誤差調整における最小二乗法と最小絶対値法の比較

Abstract

Least square method is a kind of statistical method based on probability, which is well applied to adjustment of random errors occurred in a multiple observation.However, in actual observation, there often occurs such case in which a limited numer of observation with very few but large error are only made. In this case, the least square method gives a solution to distribute the influence of the large error uniformly to other points. This phenomenon results in the case, in which it is impossible to identify the point with large error.On the other hand, least absolute value method gives a solution to minimize a sum of absolute value of residuals. This solution will be resulted from a majority of points with small error, regardless of large error. Therefore, because the residual of the point with large error will become apparently large, it is possible to identify the point with large error.The study dealt with comparisons between least square method and least absolute value method, including comparisons of solutions, distribution of residuals and the influence of redundant observation by both methods. Experimental study was made for affine transformation in the two dimensional coordinate system.From the result of the study, it can be said that least absolute value method is quite useful to identify the point with large error. However, a disadvantage of this method is to have to apply linear programming which used to need computing time.