Weighted and Unweighted Total Least Square Methods and Applications to Heteroscedastic 3D Coordinate Transformation

Traditional solution to 3D coordinate transformation problem is the optimal estimation at the cost function of the least squares(LS)for residual vector without consideration of point covariance.Whereas ordinary least squares and total least squares methods can not work well in the heteroscedastic cases.Then unweighted and weighted TLS methods are introduced and compared.The data experiments indicate that unweighted TLS method and LS method have the consistent results and the block row-wised WTLS method has the same results as the maximum likelihood estimator(MLE),and the element-wised method is not so accurate as MLE due to neglecting the correlations of the matrix elements.