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This article compares trajectory prediction methods for the collaborative operation of an autonomous surface vehicle (ASV) serving as the lead vehicle and an autonomous underwater vehicle (AUV), following the lead vehicle in a collaborative mission. The lead ASV is a WAM-V16 equipped with a multibeam sonar (MBES) to collect seafloor bathymetry data, which requires sound speed for the accurate location of soundings. The AUV, which is an Iver-3, is equipped with a conductivity, temperature, and depth sensor providing high-resolution sound-speed profiles. The collaborative mission between the lead (ASV) and the chase vehicles (AUV) is initiated by a mission plan for the ASV since it is sometimes advantageous for the underwater vehicle to dynamically respond to changes in the surface vehicle’s mission, whether due to obstacle avoidance behavior or human intervention, without needing to update the mission plan on the underwater vehicle. Therefore, the prediction of the future trajectory of the ASV is proposed using the Global Navigation Satellite System receiver onboard the ASV for accurate positioning. The position data are sent acoustically to the underwater vehicle while submerged or through radio communication when on the surface. Acoustic communication between the ASV and AUV is achieved through an acoustic modem, which interferes with the MBES data acquisition, leading to acoustic noise in the data. Predicting the future trajectory as far ahead as possible enhances the efficiency of the collaborative operation between the vehicles and helps minimize the frequency of acoustic interference. This study proposes four deterministic models—two-point, consecutive average, linear regression (LR), and nonlinear regression (NLR). The accuracy of predicted positions from the models is assessed using variance explained statistics. Findings show that with an appropriate weighting method, the prediction errors of the LR and NLR decreased, with LR having the overall best performance among all the prediction models, followed by NLR. LR also runs faster than NLR, making it more efficient in real-time prediction.