These days, more and more computer programs are available to assess water distribution system reliability and compliance with water quality standards. Extended Period Simulation (EPS) hydraulic models consist of solving mass and energy balancing equations for urban pipe networks operating with non-transient events. In such a normal functioning mode, demand is assumed to be known and leakage as part of the demand is equally distributed on the basis of the pipe lengths or the number of householders. After being calibrated in terms of demand and roughness parameters, it leads to a good prediction of tank level variation and flow rates of mains. Automatic hydraulic calibration has been stated as a constrained nonlinear least squares problem. Non-convergence situations and local solutions are often reported. Also, solving by Genetic Algorithms (GAs) to find global near-optimal solution, then speed up convergence by gradient-type methods seems to be a good trade-off. In this paper, we will show it is possible to formulate this problem so that a unique global solution exists: In that way, derivatives are explicitly written in order to lead to optimal sampling design, ensuring observability. Specific operations generating large head losses are considered so that parameter estimation is more accurate. In these conditions, the Levenberg-Marquardt (LM) algorithm converges for each initial value and at quadratic rate near the minimum. Finally, the respective merits of GA and LM methods will be given and discussed in solving for a real urban water network.