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The mathematical programming formulation for the LMR estimator proposed in [28, 29] is

(2.45a)

subject to

(2.45b)

(2.45c)

(2.45d)

(2.45e)

In (2.45b), note that each binary variable b_i indicates whether or not the ith weighted measurement error (y_i(x)) is within the range [−T, T ]. Specifically, the value b_i = 0 implies that ∣y_i(x ) ∣ ≤ T. On the other hand, the value b_i = 1 implies that ∣y_i(x) ∣ > T. Since the objective function (2.45a) minimizes the sum of all binary variables b_i, the LMR procedure searches the largest set of measurement errors within the range [−T, T].

Once problem (2.45) has been solved and the set of out‐of‐tolerance measurement errors has been identified, a WLS estimation is performed to enhance the estimation quality, considering only those measurements whose associated binary variables have optimal values that are equal to zero [28].