Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..61..239b&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 61, no. 3, p. 239-251
Astronomy and Astrophysics
Astronomy
4
Astronomy, Data Reduction, Least Squares Method, Orthogonal Functions, Regression Analysis, Approximation, Error Analysis, Kinematics, Matrices (Mathematics), Two Body Problem
Scientific paper
Total least squares considers the problem of data reduction when error resides in both the data itself and also in the equations of condition. Error may be found in all of the columns of the matrix of the equations of condition, or merely in some; the latter situation is referred to as a mixed total least squares problem. A covariance matrix may be derived for total least squares. Both memory and operation count requirements are more severe than for ordinary least squares: about four times more memory and, if the problem involves n unknowns, 15n + 4 more arithmetic operations. The method, applicable in any situation where ordinary least squares is relevant, including the estimation of scaled variables, is applied to three examples, one artificial and two taken from astronomy: the estimation of various parameters of Galactic kinematics, and the differential correction of a planetary orbit. In these two examples the results from total least squares are superior to those from ordinary least squares.
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