is shown that the computation of all unknowns can be achieved so that the largest matrix to be inverted is of the order 2rn + I where m is the maximum number of star images measured per plate. In contrast to the iterative methods, this one provides an accurate covariance matrix of the unknowns. The feasibility of this approach was tested on an example, Groombridge 1830.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 1976
 DOI:
 10.1093/mnras/174.3.679
 Bibcode:
 1976MNRAS.174..679E