Within the context of microgrids optimal voltage control, most schemes proposed in the literature either rely on (i) droop-control methods or (ii) methods involving the computation of explicit nodal power set-points as a solution to a given optimization problem. The first category of approaches is in general suboptimal as it relies on locally sensed measurements. The second category guarantees some level of optimality but requires an accurate and up-to-date model of the network that is, in general, not always available in low voltage grids. To overcome the aforementioned limitations, in this work we propose a methodology suitable for voltage control in generic low voltage 3-phase unbalanced grids. It can be used for the computation of either explicit power set-points or to define the droops of local voltage regulators. Its main characteristic is that it does not rely on the knowledge of the system model and its state. In particular, the goal is to compute linearized dependencies between voltage magnitude and nodal power injections, i.e., voltage sensitivity coefficients. The proposed method assumes availability of a monitoring infrastructure and the computation of the desired sensitivities involves the solution of an over-determined system of linear equations constructed solely using available measurements of nodal power injections and voltage magnitudes. The proposed method is also capable to account for the measurement errors and their time correlation. The performance evaluation of the proposed method is carried out using real measurements coming from a real low voltage feeder located in Switzerland equipped with an appropriate metering infrastructure.