The paper addresses object localization via a distributed sensor network. A centralized estimation approach is undertaken along with a selective node activation strategy to ensure energy efficiency. The attention is concentrated on compensating the scarcity of information in the data (i.e., few and noisy measurements) due to selective activation by the exploitation of available constraints. To this end, a recently developed softconstrained estimation algorithm [1] based on linear matrix inequalities is applied to the localization problem to get an improved quality of estimation. The performance of the proposed approach is evaluated on a case-study concerning a network of direction of arrival sensors. Keywords : sensor networks; object localization; constrained estimation; linear matrix inequalities; least-squares estimation.