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The low sound speed in water makes propagation delay (PD)-based range estimation attractive for underwater acoustic localization (UWAL). However, due to the long channel impulse response and the existence of reflectors, PD-based UWAL suffers from significant degradation when PD measurements of nonline-of-sight (NLOS) communication links are falsely identified as line-of-sight (LOS). In this paper, we utilize expected variation of PD measurements due to mobility of nodes and present an algorithm to classify the former into LOS and NLOS links. First, by comparing signal strength-based and PD-based range measurements, we identify object-related NLOS (ONLOS) links, where signals are reflected from objects with high reflection loss, for example, ships hull, docks, rocks and so on. In the second step, excluding PD measurements related to ONLOS links, we use a constrained expectation-maximization algorithm to classify PD measurements into two classes: LOS and sea-related NLOS (SNLOS), and to estimate the statistical parameters of each class. Since our classifier relies on models for the underwater acoustic channel, which are often simplified, alongside simulation results, we validate the performance of our classifier based on measurements from three sea trials. Both our simulation and sea trial results demonstrate a high detection rate of ONLOS links, and accurate classification of PD measurements into LOS and SNLOS.