Comparison of L1 norm and L2 norm minimisation methods in trigonometric levelling networks

Abstract

The most widely-used parameter estimation method today is the L2 norm minimisation method known as the Least Squares Method (LSM). The solution to the L2 norm minimisation method is always unique and is easily computed. This method distributes errors and is sensitive to outlying measurements. Therefore, a robust technique known as the Least Absolute Values Method (LAVM) might be used for the detection of outliers and for the estimation of parameters. In this paper, the formulation of the L1 norm minimisation method will be explained and the success of the method in the detection of gross errors will be investigated in a trigonometric levelling network.