Alexander S. Tsvetkov (Astronomical Institute of St. Petersburg University, 198904, St. Petersburg, Petrodvorets, Bibliotechnaya pl.2, Russia)
Reference URL: http://www.astro.spbu.ru/AI/Astrometry/tsvetkov.html
A common practice in astronomy is: gathering data, contructing a model, evaluating of the parameters of the model by the Least Squares technique.
It is well known that the Least Squares method returns the values of the parameters regardless the corespondence of the model to observations. If the model does not correspond to the data one obtains the formal values of the parameters, which have not the physical sense. Nevertheless, many people use values thus obtained in their theories and practice.
The proposed method based on the orthogonal representation of the equations of a model is free of this fault since it tests the consistency of the model and data.
This method have been used to find out the sufficiency of the standard kinematical model to proper motions of stars in the Hipparcos catalogue. It shows that there are some difficulties with the standard model of the Galactic rotation, and, on the contrary, there is a good agreement with the model of the Sun motion.