Mixed integer linear programming (MILP) has been proven to be an effective method for identifying multiple gross errors in linear steady-state processes. In this work, a location estimation-based MILP approach is proposed, which reconciles the location calculated with a location estimator instead of a horizon of data so that the problem size is reduced while the performance for gross error detection is enhanced; an offline method for tuning the model parameters is also presented here based on an analysis of their effects. Different models of measurement errors are used to evaluate the proposed approach implemented with two location estimators, i.e., weighted least-squares and biweight; the results show that the MILP approach based on both estimators outperforms the original MILP technique and that the biweight-based MILP is more robust under the presence of occasional outliers.