Seabed relief-based vessel position fixing with a neural network

Abstract

A seabed relief-based vessel position fixing system on the basis of a neural network is proposed. The neural network satisfies the conditions of the universal approximation theorem and has one hidden layer. The hidden neurons have hyperbolic tangent activation functions. The model is constructed for 1-D case that can be considered as vessel motion throw a narrow channel or fairway. A sequence of depth derivatives (in relation to the coordinate) is fed to the network input. The depth is assumed to be measured with an echo-sounder. The vessel linear coordinate registered for the last depth derivative is formed on the network output. The training set contains not only data presumably registered at the stage of preliminary depth survey but also their noise-added versions obtained with the use of a random number generator. The validation set contains the survey data only. The Adamax algorithm is implemented for the neural network training. The maximum of absolute value of the prediction error is used as a performance criterion of the net. Modeling has been conducted in Python with Tensorflow. The depth is considered to be a polynomial function of the coordinate at each path region. So, the depth derivatives can be calculated analytically. As the result it is possible to state that the neural network predicts a vessel position with acceptable accuracy even in input signal noise conditions. Moreover, the neural network architecture of the radial-basis functions has been examined, but it is not possible to achieve acceptable accuracy by using it. The conducted investigations of the influences of a mini-batch size and learning rate values on the accuracy has shown that these parameters have the significant impact and an issue of their choice remains opened and actual in the framework of the task.