Total least squares: An ideal mathematical tool for galactic kinematics.

*(English)*Zbl 0937.62130Summary: Problems of Galactic kinematics have usually been solved by the method of least squares. As has been known for over forty years, this may lead to biased results because least squares assume that error resides only in the observations, not in the equations of condition. The latter, however, generally incorporate error, at least in some of the columns of the data matrix. Total least squares represents the ideal mathematical tool for just this sort of problem. In this paper the method, or better stated a mixed total-ordinary least squares method, is applied to 3100 stars taken from the Bright star Catalog to calculate eight parameters of Galactic kinematics: two corrections to the precessional constants, the Oort \(A\) and \(B\) parameters, the components of solar motion, and the \(K\) term. Total least squares calculates a reasonable solution, whereas ordinary least squares fails completely.

##### MSC:

62P35 | Applications of statistics to physics |

85A35 | Statistical astronomy |

85A05 | Galactic and stellar dynamics |