The TRopIcal DEep-sea Neutrino Telescope (TRIDENT), a next-generation neutrino telescope in the South China Sea, requires precise position measurements to exploit the timing capabilities of hybrid digital optical modules (hDOMs), ensuring the pointing capability of the detector. This study presents a preliminary design of the TRIDENT Acoustic Positioning System (APS), which includes the acoustics transducer instrumentation and the overall calibration strategy. A dedicated positioning simulator has been developed to model acoustic signal propagation, ambient noise and transducer responses. We explored the impact of different base station settings on the final hDOM positioning accuracy, establishing critical benchmarks for TRIDENT's future operation.