Least-squares estimation using Lagrange multipliers

This paper presents a general formulation of least-squares estimation using Lagrange multipliers. It is general in the sense that it takes into account the covariance matrix of all measured quantities and allows any known constraint to be imposed on the quantities being estimated. The technique may be used to estimate parameters of a calibration curve for a transducer taking into account the uncertainty and correlation coefficients of the measured stimuli and responses. It may also be used to adjust measured fundamental constants to a coherent set obeying the appropriate physical laws.