Least squares solution of illconditioned systems.
Abstract
In a rediscussion of previous results, observations of minor planets 6 (Hebe), 7 (Iris), 8 (Flora), 9 (Metis), and 15 (Eunomia) are used to determine corrections to a number of astronomical parameters. The methods used are similar to singular value analysis, but directly employ the normal equations previously calculated for a traditional least squares solution. Solutions by individual minor planets and by various subsets of the observational data show much less variation than solutions given by traditional least squares. But there are discrepancies between the determinations of certain unknowns, particularly the equinox correction, its secular variation, and the correction to the precession given by traditional least squares and the approaches outlined in this paper. External evidence indicates that the results from traditional least squares are superior.
 Publication:

The Astronomical Journal
 Pub Date:
 October 1979
 DOI:
 10.1086/112586
 Bibcode:
 1979AJ.....84.1632B
 Keywords:

 Asteroids;
 Astrometry;
 Equinoxes;
 Least Squares Method;
 Orbit Calculation;
 Planet Ephemerides;
 Correlation;
 Eigenvectors;
 Error Analysis;
 Stellar Motions;
 Lunar and Planetary Exploration;
 Minor Planets