An Algorithm for the Statistically Rigorous and Non-Iterative Computation of Trigonometric Parallaxes*

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Abstract
A non-iterative 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 2m+ 1 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, Groom bridge 1830.

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