The comparison of L-1 and L-2-norm minimization methods

Abstract

L-2-norm, also known as the least squares method was widely used in the adjustment calculus. The weaknesses of the least squares method were the effect of gross measurements error on the solution and the disturbance and absorbance of gross error on the solution. L-1-norm, also known as the least absolute values method, was affected by almost none or very little from gross error. Therefore L-1-norm method, used for parameters estimation in some special case, has been successfully used for outlier measurements detection. In this study, the L-1 and L-2-norm adjustment methods have been taken relatively to each other's advantages and disadvantages and the numerical application of the two-dimensional similarity coordinate transformation were made and the results of both methods are discussed.