Autonomous underwater vehicles require accurate navigation. Techniques such as image registration using consecutive acoustic images from a sonar have shown promising results for this task. The implementation of such techniques using sonar images augmented with deep learning (DL) networks demonstrate high navigation accuracy; this is possible even with highly compressed images. The sonar images are estimates of sampled in time (with a ping period) magnitudes of channel impulse responses representing the underwater acoustic environment. More information about the environment is contained in (almost) continuous in time estimates of the channel impulse responses. Such estimates can be obtained using full-duplex technology. Rather than using sonar images, this paper investigates the use of channel impulse response estimates for underwater platform motion estimation. The proposed system uses a single projector and a small number of receiving transducers installed on the moving platform. A DL network is used to estimate the motion in two degrees of freedom (forward/backward and sideways), using two or more consecutive impulse response estimates as the input. To train the DL network, a specially designed simulator is used to model the underwater acoustic environment, populated with multiple objects spread on the seafloor. The proposed technique can significantly reduce the acoustic hardware and processing complexity of the DL network and obtain a higher accuracy of motion estimation, compared with techniques based on the processing of sonar images, e.g., the error achieved with the technique proposed in this paper is 1.7% of the maximum platform displacement, compared to 4% achieved with a technique using sonar images. The navigation accuracy is further illustrated by examples of estimation of complex trajectories.