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4.4.
. , !."#..
$##%& #'# 1
-
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1. ($
(2)
2. $
(1)
3. $
(3)
-
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4.1.4.1. ($($ --
( , , .),
,
( ),
( ),
(, , , ! .).
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4.1. ($" #
)&!* +, !- !"&. %/:$ ! $ # ,
# % % & !.
#' %-&%, !" %/# '"0 ,%: ( C D),
.
#' '%#-!0 !" %/# '"0 ,%:,
,
,
,,
.
,+' / &%,!+-# !" %/# '"0 ,%: , .
-
7/25/2019 Metod Odredjivanja Prostornog Polozaja Tacaka Predavanje4
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4.1.4.1. ($($ -- %,!+-%,!+-%/%/!"!"
'##'## ((,#!#"#,#!#"#%%11))
-
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4.1.4.1. ($($ -- !"&!"&'#'#
!"& '# -# '#2#: ,! $ , % # ! %# , # .
#' *#' &' ( ,1997) +30-# :%, %.
* !"& '# #! : % 1., % 2. .
&%-# !"& '# #! :, .
% I. , II, III IV.
-
7/25/2019 Metod Odredjivanja Prostornog Polozaja Tacaka Predavanje4
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4.1.4.1. ($($
--!"& '#, # ##& *!
-
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4.1.4.1. ($($ -- !"!"'##'##
' & $ % 1:5000 1:10000, %:
% ,
$ &,
& & ! 0.8 mm, $ % & ! 0.5 mm,
) ! &! 0.5 mm) ! ( ! & ! 0.2 mm) ,
, ,
( & ! 0.2 mm).
-
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4.1.4.1. ($($ -- &%#&%#!"&.!"&.*!**!*
()
.
-
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4.1.4.1. ($($
-- /02/0200!"&'!"&'*!0*!0 --!"&!"&*!*!0'#%0%0'#%0%+'#30+'#30*#*#%#%#%/#%/#
:(:Xi,Yi, i=A,B,C,D
:) -i% - dij
(:(# :Xj,Yj,=1,2,...
B
1
2 C1
2
A
B
C
D
p
zdB1
d12
d2C
-
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4.1.4.1. ($($ -- /02/0200!"&'!"&'*!0*!0 --
!"&!"&*!*!0'#%0%0'#%0%+'#30+'#30*#*#%#%#%/#%/#
C
B1
2
C1
2
A
B D
p
zdB1
d12
d2C
f = (CD -z)f *
z
CD + 4viCD=2C+2180
CC
2C + 3vi2C =
12+2180
22
12 + 2vi12 =B1+1180
11
B1=(B1 + vi)B1=P+B180
PBB
i,defii%.
vi = f/n n = 4
- , = sn
-
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(), ( # ).
% ! # # # # .
! $ , :
# . ## 30, % 1:300 1:400.
& %. # (!) % $ # # .
% . %, , % .
4.1.4.1. ($($ -- +*2#+*2#!"&"!"&"*!*!
-
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4.1.4.1.
($($ --TO19TO19))))
K =const.fd / d* 1/Kvyi= (fy/ d) x divXi= (fX/ d) x di
fd =fx2 + fy
2fy=(YC YB)-dYfx= (XC XB)- dX
(XC)
XC= X2 + dX2C
d2C cos+ vx2= dX
2C
X2= X1 + dX12
d12 cos+vx12= dX12
X1 = XB + dXB1
dB1 cos + vxB1= dXB1
XB
XX
YC - YB
dY
d2C sin
d12 sin
dB1 sin
dYdY
XC - XB
dX
d2C cos
d12 cos
dB1 cos
dXdX
d
d2C
d12
dB1
ddijij
CD + 4vi=z
2C + 3vi
12 + 2vi
B1 + vi
i,defi,def
f = (CD -z)=T-If *
(YC)z
YC= Y2 +dY2CCD=2C+2180CC
d2C sin + vy2C
= dY2C
2C =12+2180
Y2= Y1 +dY1222
d12 sin + vy12= dY12
12 =B1+1180
Y1= YB+ dYB11
1
dB1 sin + vyB1= dYB1
B1=P+B180
YBPBB
YYiiii%%
C
B1
2 C1
2
A
B D
p
zdB1
d12d2C
+
+
=
+
+
=
-
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4.1.4.1. ($($ -- --
5= 236 30 30
4= 120 45 00485.123C
3= 258 11 00612.1523
z
=106 17 302= 63 20 00359.6112
p
= 43 31 301= 104 00 30305.41A1
ugaoduzinastrana
106 17 30z
=
106 17 30-60106 18 30CD
286 18 30DC
236 30 30
49 47 12-4849 48 003C
229 48 00C3
120 45 00
109 02 24-36109 03 0023
289 03 0032
258 11 00
30 51 36-2430 52 0012
210 52 0021
63 20 00
147 31 48-12147 32 00A1
104 00 30
43 31 30p
=
def.dir.ugaopopravkapr.dir.ugaostrana
p1
2
34
5A
1
2
3C
B
z D
Date take:A,B,C,D
-
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4.1.4.1.
