weighted total least squares straight line fit 1.0

The problem of fitting a straight line to data with uncertainties in both coordinates is solved using a weighted total least-squares algorithm. The parameters are transformed from the usual slope/y-axis intersection pair to slope angle and distance to the origin. The advantages of this are that a) global convergence is assured b) a solution is found even for a vertical line. The complete uncertainty matrix (i.e. variances AND covariance of the fitting parameters) is determined. For non-vertical straight lines the usual parameters (slope/y-axis intersect.) are also given, together with their uncertainty matrix. The algorithm is especially useful for precision measurements, where the knowledge of the complete uncertainty matrix is a must. The algorithm was published in Measurement Science and Technology 18 (2007) pp3438-3442 by M.Krystek and M.Anton, Physikalisch-Technische Bundesanstalt Braunschweig, Germany. An attached script named pearson_york_tetdata.m contains a standard statistical test data set for the problem (see e.g. Lybanon,M in Am.J.Phys.52(1)1984 pp22-26)

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Intersect,  Knowledge,  Measurement,  Measurements,  Precision,  Published,  Science,  Technology
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