Error Sources in Highly Precise GPS Positioning Lecture Series UFPR Curitiba/Brasil, March 2004 Error Sources in Highly Precise GPS Positioning - Modelling and Mitigation – Part 2: Site Specific Errors
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Error Sources in Highly Precise GPS Positioning
- Modelling and Mitigation –
Part 2:
Site Specific Errors
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Site specific errors
Contents
Multipath
Antenna phase centre offsets and variations
Calibartion of GPS antennas
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Multipath
Site specific errors
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Multipath - origin
Received signal composed of
- direct line of sight signal
- one or more constituents which
have propagated along paths of
different length
Origin:
Reflection of the transmitted signal
at surfaces in the vicinity of the
receiver (or satellite) antenna
reflected signal
direct signal
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Carrier phase multipath – Theory (1)
Simplified model:
-single horizontal reflector
-specular reflection (planar surface)
-geometrical optics (reflecting surfacenot in the vicinity of the antenna)
Additional propagation path of the reflected signal:
ε⋅=ε−ε
=
ε−π⋅==
+=
sinH2)2cos1(sinH
D
)2cos(DD ,sin
HD
DDD
212
21
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Phase difference between direct and reflected signal
Carrier phase multipath – Theory (2)
ε⋅λπ=⋅
λπ=Θ sin
H4D
2
Dependence of Θ on
- elevation angle ε
- height H = d
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Signal amplitudes and phases- Direct signal voltage Sα = Ad· cos φ- Ad signal voltage amplitude, φ signal phase- Reflected signal voltage Sr = α ·Ad ·cos(φ+Θ)
α Reflection coefficient; e.g. for f = 2GHz:α=1.0 waveless water surface/metallic surfaceα= 0.8 aluminiumα= 0.6 general ground
α≈ 0.3, leaves, foliage- Phase difference between direct
and contaminated signal
Carrier phase multipath – Theory (3)
���
����
�
−=Ψ
aSb
arctand
)sin(cosAb)cos(cosAa
d
dΘ−π⋅φ⋅⋅α=Θ−π⋅φ⋅⋅α=
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Phase difference between direct and total (multipath contaminated) signal:
Maximum phase error:
�Maximum possible phase error for α=1: GPS: L1 signal ~4.8 cm, L2 signal ~ 6.1 cm (L3~10.7 cm)
Slow variations of ψ due to changing configuration of satellite, reflector and antenna
Frequency:
• fψ inversely proportional to λ and proportional to H• fψ proportional to cos ε and rate of change of ε
Carrier phase multipath – Theory (4)
����
�
�
����
�
�
��
���
� ε⋅λπ⋅α+
��
���
� ε⋅λπ⋅α
=��
���
�
Θ⋅α+Θ⋅α=
sinH4
cos1
sinH4
sinarctan
cos1sin
arctanΨ
( ) )arccos( for arcsin maxmax α−±=ΨΘα±=Ψ
dtd
cosH2
dtd
21
fε⋅ε⋅
λ=Θ
π=Ψ
°π90 or
2
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Dependence of multipath carrier phase error on αααα and H
a) H=1.0mm 1:αααα=0,1 2:αααα=0,3 3:αααα=0,5 b) αααα=0.1 H=0,1m 2:H=0,3m 3:H=0,5m αααα=0.1 1:H=0,5m 2:H=1,0m 3:H=1,5m
Reflection coefficient α Distance H principallyprincipally influences influences the frequencythe amplitude
H = 30 cm : period Tψ = 107 minH = 10 m: period Tψ = 3,2 min
If H small or dε /dt ≈ 0 : constant offset
Carrier phase multipath – Theory (5)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Extension of theory
- Reflecting surface in arbitrary direction
- Non-planar surface → diffuse reflection- Dependency of α on elevation angle- Wave optics instead of geometrical optics
→ Fresnel zone theory, diffraction
- Multiple reflections- Consideration of polarisation
(GPS signals: right-handed circularly polarized transverse electromagnetic waves)
- Consideration of antenna gain/antenna characteristics,antenna imaging due to reflections
Carrier phase multipath – Theory (6)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Daily repetition of multipath
GPS system configuration repeats after 1 sidereal day (≈23h 56m)� Lag of n · 4 min after n (solar) days
Residuals after processingof phase observationsat 3 consecutive days(sessions 1-3)
Auto and cross correlationfunctions of sessions 1-3Lag 1-2: 4.17 minLag 1-3: 8.17 min
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Identification of multipath (1)
Combination of pseudo range and carrier phase observations
L1,L2 Dual frequency carrier phase observations (m)P1,P2 Dual frequency pseudo range observatinos (m)m1,m2 Dual frequency carrier phase multipath (m)M1,M2 Dual frequency pseudorange multipath (m)B1,B2 Bias terms (const., if not affected by cycle slips)
n1,n2 Integer carrier phase ambiguities
2111211 m1
2m
12
1BML1
2L
12
1P1MP ��
���
�
−α+�
�
���
�
−α+−+=�
�
���
�
−α+�
�
���
�
−α+−≡
2122212 m11
2m
12
BML11
2L
12
P2MP ��
���
� −−αα+�
�
���
�
−αα−+=�
�
���
� −−αα+�
�
���
�
−αα−≡
22
21 f/f=α
22111 n1
2n
12
1B �
���
�
−α+λ�
�
���
�
−α+−=
22112 n11
2n
12
B �
���
� −−αα+λ�
�
���
�
−αα−=
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Concept realized e.g. inTEQCGPS-Net
First priority: P1
if P1 is not available: C/A (more affected by multipath)
Orders of magnitude:pseudorange noise < 25 cmcarrier phase noise < 2 mmcarrier phase multipath < 7 cmpseudorange multipath up to 10-15 m (low elevation)
Other procedure:Comparison of 24h time series of residuals between different days
Identification of multipath (2)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Identification of multipath (3)
WaSoft/Multipath: Studie SAPOS BW
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Identification of multipath (4)
WaSoft/Multipath: Studie SAPOS BW
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Detection of multipath in dual frequency carrier phase observationsObservation equation
R distance satellite-receiverdt/dT satellite/receiver clock errorsN ambigutiydorb orbit errordion/dtrop propagation error (ionosphere/troposphere)dmult error due to multipath dant PCV errormeasurement noiseDouble differences
Identification of multipath (5)
2L,1L for 2,1idddddN)dTdt(cR ii,anti,multtropi,ionorbiii
=ε++++−+λ−−+=Φ
ii,ant
i,multtropi,ionorbiii
d
ddddNR
ε∆∇+∆∇+
∆∇+∆∇+∆∇−∆∇+∆∇λ−∆∇=∆Φ∇
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Short baseline
coordinates known, ambiguities fixed, antenna calibrated� Residuals in L1/L2 ~ multipath
Use of ionosphere– free linear combinationDifference between ionospheric delays at the endpoints of a short baselinewill be small� residuals in L3 (differential ionospheric delay) ~ multipath
Proof:Diff. between ionospheric delays in L1/L2(C = lin. combination of ambiguities)
if actual ionospheric delay differenceis zero, and multipath exists
Identification of multipath (6)
( ) C2/
C
1122
1122
12
12
+πψλ−ψλ=∆
+φλ−φλ=∆
θ⋅λλ=θ
ii,anti,multiii ddNR ε∆∇+∆∇+∆∇+∆∇λ−∆∇≈∆Φ∇
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathDetection algorithm based on specific characteristics:• Dominant periods ~ 10 - 45 min
• Ionosphere-free LC → strong effect of multipath• Assumption: reflectors are situated below antenna horizon
→ signals at E > 50° are not affected by multipath • Multipath errors are uncorrelated between different stations
Prerequisites:• 24 h observations• Dual frequency obeservations• Min. 3 sites• Network size < 100 kn• Approximate coordinates ± 1 cm• No extreme multipath
Identification of multipath (7)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathDetection algorithm works in several steps:• Residual of ionosphere-free LC (undifferenced)• Reduction of phase observations by geometric distance, tropospheric
correction model and approximately determined receiver clock error and ambiguity
• Form 20min blocks of data, E<50°, test individually using the following steps:(1) DD residuals w.r. to the satellite of highest elevation
→ (n-1) vectors of DD observations in a network of n stations(2) Reduce each vector by average value (removal of ambiguities,
longperiodic errors due to remaining tropospheric effects and orbiterrors). Multipath is suspected if standard dev. of the majority of vectorsexceeds pre-defined threshold (e.g. 15 mm)
(3) Correlate the vectors in all combinations. If the majority of correlationcoefficient exceeds pre-defined threshold (e.g. 0.8), the detectedmultipath effects are caused by a single signal.