($($ !
fd/ d = 1/5182~1/5100
fd = 0.34
fy = 0.298fx = 0.168
1297.839164.71treba
1297.541164.542ima
(5619.243)(6405.272)d = 1762.29
5619.2436405.272C
+ 370.541313.258370.46313.21149 47 12485.12
5248.7026092.0143
+ 578.764- 199.642578.66-199.7109 02 24612.15
4669.9386291.6562
+ 184.520+ 308.731184.459308.69730 51 36359.61
4485.4185982.9251
+ 164.014- 257.637163.962-257.666147 31 48305.41
4321.4046240.562A
YXdydxdir.ugaoduzinastanica
-
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4.1.4.1. ($($ --
=20, 45, 60
n = n + b; c=0.05 ili 0.03
n - ,- #!'. *#+. 0"!* 0 *!0, b # #& *!
-
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4.1.4.1. ($($ -- +*4#+*4#0"!*0"!*&%02#&%02#
#!%*#!%*#+&%#+&%!"&.!"&.*!**!*
tanM:1 =
nE =
10101:20000
20211:10000
20281:7500
30411:5000
11 091:3000
13 261:1000
"
" #"
- E
#"
' 1:5000
n = 9 ,
=309 = 90
-
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18/63
4.1.4.1. ($($ -- %%.+%!#.+%!#%/&%%/&%
*#*#!"!"'##'##
(,1997)
1:10 0001:20 000
2. 1.
-
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4.1.4.1. ($($ -- #5-##5-#'##2'##200
!"&'!"&''#''#'
< 20 km
< 4 km ( 2.5 km)
1:3 ( 1:5
) 50 m -500 m ( 50 m -250 m
50-500 m )
(1:2500, 1:5000, 1:10 000, ! -",
-", 1. 0.6 mm, 2. 0.2 mm) (1:5000 1:10 000, , ,
#$, $, " %, " ,
, ,
" 100 cm x 70 cm 70 cm x 50 cm)
-
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4.1.4.1. ($($ --
1 2
2 ,
! ,
:
-" " " " #"
--" # ,
- #
-
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4.1.4.1. ($($ -- $#6#$#6#'##2'##20"!*0"!*
&462#&462#"#6#"#6#
e
1 2
-",
-"
stanica
signalsignal
-
7/25/2019 Metod Odredjivanja Prostornog Polozaja Tacaka Predavanje4
22/63
4.1.4.1. ($($ -- !!
# $ $
" !
.
# $
$ $ .
%
! $ $
$ .
&
$ $. $
$ "$ .
$
$ ,
$
$.
'
% .
($
# $
-
7/25/2019 Metod Odredjivanja Prostornog Polozaja Tacaka Predavanje4
23/63
4.1.4.1. ($($
-- "!"!!!
s
a
n-1
n
n
P2
T1
T2
t
)(180
sins
bsin
)xx()yy(s
)sin(
sin
ab
)sin(
sinad
)(180
t
2
2T1T
2
2T1T
1
++++==== ++++====
====
++++====
++++
====
++++
====
++++====
b
d1
Mereno: ,, , aDato: koordinate T1, T2Nepoznato: t
""!!
