Application of a hybrid least squares algorithm in astronomical positioning

In order to reduce the digital zenith camera identify stars data that exist in the gross error influence on astronomical calculating, improve positioning accuracy. The mapping relation between the CCD image coordinate system and the celestial tangent plane coordinate system is established by using the robust weighted hybrid least squares algorithm. Using the least squares algorithm did not consider of the errors in the coefficient matrix and the data of the gross error. So the least squares algorithm and the total least squares algorithm are effectively combined to form the hybrid least squares algorithm. Then the hybrid least squares algorithm is used for robust weighting, reduced the identify stars possible gross error in the data, and reasonable weight matrix is set in conjunction with the magnitude. Experiments show that the robust weighted hybrid least squares algorithm has high accuracy in astronomical solution. INTRODUCTION When using digital zenith camera positioning used Helmet model for conversion between coordinates. The coordinates of the CCD image of the star and the coordinates of the celestial plane have some errors, and in the coordinate transformation parameters to solve the time often use the least squares algorithm. The least squares algorithm only considers the error of the observation, but does not take into account the error of the coefficient matrix, the overall least squares algorithm can take into account the error of the coefficient matrix and the observation,but the values in the overall least squares coefficient matrix contain some errors. In fact, there is a constant series (or row) with no errors in the coefficient matrix.In order to identify the coordinates of the star's coordinate transformation parameters with high precision,the least squares algorithm and the total least squares algorithm are combined to form a mixed least squares algorithm. The mixed least squares algorithm takes into account both the constant series (or row) in the matrix and the errors in the coefficient matrix and observations. However, there may be a rough error in the data, Considering the poor ability of the mixed least squares algorithm to resist the coarse error, a robust weighted mixed least squares algorithm is proposed, the weighted star data is weighted and the influence of the coarse error on the solution parameters is weakened. COORDINATE TRANSFORMATION MODEL In the process of positioning with a digital zenith camera meter, the star map of the zenith is photographed by the CCD star sensor. Through the star table for star map recognition, the establishment of the stars to determine the celestial plane coordinate system and CCD image coordinate system, the conversion between the two coordinates using Helmet conversion model, there are: