International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 2
Number 1
March 2008
The Process of Radar Tracking by Means of
GRNN Artificial Neural Network with
Dynamically Adapted Teaching Sequence
Length in Algorithmic Depiction
A. Stateczny & W. Kazimierski
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: The radar with the function of automatic target tracking is the navigator’s basic aid in
estimating a collision situation with regard to his own vessel. The quality of radar tracking process affects the
reliability of data provided to the navigator for situation assessment, including the vessel’s safety. The use of
artificial intelligence methods (GRNN network in particular) for this purpose permits a decrease of tracking
errors and the shortening of delay of the vector presented in relation to real time. The article presents an
algorithmic depiction of radar tracking by means of GRNN-based neural filter. There have been presented a
filter diagram, an algorithm of GRNN parameter selection, manoeuvre detection, as well as the process of
radar tracking by means of this filter.
An effective avoidance of collision at sea is one of
the main tasks of the navigation officer keeping
watch on the vessel. His basic aid is the radar with
automatic target tracking. It is a very good supple-
ment of visual observation, and in conditions of
restricted visibility it provides the basis for
estimating a collision situation around the vessel.
The quality of radar tracking affects the reliability of
data supplied to the navigator, and therefore also the
vessel’s safety.
As shown by research at the Maritime University
of Szczecin, the use of artificial intelligence methods
for estimating the vector of targets tracked by radar
permits a decrease of tracking errors and the
shortening of delay of the vector presented in
relation to real time. In particular, good results were
obtained with the application of General Regression
Neural Network (GRNN). (Juszkiewicz & Stateczny
2000, Stateczny 2000, Stateczny & Uruski 2003)
The parameters of the network applied depend on
the dynamics of changes in the target’s movement.
When the tracked target moves at uniform speed, a
network with longer teaching sequence should be
applied; when the target performs a manoeuvre it is
necessary to shorten the teaching sequence. The
construction of a filter applicable for both
manoeuvring targets and targets moving at uniform
motion requires the application of GRNN network
with automatically changing teaching sequence.
(Stateczny & Kazimierski 2006b,d)
The General Regression Neural Network was de-
signed for solving regression problems. By means of
a mathematical algorithm of general regression the
output value is estimated as the weighted mean of
model values depending on the distance of input
argument from the model. Its usefulness for solving
particular problems depends on the proper selection
of parameters. There are two most essential control
elements: the length of the teaching sequence and
the network smoothing factor. (Specht 1991)
The length of the teaching sequence is determined
by the amount of models the input value will be
compared to. As each model is implemented in one
teaching neuron, it is this value that determines the
network structure. The smoothing factor is mostly
determined empirically and depends, inter alia, on
the distribution of input values and possible
normalisation of input signal. (Lula & Tadeusiewicz
In the process of radar tracking with models, past
values of the estimated vector are implemented in
the teaching neurons. Their number has effect on the
output vector. If in the case of the target’s uniform
movement, the highest possible number of models is
desirable for smoothing the output, then in the case
of manoeuvre, models too distant in time introduce
larger errors, as vectors from before the manoeuvre
are taken into consideration. They cause larger errors
and the vector is smoothed on improper values.
(Stateczny 2001a, Stateczny & Kazimierski 2006a)
The smoothing factor is selected in an empirical
way. Smaller factors cause higher sensibility of the
filter. The estimated values have small errors, but are
unstable and vulnerable to possible accidental
disturbances. A high value of this factor causes a
strong smoothing of the signal; at the same time,
tracking errors and delays are larger, as the filter
reacts less dynamically to new models, significantly
different from existing ones.
The selection of proper GRNN parameters is a
compromise between smoothing the output signal
and decreasing its errors. The fact is also essential
that there are no single ideal control parameter
values for each situation; they should always be
adapted to the nature of the target’s movement, so
that the filter should find universal application.
(Stateczny & Praczyk 2004)
One concept of a GRNN filter permitting the
tracking of targets both during manoeuvring and in
steady movement, is a GRNN neural filter with
dynamically adapted length of the teaching sequence.
Its flow chart has been presented in Fig. 1.
Fig. 1. Flow chart of GRNN filter with dynamically adapted
length of teaching sequence. (Stateczny & Kazimierski 2006c)
The filter presented consists of two independently
functioning filters and a manoeuvre detector. Each
filter consists of two GRNN networks, which
estimate the speeds on axes X and Y respectively.
One of them (the manoeuvre filter) with a length
of the teaching sequence in the range from 10 to 20
measurements is responsible for estimating the
vector during the target’s manoeuvring; the other
with a teaching sequence above 40 measurements
(stable filter) estimates the state vector during steady
motion. The lengths of the teaching sequences were
determined empirically. It was established that the
shortening of the teaching sequence to fewer than 10
measurements causes the estimated vector to be not
stable enough to be used in navigation. Lengthening
of the teaching sequence to more than one minute,
on the other hand, causes too large estimation errors.
The task of the manoeuvre detector is, besides
detecting the manoeuvre, to switch over the system
to obtaining results from a respective filter.
