A weighted total least-squares algorithm for fitting a straight line

The well-known problem of fitting a straight line to data with uncertainties in both coordinates is revisited. An algorithm is developed which treats x- and y- data in a symmetrical way. The problem is reduced to a one-dimensional search for a minimum. Global convergence and stability are assured by determining the angle of the straight line with respect to the abscissa instead of the slope. As opposed to previous publications on the subject, the complete uncertainty matrix is calculated, i.e. variances and covariance of the fitting parameters. The algorithm is tested using Pearson's data with York's weights. Although the algorithm is implemented in MATLAB, implementation in a different programming language is straightforward using the formulae presented. An application example is given, a calibration line for dosimetry based on electron spin resonance of alanine is investigated.