A key technology in the movement tracking of marine animals is localization using acoustic transmitters. These are attached to marine animals and are detected by an array of receivers. Then, offline localization is performed by multilateration. However, due to the transmitter's low power and environmental conditions, emissions may be detected by only a limited number of receivers, causing localization ambiguities to arise. This work proposes a solution for such localization ambiguities. The proposed method assumes that the position of acoustically-tagged marine animals follows a hidden Markov model, such that localization ambiguities can probabilistically be resolved using a Forward-Backward algorithm. Our method is able to extrapolate the positions in a data series, as long as one sample in that series is picked up by three receivers, or if the identity of the receivers changes during tracking. Performance analysis shows that the localization accuracy of our method approaches the Cramér-Rao lower bound. Furthermore, to demonstrate the suitability of our method in a real sea environment, we have established a testbed that operated for three months, demonstrating localization of 20 acoustically-tagged sandbar sharks. Compared to the available solutions, roughly 20 times more location estimates were made; thereby, significantly increasing the impact of the test-site.