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.

1 INTRODUCTION

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)

2 THE PROBLEM OF SELECTING GRNN

NETWORK PARAMETERS IN THE PROCESS

OF RADAR TRACKING

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

2001)

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)

3 NEURAL FILTER WITH DYNAMICALLY

ADAPTED LENGTH OF THE TEACHING

SEQUENCE

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

theorem.

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)

























−=

),(

exp)(

xxd

(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

detector.

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

itself.

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),

( )

∫

∞

∞−

∞

∞−

dyVeVof

dyVeVoVof

),(

(3)

where f is Gaussian function presented by formula

(2).

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.

4 MANOEUVRE DETECTION FOR THE NEEDS

OF RADAR TRACKING

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

solution.

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.

5 RÉSUMÉ AND CONCLUSIONS

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

structure.

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

coefficient.

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.

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