This work proposes a robust tracker based on the Poisson Multi Bernoulli Mixture (PMBM) filter for multistatic sonar networks (MSNs) systems. The PMBM based trackers estimate the number of targets and provide the target information via Bernoulli and Poisson Point Processes. The PMBM based trackers handle existing tracks, undetected targets, and new births separately at each computation step by using these two processes together. In practice, the PMBM tracker aims to initiate the track as soon as possible and maintain the track continuity. Initiating track and maintaining track continuity are hard in challenging underwater environments without adapting the algorithm to changing environmental conditions. This paper uses the adaptive measurement-driven birth process and multistatic acoustic model-dependent probability of detection specifications. The adaptive measurement-driven birth process improves the robustness of the track initiation, and the multistatic acoustic model-dependent probability of detection advances the track continuity through the transition regions. These contributions to the PMBM tracker make it robust in terms of tracker performance in challenging underwater environments and acoustic transition regions where it is hard to get an accurate measurement.