Analytic sensing is a new mathematical framework to estimate the parameters of a multi-dipole source model from boundary measurements. The method deploys two working principles. First, the sensing principle relates the boundary measurements to the volumetric interactions of the sources with the so-called "analytic sensor," a test function that is concentrated around a singular point outside the domain of interest. Second, the annihilation principle allows retrieving the projection of the dipoles' positions in a single shot by polynomial root finding. Here, we propose to apply analytic sensing in a local way; i.e., the poles are not surrounding the complete domain. By combining two local projections of the (nearby) dipolar sources, we are able to reconstruct the full 3-D information. We demonstrate the feasibility of the proposed approach for both synthetic and experimental data, together with the theoretical lower bounds of the localization error.