In this paper, we propose a method to localize a wireless and stationary blind node based on received signal strength measurements; the positioning scheme relies on the statistical path loss model. The operating environment is either non-homogeneous, i.e., the attenuation factors of the various links are different, or homogeneous, i.e., all links share one and the same attenuation factor. We introduce a cognitive procedure to circumvent the a priori uncertainty on the actual scenario being in force: the first stage is a properly designed hypothesis test, fed by measurements between anchors, moving along known trajectories, to decide whether or not the environment is homogeneous. Based upon the output of the test, a model-dependent maximum-likelihood localization algorithm is adopted using the measurements made by the blind node and the parameters estimated by the anchors at previous stage. The performance assessment shows that the proposed approach could be a viable means to handle localization in uncertain scenarios.