• Verification of the results by a comparison of several days
Identification of multipath (8)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathExample (Wanninger & Wilde, AVN 1/97)
Identification of multipath (9)
DD residuals,34 km baseline, multipath periods6-9 min
Standard dev. and correlationcoefficients of 15 min sections of DD
DD residuals, Lo LC site A w.r. to 7 othersites (B-H)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathResults: Multipath map for each processed station
0 ≤α<360°, 0≤z≤50°
Identification of multipath (10)
< 5 mm5 mm – 15 mm
>15 mm
weakMedium
strong
.1
2
Multipath influence
MagnitudeSymbol
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathExamples
Identification of multipath (11)
STUT PG1
11...1 .. ....122 .....21 49 11...1 .. ....222 1.. 121 47 .111 .11 11....222 1.. 1222 45 .2.1 . 1 .1....22211.. 1212 43 .2..1. . .1....22 .2..11212 41 .21. 1 ...1....22 .2..11212 39 221. .....1.....2 .2..11.1. 37 2.1...2...2.....2.22..11.1. 35 2.1.. 2...2.......2 .....1. 33 2.1.. 22..2....2..2 ....... 31 ..... .2..2....22.2 . ..... 29 ..11......2....2........... 27 222212.2........2.......2.... 25 2.22.2.2........2.......2.... 23 2.22.2.22............ 2222..2 21 2222.22.2............ 2222.22 19 2.222 ..2............22222..22 17 22.......2............22222..22 15 .........2............2222.2.2. 13 .......2.2. ..........22222..2. 11 222....2.2. ..........22222.... 9 ........22.............22.2...... 7 .. . . . ...... . . 2 . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384201A.map M= 28 .
...... .. ......1 111.... 49 ...111 .. ...1..2 1.1 .1. 47 .... 1.1 22...1.22 1.1 111. 45 .111 1 1 .2...1.21...1 112. 43 .111.1 1 .2...1.2 .11111121 41 1111 1 ...2...1.1 .11.11121 39 1111 1....1...1.1 .12.1.221 37 1.111.....1...1.1.112...221 35 1.1.1 ....1.......1 2....21 33 ..1.. ....1.......1 2.....1 31 ..... ....1.......1 . .2... 29 ..........22......2....2... 27 ...2........2......2....2..2. 25 ...222.....22.....22..222..22 23 2.2222.....22.....2.. 2222.22 21 2..2222....22........ 22.2.22 19 2...2 .....22........2222..222 17 22...2....2.2..2.......222...22 15 22...2....2.2..22....2222..2... 13 .2........2 2..22....2222.2.... 11 .2........2 ...22....22.2.2...2 9 ..2............. 22..2.2..22..... 7 .. . . ..... .. . 2 2 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384202A.map M= 27 .
