Download - GPS processing . Sat05_82, 2005-12-05
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GPS processing. Sat05_82.ppt, 2005-12-05.
1. Directly from the observations
2. From differences (especially if vectors between points are to be determined)
(1) Is flexible, no requirements about same satellites or sam epoch
(2) Can only be used for shorter distances
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GPS Integer-ambguities, Sat05_82.ppt, 2005-12-05.
One more frequency will help (is comming)Methods:• Geometric• Combination of measurements• Search in integer space• Combined
(1) N fixed at beginning, and is kept fixed. Waves are counted. 1.-differences used to eliminate N
(2) Regarded as integer: 2521.08 -> 2521.00Closest integer used
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Search in integer space. Sat05_82.ppt, 2005-12-05.
.Software will tell how much better chosen solution is compared to next-best.
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Cycle-slips. Sat05_82.ppt, 2005-12-05.
Due to:
Obstructions
Large ionospheric activity
Multipath
Low height angle
Interference
Sloping antenna
Errors in processing
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Cycle-slips. Sat05_82.ppt, 2005-12-05.
If station coordinates and orbits well known then one may follow how double differences change.
AtmosphtRtRtRtRttr pi
qi
pj
qj
pqij )()()()(
1)()(
:subtractedposition andorbit from computed Ranges
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GPS Accuracy, DOP. Sat05_82.ppt, 2005-12-05. Accuracy depends on instrument range error, σr
And on geometric configuration of satellites. Expressed using ”dillution of precision”, DOP.
..
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DOP. Sat05_82.ppt, 2005-12-05.
..
22
*
PDOPGDOP
time,*
position D-3 ,*
al vertic,*
horizontal ,*
:expression General
TDOP
TDOP
PDOP
VDOP
HDOP
DOP
rT
rP
rV
rH
r
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DOP computation. Sat05_82.ppt, 2005-12-05.
.
)(
...
..
.C
:obst independen if where
matrix. 4 x 4 ,C
matrix covariance-Variance
22
12XX
11XX
ZZYYXXrP
tt
ZtZZ
YtYZYY
XtXZXYXX
Tr
T
qqq
q
qqq
qqqq
AA
APA
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H and V DOP. Sat05_82.ppt, 2005-12-05.
Rotation of coordinate system needed:Local East, North, Up
.T
zz
yzyy
xzxyxx
B
q
qqq
B
BXxzyxx
B
..
.C
:matrix covariance- variancedTransforme
),,,( scoordinate Local
sinsincoscoscos
0cossin
cossinsincossin
xx
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Error measures. Sat05_82.ppt, 2005-12-05.
2-D accuracy: Distance Root Mean Square
Probability of being in a circle with this as radius between 63 % and 68 %.
Sometimes multiplies with 2:
Circular radial error: 95 % - 98 %.
Circular probable error: 50 %
3-D accuracy: Mean radial Spherical error (MRSE):
22DRMS
222MRSE h
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Earth Rotation. Sat05_82.ppt, 2005-12-05.
We must know Earth rotation:
The Earth moves while the signal is send:
'
sin'cos',sin'cos'
1".about or m 33
iseffect so m/s, 500about rotatesEarth
066.0)/103/(102
on time.transmissi ,87
ZZ
XYYYXX
ssmm
e
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Relativistic effects on the clocks. Sat05_82.ppt, 2005-12-05. Special theory of relativity: velocity dependent
General theory: Potential difference Earth - Satellite
Main part the same for all GPS satelites (same distance from the Earth):
MHz 9954510.2299999
: tochangedFrequency
s/day.38.3 ChangeHz0045.0
:MHz 10at operatesocillator Basic
107105.1
4.45x10
1-9
10-
f
Hzff
f
f
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Relativistic effect. Sat05_82.ppt, 2005-12-05.
Potential difference in the Orbit is not constant with respect to the Earth.
Generally corrected in Receivers. What is left disappears in relative obervations.
drift""for ns/s 0.01 and ns 70 : valueMaximal
cos10443.4
derivative-with time
sin10443.4
10
10
dt
dEEAt
EAet
s
s
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Relativistic correction. Sat05_82.ppt, 2005-12-05.
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Ionospheric delay. Sat05_82.ppt, 2005-12-05.
…. short too-Carrier
long, too:phase code from Range
:p of negative
,3.40
)1(
3.401,30.41
2
22
s s
egION
eg
ep
dsnf
dsnR
f
nn
f
nn
g
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First order correction (Code). Sat05_82.ppt, 2005-12-05.
Range on both frequencies must be the same:
See Table 7.15 for magnitudes.
22
21
2221
,1
22
21
22
21
21
22
21
21
,22,11
)(
)(
)11
( then ,*3.40put
ff
fRRR
ff
ffRRK
ffKRRdsnK
RRRRR
ION
s
e
IONION
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1. Order correction, Phase. Sat05_82.ppt, 2005-12-05.
)2()1()(L
:L2 and L1 Combined
L1.for advance-phase cIonospheri
)))2()2(()1()1((
)1(
22
21
212
22
1
22
0
2
12
12
2
22
Lff
ffL
ff
f
LNLf
fLNL
ff
f
LION
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1 Frequency receiver correction. Sat05_82.ppt, 2005-12-05. Klobuchar empirical model gives 50% at middle
latitudes:
Or obtain values from GSP-observatories like CODE,Analysis centers: IGS – IAAC. Or predicted values
http://igscb.jpl.nasa.gov/components/dcnav/cddis_products_ionex.html
s.polynomial P,A,
timelocalh 14at sett -of toscorrespond
ns) 5 (night at
dayat )/)(2cos(
(ns)delay Vertical
DCT
PtADCT
T
ION
ION
ION
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Other effects:. Sat05_82.ppt, 2005-12-05.
• Antenna phase-center variations
• Oscillator instabilities
• Receiver noise
• Troposphere
• Militaty restrictions or noise (SA)
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GPS Advantages. Sat05_82.ppt, 2005-12-05. • High 3-D precision for both position and velocity
• Independent of weather (- magnetic storms)
• Unlimited number of users
• Precise time-transfer
• Low costs (only receiver) for 1-frequency receivers
• Resistent ot Jamming
But the system does not give physical heights !
Geoid model needed !
Users need coordinates in Local system. Datum-transformation.
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Datum-shift. Sat05_82.ppt, 2005-12-05. (a) If datum-shift known:
GPS
GPS
GPS
GPSN
GPSN
GPSN
GPS
GPS
GPS
N
N
N
Z
Y
X
C
Z
Y
X
Z
Y
X
Z
Y
X
1
1
1
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Datum-shift. Sat05_82.ppt, 2005-12-05. (b) Datum-shift un-known:
1. Observed with GPS in a number of points where (XN, YN, ZN ) is known
2. If only one point, Translation vector determined by taking difference
3. If two points also rotation, 3 or more points C (scale-factor)
But often only latitude, longitude and height above mean-sea-level (orthometric height) known. We need ellipsoidal height. (Geoid height needed !)
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Datum-shift. Sat05_82.ppt, 2005-12-05. In Denmark:
KMS has established points with kown coordinates in ED1950, WGS84
Main-station: Satellite station in Buddinge
Determined in European GPS Campaigns.
7-parameter-shift not satisfactory, and does not agree if more than 2 points. Polynomials are used:
)(),(
)()(
)()(),(
)()(
)()(),(
01000
2002
2020
00101000
2002
2020
00101000
NNN
NN
NNNN
NN
NNNN
cch
bb
bbb
aa
aaa