This article is devoted to the comparison of algorithms for estimating the position and heading angle of the autonomous underwater vehicle (AUV) relative to the stationary landing platform (SLP) using a short-range hydroacoustic system. The problem is mathematically formulated using the Bayesian framework. Three algorithms are compared. One of them involves non-inertial processing, while the other two take into account the accumulation of measurements during the AUVs movement. One of the two latter algorithms is implemented in a recursive scheme: the recursive iterative batch linearized smoother (RI-BLS), while the other one follows a non-recursive scheme: an algorithm based on factor-graph optimization (FGO). Simulation results comparing the root mean square errors (RMSE) for the AUV’s position and heading angle estimates are presented, evaluating the performance of the algorithms. These RMSEs are also compared with the Cramer-Rao lower bound.