...... .. ......2 111...1 49 .1.... .. .....12 1.1 1.1 47 ..11 ... 22.....22 1.1 1.2. 45 ..11 1 . 12....122...1 1.2. 43 ..1111 . 12....12 .11111.22 41 ..1. 1 ..12....12 .11211.22 39 ..1. 1....2.1..12 .1.21.222 37 ..1..11...2.1..12..1.22.2.2 35 ..... 1...2.1...2.. .2..2.2 33 ..... 1...2.1...2.. 22..2.. 31 ..... 1...2.1...2.. 2 ..... 29 ..21.11...2.....2...2...... 27 ..22..11..22.........2....... 25 .2222.1...22.........22...... 23 22222.....22..2...... 2....22 21 22222..2..22..22....2 2....22 19 2.2.2 .2..22..222...2222.2.22. 17 .2.....22...2..2222..2.2222222. 15 .2.2...2....22.22.2.22.2222222. 13 .2.2...2... 22.22.2.22.2222222. 11 22.....2... .2.2..2.22.22.222.. 9 222......... .2. ..2.2..22.2.2... 7 2 . ..... .. .. .. 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384203A.map M= 33 .
....11 .. .....11 ....221 49 1..... .. ....111 1.. 121 47 .1.. ... .2....111 1.1 122. 45 .1.. . . 12....12211.1 122. 43 .1.... 1 12.....2 1.111122. 41 .2.. . 1112..1..2 ..1.12222 39 .2.. ...112..12.2 ....1222. 37 .2..2...112..12.1.11..1122. 35 12..2 ..1.2..12...1 ...222. 33 .2..2 ....2..12...1 ...222. 31 .21.2 ........2...1 . .22.2 29 ..222.............1....22.2 27 .2..22....2.............22.2. 25 .2........2....2......2.2..2. 23 .2.2......2....2..... 2.22222 21 22.22....22....2..... 2.22222 19 ...22 ...2.....222....22222222 17 .22.......2.....2222...22222222 15 .2........2.....2222..2222.222. 13 ..........2 ....2.22..2222.222. 11 ......... .. ....2.22..2222.222. 9 ...................22...222.2.... 7 .. . ......... . . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384204A.map M= 31 .
...1.. .. .....11 11..221 49 .1.11. .. ....111 1.. .21 47 ..11 1.. 11....1.2 1.. 121. 45 ...1.2 . 11....122.... 121. 43 ...1.2 1 11....12 ....1122. 41 ..1. 2 1111....12 ....11222 39 ..1. 2..1.1.....2 .1..11222 37 1111.22.1....2....21..1.212 35 1111. 2......2....2 ....212 33 11111 2......22...2 .2..212 31 .1..1 2......22...2 2 ....2 29 2.....2......22...2.2...... 27 2222...2.......2.....2....... 25 2.22.2.........2....2222.22.. 23 2.22.2.........22...2 2222.2. 21 ..22222........22...2 222..2. 19 2.22. 2...2.2..222..2.2222.22. 17 .2..2......2.2..222..2.2222222. 15 .222.......222..2222.22222.222. 13 22.22.22.2. 22..2.22222222.222. 11 2...2222.2...2.....22.2.22..2.. 9 .2....222.2...2.....22.2.22...... 7 .. . 2.. 2.... . 2 . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384205A.map M= 36 .
...1.. .. ...1121 1.1..1. 49 ...11. .11...1221 1.1 11. 47 .1.. 1.. .1...1212 1.2 111. 45 11...1 . .1....2221112 112. 43 11111. . .1....22 112211121 41 111. . ...1.1..22 .12.11121 39 111. .....1.1...2 .12.11221 37 ..1.1.....1.2...2.11..11222 35 ..1.1 ......2...2.2 ....212 33 ..2.2 ......2.....2 ....212 31 2.2.2 ......2.....2 . ...1. 29 21222.............2........ 27 22.222....................... 25 .1.22......................2. 23 ...22................ .....2. 21 22.22................ 2.22.22 19 2..22 .....2.........22.22.22. 17 ..2.2.......2.........22222222. 15 ..2.....2...2.........2222.222. 13 2.......22. 2.........22.2.222. 11 2........2. ..........2..2.222. 9 .2........2............2..2.2.... 7 .2 . . ..... ..... . . 2 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384206A.map M= 25 .
