Abstract
L1 norm minimization is a powerful mathematical tool used in surveying to detect gross errors in survey data. We describe the basic theory underlying L1 norm estimation and its implementation through linear programming and the simplex method. Two numerical examples describe linear and nonlinear L1 estimation. The first example illustrates the process of computing the L1 norm parameter estimate (median) of a quantity observed directly three times. The second example describes L1 norm estimation for a typical survey network with distances, angles, and weights.
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