Least Squares Adjustment with Finite Residuals for Non-Linear Constraints and Partially Correlated Data,

摘要

The subject of the paper is the adjustment (curve fitting) of data by the least squares method. Based on general formulas,which are derived in the paper, a new algorithm for the least squares method is established. It can be applied to cases where more than one observable contain observational errors and where the postulated relation between the observables is non-linear. Also taken into account are accuracies of the observations and correlations between the components of each observation vector. New formulas are derived for the estimation of the variance-covariance matrix of the fitted parameters. It is shown that the conventionally used estimation formula is theoretical wrong except for very limited special cases. Numerical tests of the algorithm demonstrate its accuracy and exceptional convergence characteristics. They also show that the conventional estimate of the variance-covariance matrix of the parameters is a very bad approximation to the theoretically correct estimate derived in the paper. (Author)