...... .. .....11 ....11. 49 11.... .......111 2.. 112 47 .11. ... ......111 2.. 112. 45 .11..1 . .....111122.. 112. 43 .111.1 . .....111 1...1112. 41 .111 1 .......111 1...1112. 39 1111 111......1.1 ....1122. 37 11111.11........1.2...112.. 35 1..11 .1..........2 ..11... 33 1.111 ............2 ..1.... 31 1.1.1 ............2 . ..... 29 ..1.......2.......2........ 27 ..2122.....2................. 25 ..22.2.....22..............22 23 ..22.2.....22........ 2....22 21 22222.......2........ 2....22 19 222.2 ......2.2.....222222..22 17 ..22...........2.....222222.222 15 ...2...........2...22222222.222 13 ...2....... ...2...22.2.222.222 11 ...2..2.2.. .......2..2..2..222 9 ....2..2.2..........2..2..2..2... 7 .. . . 2.. ..... . 2. . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384207A.map M= 24 .
...... .. .1...21 .1...1. 49 ...... ....11.221 ... 111 47 .2.. ... ....1.221 1.. 1121 45 121... . ......221.1.. 1121 43 121... . ......22 .1..22222 41 1121 1 ........22 .1.221222 39 1121 1.........22 .1.2.1.22 37 11211.1........22.11...1.22 35 212.1 .2.......22.2 .2...2. 33 222.. .2..2.......2 22...2. 31 2.2.. .22.2.......2 2 ...12 29 2.22....2.2.......222....12 27 .2.2.....2.2........2..2..22. 25 .2.........22.........22.2222 23 .222.......22.....2.. 2..2222 21 .2.2.....2.22....22.2 2.22.22 19 ...22 ...2.22....22.222222.222 17 ..2.2..2..2..2....22.2222222222 15 222.2..22.2.......2..22222..222 13 2.2.22.2222 ......2..2.222..22. 11 ..2..222222 ...........2....22. 9 ...22..2.22 ...........2.....2.. 7 .... . .. . ...... . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384208A.map M= 35 .
Bad station (Stuttgart)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Software WaSoft/MultipathExamples KARL PG1
Identification of multipath (11)
1..... .. ....... ...111. 49 1..... .. .1..... ... 11. 47 .1.. ... ...1..... ... .1.. 45 .... . . ...1......... .... 43 ..2... . ...1.... ......... 41 .12. . .....1.... ..2.2.... 39 .12. .......1.... ..2.2.... 37 2.2......2......2...2.2.... 35 222.. ...2......2.. 2.2.... 33 222.2 ...2......2.. 1.2.... 31 2.2.2 ...2......2.. 1 2...2 29 212.22..........2.....2...2 27 .................2.........2. 25 .2...............2....2...22. 23 22.............2..... 2.....2 21 .2.2........2..2..... 2.....2 19 22.22 ......22.2......2.2...2. 17 22...........22.2......222.222. 15 22...........2.22...2.222..2... 13 22......... .2.2....2.2.2...... 11 .2......... ........2.2........ 9 ..2 .. . .. ... .... 2......... 7 .. .. . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL201A.map M= 19 .
1..... .1 .1..... ....111 49 1...2. .1 .1..... ... .11 47 .1.. 2.. .1....... ... .1.. 45 .... 2 . .1........... .1.. 43 .....2 . ........ ......12. 41 .... 2 .......... ......12. 39 .... 22.........1 .......22 37 ..1.............1.........2 35 .221. ..........1.. .1..... 33 ..... ..........1.. 21..2.. 31 ..... ..........1.2 2 ..2.2 29 ..................222...2.2 27 ...................2.....2.2. 25 ..................22.....2.2. 23 ...........2..22....2 ....... 21 ...........2..22....2 ....... 19 ...22 .....2.2.2...22......... 17 22...2......2.2.2...2.......... 15 22..2.........2.2.............. 13 22..2...... ................... 11 222.2...... ................22. 9 2.... ... ........... ......2... 7 . . . . . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL202A.map M= 13 .