Because of the relatively small calculation load
caused by the GRNN network, the most practical
solution seems to be the one that assumes both filters
to be working without interruption and the manoeuvre
detector to switch over the system output to a
respective filter. (Stateczny 2001b, Stateczny 2004)
Figure 2 presents the functioning algorithm of a
filter with dynamically adapted length of the
teaching sequence.
The filter estimates the target movement vector in
particular stages, each signifying a successive position
measurement. The watched movement vector is then
calculated as the difference between successive
position coordinates. Such a vector is burdened with
radar errors. It is the input signal for the filter.
Fig. 2. Functioning algorithm of tracking filter with dynamically adapted length of teaching sequence
In each stage, the operation of the filter on
obtaining input signal is to single out speed on axis x
and speed on axis y by means of Pythagorean
Vx = Vo * cos KRo (1.1)
Vy = Vo * sin KRo (1.2)
Next, values Vx and Vy are subjected to the
decision block to determine the filter’s estimation
moment: if it is only the first step (the target has
been introduced for tracking), the second, or a
further successive step of calculation.
If it is the first step, i.e. the moment of the target‘s
acquisition, the filter must start working. The first
stage is to create suitable GRNN structures. The
module responsible for construction takes from
memory the elements indispensable for the
network’s creation, introduced by the user in the
stage of conceptual filter construction; these are,
smoothing factor σ, lengths of teaching sequences of
networks applied in the manoeuvre and stable filter,
as well as the radial transition function of neurons
from the second hidden layer. Gaussian function is
the most frequently applied (2)
In the first stage the estimated values are the same
as the observed ones; they are copied to the model
neurons and become the first model. The result is
passed to the manoeuvre detector, the activities of
which do not as yet affect the result, as both filters
(stable and manoeuvre) have the same values
implemented in them.
The second step of estimation starts like the first
and each successive one from calculating Vx and
Vy. Next, the structure of each network is developed
by one neuron in the radial layer. The observed
vectors become now the output values of the filter,
which are then copied to the second teaching neuron
as models; only from now on is it possible to
average the past vectors. As in the first step, in the
second step, too, the output signal of the filter is
independent from the indications of the manoeuvre
Successive steps of the filter’s work now carry
out complete estimation of the target’s movement
vector. The calculation pattern is similar in each
step. First, values Vxo and Vyo calculated from the
watched velocity vector are given as input signal to
respective networks. Next, estimation of the output
vector takes place, on the basis of existing models.
In the following part of the step the estimated
vectors join the models and are copied into the last
radial neuron. Thus, in each step the network’s work
cycle is carried out, and then teaching it a new
model, possibly coupled with developing the
structure. Each network functions independently
from others, estimating the vector respective to
Neurons of the first layer have only the task of
passing the input value to all neurons of the radial
layer; they are linear neurons, their output signal
being a linear function of the input signal.
In the radial layer there follows the calculation of
Euclidean distance between input and model vector,
and then the value of activation function for this
distance, according to formula (2).
This value is passed to the third layer, that is, to
two summing neurons. The first sums the values
passed from all neurons in the hidden layer. The
values passed to the second of summing layers are
multiplied “on the way” by the values corresponding
to the arguments from the models. Neurons of the
third layer sum the numbers obtained and pass them
to the fourth layer.
The neuron in the fourth layer divides the sums
obtained from summing units by itself, obtaining as
regression result the estimated velocity vector on
axis x or axis y (depending on which network).
Mathematical calculations performed by GRNN
network may be presented by means of
formula (3),
( )
where f is Gaussian function presented by formula
So long as the planned length of the teaching
sequence is not reached, it is also necessary to
develop each network by one model neuron; this
development is performed before the teaching
process. After calculating the estimated vector the
filter checks if the number of current estimation step
(equal to the number of model neurons) has already
reached the required length of the teaching sequence
for the manoeuvre filter. If not, a successive neuron
is added both to the manoeuvre and to the stable
filter along with a set of connections. If the rated
length of the manoeuvre filter has been reached, the
sequence length of the stable filter is checked. If
there are still fewer teaching neurons than previously
assumed, one neuron is added along with
connections. If the teaching sequence lengths of both
filters have already reached the required value, the
teaching process begins. It consists in copying the
vector of this step to the last (empty) model neuron.
In the case when the teaching sequence already has
the rated length, the values of all models are copied
earlier to the previous one, whereby the value most
distant historically disappears from the teaching
sequence and the last neuron is set at nought, in
order for the new model to be copied in.
After calculating the estimated values by the
manoeuvre filter and stable filter, one of these values
is selected by the manoeuvre detector. The current
target movement dynamics is checked. If the target is
manoeuvring, then the value obtained from
manoeuvre filter is the output value. If the target is
moving with uniform motion, the value from stable
filter is assumed as final.
The estimated values Vxe and Vye thus obtained
permit an easy calculation of the Ve target’s speed
vector, as well as the estimated target’s course.
There follows the next measurement of the
target’s position and the next step of estimation.
