Polynomial Curve Fitting When Abscissas and Ordinates are both Subject to Error

An iterative method is described for the least-square curve fitting of a polynomial to a set of points in two dimensions when both the abscissas and ordinates are subject to error and when the weights of all the readings are known. The process converges, in general, to a polynomial giving the exact minimum of the ‘weighted’ perpendicular distances onto the curve. It is shown that in practice Deming's method gives a solution close to this optimum polynomial.