-
7/25/2019 Metod Odredjivanja Prostornog Polozaja Tacaka Predavanje4
24/63
4.1.4.1. ($($
-- "!"!!!!!--
:
= 68-47-58 = 48-26-44a = 76.50 m
= 127-05-16
:
53c x = 59110.16 y = 37084.4025c x = 58948.42 y = 36411.43
: t= 111-24-40
a
143
25c
53c
144P
-
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4.1.4.1. ($($ -- &%!#&%!#'#%#'#%#.+%!".+%!"
+2+2
,
+ -%, , ,
-" #.
-
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4.1.4.1. ($($
-- #3*2##3*2#!-!-#+%.#+%.%/%/##'##' -- &*0&*00#0##"#"0"!0"!
( )[ ]
AC
ACC
A
2
AC
2
AC
XX
YYarctan
)XX(YYb
=
+=
)(180 +=
B
AA'B
B
AA'B
coscXX
sincYY
+=
+=
B
CC"B
B
CC"B
cosaXXsinaYY
+=+=
1
2
3
4
5
sin
sinbc
sin
sinba
=
=
2
)XX(X
2
)YY(Y
''B'B
B
''B'BB
def
def
+=
+=
-
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4.1.4.1. ($($
-- /02#/02#%%#+%##+%#%/#%/###'##'#'#'**&&*#*#%#%#%/#%/# ((%#%#,+#,+#))
( ) )cos()sin(
sinbXcossinsinbXcosaXX ACC
A
CC
B
CCB
+
++=++=+=
b
XXcos
,b
YYsin
CAA
C
CAA
C
=
=
sinb
YYcos
b
XX)cos( CACAAC
=+
BACAC
CACAC
CACACB
Xctgctg
ctgXctgX)YY(
ctgctg
)YY(
ctgctg
ctg)XX(X
)sin(
sinsin)YY(
)sin(
cossin)XX(XX
=+
++=
=+
+
+=
+
+
+=
ctgctg
ctgYctgY)XX(Y ACCAB +
++=
1
2
3
4
5
sincoscossin)sin( =
-
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4.1.4.1. ($($-- /02#/02#%%#+%##+%#%/#%/###'##'
##50-#50-#%"#&%"#&
0XctgYctgYX
ctg)YY(XX
C
B
CC
B
CBB
B
CCBCB
=+
=
0XctgYctgYX
ctg)YY(XX
A
B
AA
B
ABB
B
AABAB
=+
=
B
C
B
A
B
AA
B
CCACB
ctgctg
ctgYctgY)XX(Y
+=
B
AABA"B
B
CCBC'B
ctg)YY(XX
ctg)YY(XX
+=
+=
1
2
3
4
-
=
)
B
C
XB - XA
XB - XC
YB - YCYB - YA
X
Y
AB
CB
-
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4.1.4.1. ($($-- #3*2##3*2#!-!-#+%.#+%.%/%/00+'#30+'#30
*#*#%#%#%/#%/#0*-0*-
)YY(d
dYY
)XX(d
dXX
AB
AB
AiAi
AB
AB
AiAi
+=
+=
AB
AB
iABAB
AD
A
B
AiDi
AB
ABiAB
AB
ADA
BAiDi
d
)XX(
d)YY(d
d
Y
cosdYY
d
)YY(d)XX(
d
dX
sindXX
+
+=
=+=
+
==
AB
ABiAB
AB
ADA
BAiDi
AB
ABiAB
AB
ADA
B
AiDi
d
)XX(d)YY(
d
dY
cosdYY
d
)YY(d)XX(
d
dX
sindXX
+=
==
+
+
=+=
1
2
3
didAD
B (YB,XB)
A (YA,XA)
YB YA
XB XA
Y
X
i
dAi
B (ZB,XB)
A (YA,XA)
i (Yi,Xi)
YB YA
XB XA
Y
X
-
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4.1.4.1. ($($-- /02#/02#%%!-!-#+%##+%#%/#%/#
&*0&*0'##2'##200
AB
ABB
AXX
YYarctan
=
2
AB
2
ABAB )XX()YY(d +=
APAB
2
BP
2
AP
2
AB
dd2
dddcos
+
=
+= BAP
A
P
AAPA'P
P
AAPA'P
sindXX
sindYY
+=
+=
BPAB
2
AP
2
BP
2
AB
dd2
dddcos
+=
= ABP
B
P
BBPB"P
PBBPB"P
sindXX
sindYY
+=
+=
2
XXX
2
YYY
"P'PP
"P'PP
+=
+=
ABBPAP dcosdcosd =+
sindsind BPAP =
1
2
3
4
5
6
7
8
9
dCP
dBPdAP
AB
P
C
1
2
2-3 cm
-
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4.2. $&-
) - . % %
. % % . $ #
. .
