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)
162
2 DEFINING THE TASK
Suppose we have a right angle coordinate system
XOY, wherein there are navigation points (NP)
marked with digits from 1 to N. For the sake of
simplification let us reduce the three-dimensional
task of determining the position of the FO to a two-
dimensional one. In that two-dimensional coordinate
system, let there be located N number of NPs with
known coordinates x
k
, y
k
, where k = 1, 2,....N and
the flying object FO with y, x coordinates is to be
measured (Figure 3).
Fig. 3. Determining position of a flying object
Difference R
i
can be obtained by expression
:
R
1
2
=(y
1
- y )
2
+ ( x
1
- x )
2
; (1)
R
2
2
= ( y
2
- y )
2
+ ( x
2
- x )
2
; (2)
R
3
2
= ( y
3
- y )
2
+ ( x
3
- x )
2
; (3)
Solving the equations (1-2) the y is expressed as
follows:
y = c.x + e, (4)
where
c = a/b; e = d/2.b; (5)
a = x
2
- x
1
; b = y
2
-
y
1
; (6)
d = - y1 + y2 - x1 + R21 - R22; (7)
Subsituting (4) into (3) we arrive at expression:
h.x
2
+ f.x + g = 0, (8)
where h = c
2
+ 1; f = 2.e.c - 2.y
3
.c - 2.x
3;
g = e
2
- 2.
y
3
.e + y
3
2
+ x
3
2
- R
3
2
; (9)
Then, by solving the equation (8), we obtain the
coordinates of the flying object (FO point) by the
following functions:
X
LO1
= (- f - ( D )
0,5
)/2.h; (10)
Y
LO1
= c.X
c1
+ e;
X
LO2
= (- f + ( D )
0,5
)/2.h (11)
Y
LO2
= c.X
c2
+ e;
where D
2
= f
2
- 4.h.g.
From expressions (10-11) it is evident that the
task of determining the coordinates of a FO is
ambiguous. As it follows from Figure 1, this
problem can be solved through proper choice of the
coordinate system and choosing the proper
coordinates of the FO (X
LOi
, Y
LOi
) on the basis of
known coordinates of NB and the distance R
i
.
3 THE INFLUENCE OF THE ACCURACY OF
MEASURING R
I
ON ACCURACY OF
DETERMINING THE POSITION OF THE FO
Expressions (10) and (11) can be used in modelling
the influence of inaccuracy of measuring the distance
dR
i
onto the accuracy of determining the position of
the FO which can be expressed using the quadratic
error of determining the position of the FO(SKLO)
S
r
. Values of dR
i
and S
r
is calculated the following
way:
dR
i
= R
i
- R*
i
S
r
=(dx
2
+dy
2
)
0.5
, (12)
where R*
i
stands for the measured position of the
FO,; dx, dy are errors of determining the coordinates
of the FO as a result of errors in measuring the
distance dR
i
.
Further I am going to present examples of
modelling the influence of dR
i
onto the accuracy of
determining the position of the FO. To perform
simulation of the function of the ASDC in RELNAV
mode a new program was developed in the Delphi
program environment. We expect that determining
the position will be effected in compliance with the
derived algorithms on a selected area of the Slovak
Republic. NP as FO and their coordinates on the
map are given in pixels.
Figure 4. illustrates the dependence of S
r
upon
dRi, for the case when dR
1
= dR
2
= dR
3
and these
coordinates are (Figure 3): x
1
= 31.0 pixels; y
1
=
= 457.0 pixels; x
2
= 11.0 pixels; y
2
= 230.0 pixels; x
3
= 28.0 pixels; y
3
= 1.0 pixel; x = 615.0 pixels;
y = 231.0 pixels.