Artificial Neural Networks for Comparative Navigation

Abstract

The article presents methods of computer ship’s position plotting by means of comparative methods. A new approach in comparative
navigation is the use of artificial neural networks for plotting the ship’s position. Two main problems should be solved during
ship’s positioning process: compressing (coding) image and recognition (interpolation) ship’s position.

Full text

Artificial Neural Networks for Comparative Navigation
Andrzej Stateczny
Maritime University Szczecin, Wały Chrobrego ½, Szczecin, Poland
astat@wsm.szczecin.pl
Abstract. The article presents methods of computer ship’s position
plotting by means of comparative methods. A new approach in
comparative navigation is the use of artificial neural networks for
plotting the ship’s position. Two main problems should be solved
during ship’s positioning process: compressing (coding) image and
recognition (interpolation) ship’s position.
1. Introduction
Satellite and radar systems have been the main information sources in
marine navigation in recent years. Apart from commonly known anti-collision
functions, the marine navigational radar constitutes the basis for a future
comparative system of ship positioning. The sonar is an additional source of
image information in the system. In this way, the data are derived from
observing the surroundings of the ship’s total measuring area. The system of
comparative navigation is an attractive alternative to satellite navigation due
to its autonomy and independence from external appliances.
Plotting the ship’s position by comparative methods can be performed by
three basic methods:
 Determining the point of best match of the image with the pattern.
The logical product algorithm is used in this method which makes it
possible to find the point of best matching of images recorded in the
form of digital matrix.
 Using the previously registered real images associated with the
position of their registration. This method uses the artificial neural
network taught by a sequence created from vectors representing the
compressed images and the corresponding position of the ship.
 Using the generated map of patterns. The artificial neural network is
taught by a representation of selected images corresponding to the
potential positions of the ship. The patterns are generated on the basis
of a numerical terrain model, knowledge of the hydrometeorological
conditions effect and the observation specificity of the selected
device.

During using artificial neural networks for plotting the ship’s position there
is the problem of selecting the teaching sequence designed to teach the
network. The images must be subjected to treatment for the purpose of data
reduction and compression. The advantage of this method is that once thought
neural network (neural processor) can be use many times and new
measurements might be added to increase the accuracy and reliability of
system.
After initial treatment of the analyzed image a teaching sequence of the
artificial neural network is prepared. In the process of teaching the network it
is the task of the network to work out a mapping function associating the
analyzed image with the geographical position. Numerous experiments have
shown a decided advantage of the GRNN network over other solutions.
SYSTEM OF VESSEL
POSITIONING
Subsystem of
radar image
compression
(coding)
GRNN network

GRNN network



Fig. 1. Diagram of a ship positioning system.
2. Kohonen Network
Kohonen network changes the image given at its input (image segment) into the
index of one of its neurons. The return number obtained corresponds to the neuron
which is closest to the input image according to selected metric. And so, if image
segments are given successively at the input of Kohonen network, an index vector of
Kohonen network will be obtained at the output. The size of the vector will be equal
to the number of segments.
The accuracy of the mapping obtained in this way depends on the
number of neurons in Kohonen network in relation to the number of various
possible pixel combinations in the input picture. For example, for black-and-
white images with size NxM (N – image width in pixels, M – image height in
pixels) the maximum number of various images possible to obtain equals
2NxM. With a large number of network neurons – closest to the maximum
value – compression will be very accurate and each image will have its unique
compressed counterpart. A network poorer in neurons will make larger

generalizations which will bring about a situation with similar images having
the same counterpart on the compressed side.
A more accurate mapping of image concentration during their
compression can also be obtained by proper selection of indexes for the
neurons of Kohonen network. Their ordering should represent in the best
degree the distribution of images associated with each neuron in the image
space. Neurons similar to each other should have close indexes. Neurons
differing strongly by weight should be characterized by distant indexes. This
effect can be obtained by using Sammon mapping; it allows to project multi-
dimensional vectors into spaces of smaller dimensions. Thanks to this
mapping of vectors we are able to assign a real number to each image (image
segment). This will make possible to bind every neuron of Kohonen network
with the value corresponding to it. In this way, during compression the
network will not return to us the neuron number selected at random, but the
real number associated with it corresponding to the location of this neuron
(image associated with the neuron) in the image space.
Neural
network
Neural
network
Neural
network
Neural
network
[2, 5, 9, 1, 4, 6, 5, 9]
Fig.2. Increasing compression accuracy – two-output network [17]
3. GRNN Network
Kohonen network has a limited number of values which it is able to
return to us. It is the set of indexes or numerical values associated with each
neuron. In the case when the image appears at the network output, the
network will return to us the value bound with the neuron most similar to this
image. The more neurons there are in the network the smaller the degree of
generalization made by it, and the compressed image will be more similar to
the original after decompression. GRNN network, on the other hand, instead

of the value associated with the most similar neuron will return to us the value
adequate to the degree of similarity of the input image to particular network
neurons.
The compressing GRNN network can be constructed based on
information included in Kohonen network. Pairs (x,y) of the GRNN-network
teaching sequence will in this case contain neurons of Kohonen network as
images x and the values associated with each neuron of this network (neuron
index or value determined by means of Sammon mapping) as parameters y.
The construction of GRNN network can also be based directly on images
(image segments) placed in the teaching sequence, completely omitting the
stage of constructing Kohonen network. For this purpose every teaching
image should be assigned by Sammon mapping a number value or a 2- 3-
dimensional vector, and then GRNN network should be constructed on the
basis of teaching pairs (x,y) thus obtained.
Network neurons –average images
remembered by the network
Value
returned by
the network
Network neurons
Input image
Response of
Kohonen network
Response of
GRNN network
Fig. 3. Functioning principle of GRNN network in image compression. [17]
4. Numerical experiments
Original radar images reduced to the size 100*100 pixels were used for
the research. All images were subjected to the process of segmentation. Each
of them was divided into 100 equal-sized segments of 10*10 pixel
dimensions.
Comparing the effect of neuron number on the described methods it
should be stated that the small number of neurons in each case causes the
approximating system to generate very inaccurate positions. The classical
Kohonen network of small size makes it possible to plot a more accurate
position than other compression methods, but in spite of this the system’s
accuracy in this case continues to be extremely insufficient. With a larger

number of neurons for each method it could be obtained more and more
accurate positions. For 2-output networks the effect of each method on the
approximating system and the generated results is similar. The differences are
perceptible with 3-output networks. In this case it could be observed a better
functioning of the positioning system when compressing the radar image by
GRNN network and Kohonen network with ordered structure than for the
classical Kohonen network. The application of GRNN network and Kohonen
network with ordered structure makes it possible to obtain equally accurate
positions as in the case of the classical Kohonen network, but with a smaller
size of each. It should be remembered that a result like this is obtained using
3-output networks which causes the amount of information flowing into the
approximation system to be larger than in the case of 2-output and 3-output
networks (smaller degree of compression – longer functioning time of the
position approximating subsystem). In this case, however, due to the smaller
number of processing elements at the stage of compression the time of
performing it will be shorter, which can compensate for the longer time of
calculations made in the position approximating subsystem.
Sum-up
It is a merit of comparative navigation that the knowledge about the ship’s
nearest surroundings, i.e. the coastline and the sea bottom, is used for plotting
the ship’s position. The direct control of potential navigational obstacles
decisively increases the safety of the navigational process.
Many numeric experiments have shown considerable resistance of the
presented method to disturbances of registered images.
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