# # #
-
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4.2. $ -)*
: #
& (, )
+: # # !$ #
-
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4.2. $ -'-'""##!"##!"*#!'*#!'
#
.
+
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4.2. $&* #!#'#% "#'#%-&"
*#!'
RR11
22
RR22
22
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RR1212
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RR1212
RR11
RR22
RR33
RR44
''
$
7
*##" '2#'++%%1.1.
2.2.
3.3.
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4.2. $
#! &*# %#&%#"#'#%-&" *#!'
11258 mm+
2225 755 mm+
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+
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+
$
&
+
-3 m100 - 130 220 - 40+
0.32 3 m60 8020 -3015 20+
0.31 2 m50 6025 3610 15+
0.51 m35 40 (65)35 405 -10+
0.6 0.71 m25 -35 (50) m40 5 10 +
-
%
)
!
+
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4.2. $ -#%-#%,, 0'#-0'#-%/%/&%,!+-&%,!+-%/%/00"#'#%-&'"#'#%-&'*#!'0*#!'0
+ 1:5000 - , - & - - %
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+: + - , + % , + + +("
% +8 ( , , %, , , , , , ! , ( , , &
4040 140140
3030
30305050
1.21.21.81.8
6060
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4.2. $ -%##%##*&*&+!#+!#*#!'*#!'&%#&%#
( )
( )
)obostrano...S2
kili(,
S
kpili
ojednostran...
S2
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obostrano...S
1p
km1Sza,1pkm1Sza
S
sKKp
3...
s
S
12
2...s
SnnsS
)1(...n
...
...
s...ss
hh...hhhH
H
i
H
i
H
H
2
h
2
H
H
2
h
2
H
2
h
2
H
hhhh
2
h
2
h
2
h
2
H
n21
n
1i
in321AB
n21
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++=
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HHABAB
ss11
ss22
sszz sspp
ssnn
hh11
hh22
hhnn
ss
*4 %## #*4 %##
( )
( )
( )3...kp
2...1
p
1...n
k
n
Kp
2
H
H
2H
2
h
H
=
=
=
=
++
++2H
2
H
2
H
2
H
S06.0S40
S04.0S25
S06.0S32
S04.0S20
+=
+=
+=
+=
++++
!!
+!+!
+*4# &%02# #-
+
-
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4.2. $ -%##%##*&*&+!#+!#*#!'&"*#!'&"*!*!
( )
( )2...k
P
1...S
1P
SS
SS...SSp
1
p
p1...
p1
p1
p1
p
1
1P
H...HHHH
2
i
H
H
i
n21
i
n21
n321
=
=
=+++=
+++=
=
++++=
%
%
% e
11.04[1/p]=
3.620.275936242.02
1.890.528018941.11
2.100.477320951.22
3.430.211934261.92
1/piPi =1000/i2i
2Si (km)
P=1/P=1/ [1/p]=1/11.04=0.09
!
+!
RR//
RRBB
RR11RR22
RR33
++
-
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4.2. $ -+*2#+*2#0'#%0%"0'#%0%"*#!'&"*#!'&"*!*!
Hn21
i
H
HH
n
1iiABH
AB
n
1i
i
AB
n
1i
i
fv...vv
p
1
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1
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f
H)HH(f
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2
H
2
H
2
H
S06.0S24S04.0S15
S06.0S16
S04.0S10
+=+=
+=
+=
++++
++++
!!
+!+!
!
