This paper proposes a generalized likelihood ratio test to detect whether a blind node is moving or not as a first step toward its localization. The proposed test can process received signal strength (RSS), time of arrival (TOA), or angle of arrival measurements. Doing so, an algorithm can be designed capable of improving the overall localization accuracy. As customary, measurements between nodes at known positions (anchors) are used for parameter estimation purposes. The decision statistic of the test is analytically characterized under both hypotheses and, remarkably, it guarantees the constant false alarm rate property with respect to the unknown parameters. The application of the test to localization based on either RSS or TOA measurements is also considered.