Depth-based vessel position fixing by means of a neural network

Abstract

A depth-based vessel position fixing method on the basis of a neural network is proposed. The network takes as an input a sequence of depth values measured by an echo-sounder and predicts vessel latitude and longitude for the moment of the latest depth measurement. The neural network has a fully-connected feedforward architecture with several layers which satisfies conditions of the universal approximation in compliance with the Stone-Weierstrass theorem. The Adamax algorithm for the neural network training with controlling a maximum value of position error at each epoch is implemented. Modeling is conducted with the Python programming language and the Tensorflow library. The model surface of seabed is performed as a second-order polynomial. Training samples on the basis of virtual soundings at the coordinate net knots with the space resolution not worse than one cable are obtained. After samples obtaining the training of the neural network is conducted. A validation set is not used. Several neural networks are trained. They have different number of hidden layers and different number of neurons per each hidden layer. After training the test procedure is performed. Test samples are generated in the assumption that a vessel is moving along meridians which are not used at the stage of the preliminary soundings survey. The cases of mean and random test meridians are considered. The random meridians are obtained with a uniform random number generator. As the result, all the tested neural networks have shown approximately identical navigational accuracy which is close to the accuracy for the training set.