RRAA
RRBB
RR11
RR22
RR33
HH11
HH44
HH22
HH33 HHBB -- HHAA
ffHH
-
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4.2. $ -###&+&+&11
3.019
5.2098.228400
2.0411.16980R3
3.21080B3
2.1000.75070B
2.85070A2
1.0681.10050A
NivelirNi025
br. 2245
B.B.
21.04.2005.
2.16850R21
h = Z - P8itanjena letvi
DuzinaVizuraSt.
Z=8.228-P=3.019
5.209
RRAA
RRBB
RR11
RR22
RR33
HH11
HH44
HH22
HH33 HHBB -- HHAA
ffHH
-
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4.2. $ -
+*2#+*2#*!*!0'#%0%"0'#%0%"+'#30+'#30**%%#### 33
6.228fH = +0.013
H=(0.053)
102.5406.228+ 0.0137.66.2156.228
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RB
+ 1.410+ 0.0063.7+ 1.404
101.13R3
+ 5.210+ 0.0010.4+ 5.209
95.920R2
- 3.013+ 0.0031.9- 3.016
98.933R1
+ 2.621+ 0.0031.6+ 2.618
96.312N2.8RA1
Primedba
H
Definitivna
visinskarazlikaH + v
Popravka
- vn
Duina(m)
Merena
visinskarazlika (m)= H
Odakle
je uzetpodatak
Rn
B.V.
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4.2. $ -
#3*2##3*2#*&*&%/%/'#%''#%'%"'#%-&"%"'#%-&"*#!'*#!'
12kAB klizcosdH ++=
( )k1R2
dk
2
H
12 =
2
)li()li(
2
zcosdzcosd
2
HHH
ABBA2k21k1
ABAB
AB2Z1Z
++
=
=+
=
2
i
id2
1p =
2
i
id
1p =
[ ]2n21 d1
p
1...
p
1
p
1
p
1
1p =+++=
=
[ ]2
i2
H'h d
d
fv =
[ ] iH
'h
dd
fv =
)m(h
2
)cm( d)zctg1(00075.0 +=
)d05.48.1(4 )km(h)cm( +=
Knd4 0)cm( +=
.".+"(/ /',.(/ 1+ "/+-1+"/+
/(/ '/ '/(.2+" . 3/(4.1)
.".+"(/ /',.(/ 1+ "/+ -5"/+
6.+/ "/+ -1+"/+
6.+/ "/+ -5"/+
6.+/ ,/(/
/( .".+"(.0 /',.(/ ) +
/( .".+"(.0 /',.(/ ) -+
'2+ ")/7 .".+"( /',.(
) + )$.6.
'2+ ")/7 .".+"( /',.( ) + )$ .6.
'2+ ")/7 .".+"( /',.( ) ,/() +
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4.2. $ -#3*2##3*2#*&*&%/%/#%4#%4 -- #%4#%4*#!'*#!'
7
/2+. +.,/+ 8. /2+. +.,/+ ,.+.1/
& #
&
&
)%
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'*6- *#!'*#!'*6*6&0%.&0%.%/%/
. ; " & ;
( ! ,
.; " &,
&;
: + 2(3) ;
;
: , , , , !, (+1), (
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'*6- *#!'*#!'*6*6&0%.&0%.%/%/%%*#!2*#!2
; ! , ,
, ;
# ;
+ ;
$ !# 1:500 1:1000 - 30 m;
+ ! cm; ! & 1 999 , ! ;
130 m (150 m ), # 100m (120 m);
+ & ! ! (3-4 mm! );
40 -50 & ; ! & ;
+ ;
: + .
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'*6- *#!'*#!'*6*6#5#5*'*'
! 30 50 m;
; ;
/ ; +
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$ dm; ;
.
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'*6- *#!'*#!'*6*6#5#5*!'*!'5"0'5"0'
AB% ! ;
% ;
% , $ dm
;
! & +0,07 - 0,05& ! ;
.$ .
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'!-- *#!'*#!'0+0"0+0"5!5!
" : (, "(,(( #; ; ' %; ! ; " % ,
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%; + %
, # % $ ## ;
% #%;
! $ %;
;
, % cm, mm;
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0+120,68; + % !
% % .
