A special least squares method for curve fitting

A special least squares (SLS) method is proposed which is based on minimizing the sum of squared relative deviations. The author analyzes the problem of classical least squares (LS) in fitting a static characteristic equation and points out the shortcomings of the LS method under some experimental conditions. It is noted that the proposed SLS method could overcome the shortcomings. The formulas of SLS are given and its mathematical characteristics are analyzed. Under the given conditions, this method is unbiased, consistent, and efficient. An example is given of fitting a static characteristic equation of a potentiometer by using the SLS method. The results show that, under the given experimental conditions, the SLS method is superior to the traditional LS method