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The paper presents an algorithm for water-system state estimation in presence of gross errors in measurement data. Application of a modulus norm in place of the more usual least-squares criterion for the minimisation of measurement inconsistency is shown to result in a linear programming formulation. A high computational efficiency for the algorithm is obtained by utilisation of both sparsity techniques and some special features of water distribution systems. Test results are included which demonstrate the applicability of the algorithm for online computer-based state estimation.