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'!- -
(1,208)101
108,981,296
109,031,245
108,761,512224
109,072+ 1,334(+ 0,003)
1,20762101
110,27107,7352,54160a2
(2,470)a
109,290,913
109,680,522
109,500,701
107,735- 2,020
(+ 0,003)
2,47150a
Ima = - 0,686treba = - 0,680
fn = +0,006 m
Dozvoljeno
H101 = 109,072H100 = 109,752
H101-100 = - 0,680
110,20109,7520,451501001
PrimedbaHVH = HV - ldhldVizuraStanica
(1,208)101
108,981,296
109,031,245
108,761,512224
109,072+ 1,334(+ 0,003)
1,20762101
110,27107,7352,54160a2
(2,470)a
109,290,913
109,680,522
109,500,701
107,735- 2,020
(+ 0,003)
2,47150a
Ima = - 0,686treba = - 0,680
fn = +0,006 m
Dozvoljeno
H101 = 109,072H100 = 109,752
H101-100 = - 0,680
110,20109,7520,451501001
PrimedbaHVH = HV - ldhldVizuraStanica
60,330Hn V=[ ] 13,2h =
[ ] 47,327H =
m016,0d36 =
81,330HnV=
[ ] 04,4h =
[ ] 77,326H =
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'!-- *#!'*#!'#/.#/.5!5!
8 &
;
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) %
;
%
0,0 5
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10,
10
15,
5
15,
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0+090,40
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10,
10
15,
5
15,
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12
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4
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0+090,40
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4.2. $ -
#3*2##3*2#*&*&%/%/#%4#%4#%4 *#!'!- -
2
1
PR2
6,87 598,73
PROFIL 2: 0+060,20
150,780,624
150,500,903
148,253,152
149,202,201
151,40150,301,10PR1
PROFIL 1, 0+000,00
SITUACIJAHv
proba
H = Hv -lhld.".
2
1
PR2
6,87 598,73
PROFIL 2: 0+060,20
150,780,624
150,500,903
148,253,152
149,202,201
151,40150,301,10PR1
PROFIL 1, 0+000,00
SITUACIJAHv
proba
H = Hv -lhld.".
60,605Hvn =
[ ] 87,6l =
[ ] 73,598H =
15,
30
10,
20
0,
00
10,20
15,5
1
2
3
4
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4.3.4.3. $$ $$
=
=
H =
t=
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4.3.4.3. $$$$ -- &*#&*#%#&%#%#&%#$$
;
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+ &, & # -" ;
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4.3.4.3. $$
$$ -- &*&*#%#%+-2+-2$$&&%#'&&%#'
" , . ;
" # ! # & (spread spectrum techniques);
# # # ;
" ; " & & !
# % ; "
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4.3.4.3. $$ $$ -- '#%#'#%#"&"&
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4.3.4.3. $$$$ -- '#%#'#%#$$ -- &'/&'/"'#%"'#%
# $ :
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$ $L
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#&&' & $ & ! $L
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( :
)
$
Hz
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4.3.4.3. $$
$$ -- '#%#'#%#$$ --%!%!"'#%"'#%
! ( # );
1 (ColoradoSprings) $
( % ) # ();
(Ascension Is., DiegoGarcia, Kwajlein) #
( , , ...)&! .
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4.3.4.3. $$
$$ -- '#%#'#%#$$ -- &/&/"'#%"'#%
.(#);
;
(#).
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4.3.4.3. $$
$$ -- +2#+2#%/%/$$%#.!"-'%#.!"-'
/
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4.3.4.3. $$$$ -- $$%%&&%#'&&%#'
4 34 3 $$
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4.3.4.3. $$
$$ -- #+#+"!,!""!,!" (($$)) !!"!!" ((*"*"))%"%"&&%#'&&%#'
XGPS
ZGPS
YGPS
XL
ZL
YL
SGPS
SL
SGPS= c + RSlC vektor translacije
R matrica rotacije
- faktor razmere
4 34 3 $$
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4.3.4.3. $$
$$ -- $$'##2'##2 5+5+'##2'##200&%#!%&%#!%
(%
3
%
4.3.4.3. $$
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4.3.4.3. $$
$$ -- +2+2
"
"
"
$
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$