The algorithm presented in Figure 2 presents the
manoeuvre detector merely as a block part of the
whole filter. A precise detection algorithm has not
been worked out yet; research on it is in progress, as
it significantly affects the quality of suggested
The problem of manoeuvre detection is very
essential for the filter’s functionality. Incorrect
functioning of this element will produce an improper
signal given on the output; as a result, the obtained
vector will be burdened with a larger error than the
one worked out within the filter. There are two
concepts of manoeuvre detection. The first consists
in comparing the increments of the estimated vector
obtained by means of one of the filters. The second
compares the values of estimated parameters
originating from the manoeuvre and the stable filter.
The first method is more manoeuvre sensitive, but it
depends on prevailing external conditions. In various
conditions there are different increment values in the
same time unit, which makes the method not
universal enough, requiring constant tuning
according to prevailing conditions. A merit of the
other method is independence from external
conditions. In both methods manoeuvre detection
according to a definite value in one step only seems
pointless due to disturbances. It results from the
research conducted that the moment when in three
successive steps the assumed value determined in
further empirical research is exceeded, it can be
considered as the moment of starting the manoeuvre.
The correct construction of a neural filter based on
GRNN network requires a detailed functioning
algorithm of such a device. The GRNN network
itself, like most tools of artificial elements, is a
rather complicated element and a fluent management
of its parameters requires good knowledge of its
It turns out that the selection of proper values of
the network’s control elements essentially affects the
accuracy of results obtained.
A filter based on network with dynamically
adapted length of teaching sequence is a proposal
possible to be applied for various dynamics of target
movement, permitting the estimation of target
movement vector in the process of radar tracking
with higher accuracy and smaller delays than in the
solutions applied so far. The concept presented still
requires the improvement of certain elements, with
the manoeuvre detector seeming to be of most
essential significance; an improvement factor could
also be the automation of selecting the smoothing
The chief merit of the algorithm presented is its
universality; the filter itself is able to adapt to
changing circumstances and apply networks with
various parameters. Introducing more than two
networks working in parallel seems pointless, as it
would cause an unnecessary complication of the
filter structure, whereas the existing structure
permits sufficient adaptation to the situation.
Interference in the network structures increasing
and decreasing the length of the teaching sequence
is uncomplicated enough to consider constructing a
filter composed of only two networks (one for
estimating Vx, the other for Vy), with the
possibility of altering the length of the teaching
sequence depending on the situation.
Bar Shalom Y. & Li X.R 1998, Estimation and tracking:
principles, techniques, and software, YBS, Norwood.
Duch W. & Korbicz J. & Rutkowski L. & Tadeusiewicz R.
2000, Sieci neuronowe (Neural Networks), Akademicka
Oficyna Wydawnicza Exit, Warszawa.
Juszkiewicz W. & Stateczny A. 2000, GRNN Cascade Neural
Filter For Tracked Target Manoeuvre Estimation,
Proceedings of the Fifth Conference Neural Networks and
Soft Computing, Zakopane.
Lula P. & Tadeusiewicz R. 2001, Wprowadzenie do sieci
neuronowych (Introduction to Neural Networks), Kraw.
Specht, D.F. 1991, A Generalized Regression Neural Network,
IEEE Transactions on Neural Networks.
Stateczny A. 2000, Neural State Estimation in Sea Navigation,
Geodezja i Kartografia nr 4.
Stateczny A. 2001a, Nawigacja porównawcza (Comparative
Navigation). Gdańskie Towarzystwo Naukowe, Gdańsk.
Stateczny A. 2001b, Neural manoeuvre detection of the tracked
target in ARPA systems, Proceedings CAMS 2001
Stateczny A. (red) 2004, Metody nawigacji porównawczej
(Methods of Comparative Navigation), Gdańskie
Towarzystwo Naukowe, Gdańsk.
Stateczny A. & Kazimierski W. 2006a, Automatic Target
Tracking in Radar Systems Using GRNN, Konferencja
Morska Gdynia 2005- Polish Journal of Environmental
Studies, Vol., supp. 1
Stateczny A. & Kazimierski W. 2006b, Aspects of Tuning
GRNN Networks for the Needs of Estimating Target
Movement Vectors in Marine Radars, Polish Journal of
Environmental Studies, Vol.15, No.4B.
Stateczny A. & Kazimierski W. 2006c, Detection of
Manoeuvre for the Needs of Estimating the Target’s State
Vector in the Process of Radar Tracking, International
Radar Symposium, Kraw.
Stateczny A. & Kazimierski W. 2006c, The Length of GRNN
Network Teaching Sequence in the Process of Estimating a
Target’s State Vector in an ARPA Device, Proceedings of
the ICAISC, Zakopane.
Stateczny A. & Praczyk T., 2002, Sztuczne sieci neuronowe w
rozpoznawaniu obiektów morskich (Artificial Neural
Networks in recognizing Marine Targets), Gdańskie
Towarzystwo Naukowe, Gdańsk.
Stateczny A. & Uruski P., 2003, Comparison of neural-network
and Kalman-filter approaches to a maritime target tracking,
Proceedings of the International Radar Symposium,