...... .1 .1..... ...222. 49 ...... .1 .1..... ... .2. 47 .... ... ......... 1.. .22. 45 .1.. . . ....1.....1.. .... 43 .11... . ....1... .1....... 41 ..2. . ......1... .1....... 39 ..2. ........22.. ...111... 37 ..2..........22.....11..... 35 ..2.. .......22.... 1...... 33 ..... .......222... 1...... 31 ..... .......222... . ..... 29 ...............2........... 27 ................2............ 25 ..................2.......... 23 ...............2..2.. ....... 21 .2.............22.2.. ....... 19 22... ......2..22.2.........2. 17 .22..........2..22.2.........22 15 22.222....2..2..22............2 13 22.222....2 .2......2.........2 11 222..2....2 ........2.......222 9 2........ 22........2.. ....2... 7 . .. . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL203A.map M= 15 .
.1.... .. ....... .....11 49 11.... .. ....... ... ..1 47 .1.. ... ......... ... ..1. 45 .1.. . . ............. .... 43 .1.... . ........ ......... 41 .1.. . .......... ......... 39 .1.. ............ ......... 37 ........................... 35 .2... ............. ....... 33 .22.. ............. .....2. 31 ..2.. .....2....... . ...22 29 ..2........2............... 27 .2..........2................ 25 .2..........2................ 23 ............2........ ......2 21 ............2........ ......2 19 ..... ......................2. 17 .2......... ................... 15 .2...2..... ................... 13 22...2..... .2.2............... 11 2....2..... .2.2............... 9 2. .. .... .2.2..... .. ... 7 . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL204A.map M= 7 .
...... .. .1..... ....... 49 1..... .. .1..... ... ... 47 .1.. ... ...1..... ... .... 45 .1.... . ...1......... .... 43 .1.... . ...1.... .....1111 41 11.. . .......... 1.....111 39 11.. ............ 1....11.1 37 11...............11.......1 35 ..... ...........1. ....... 33 ..... ...........1. ..2.11. 31 ..... ............. . 2.... 29 .....................22.... 27 ......................2...... 25 .2.........................1. 23 22..............2.... .....2. 21 2.....2.........2.... ......2 19 ..... 2.........2...........22 17 .......2... .....2.2.......2..2 15 22......... .....2.2.......2... 13 2.......... .......22.....22... 11 ......2... ........2.....22... 9 ...... 2. . ...... .2. ....2... 7 .. 2 ... . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL205A.map M= 9 .
...... .. ....... ..2...1 49 ...... ....1..... .22 .11 47 .... ... ...1..... .2. .11. 45 ...... . ...1......... .... 43 ...... . ...1.2.. ......... 41 .... . .....1.2.. ......... 39 .... .........2.. ......... 37 ..............2............ 35 ..... ........2.... .1..... 33 ..... ........2.2.. .1..... 31 ..... .......22.2.. 1 ..... 29 .............2222.....2.... 27 ..............2.22....22..... 25 ..............2.22....2...... 23 ..............222.... ...2... 21 ...2...........22.... ..22... 19 ...22 ......2..2........2..... 17 .22..2..... .2..2.......22..... 15 .2...22.... .2..2.......2...... 13 22....2.... .2..........2...... 11 2.......... ............2....22 9 2.... .. . ......... ..2... .. 7 . ... 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL206A.map M= 12 .
.1.... .1 .1..... ....1.1 49 11.... .1.11..... ... 1.1 47 .1.. ... ..11..... ... 1... 45 .1.... . ..1.......... ...1 43 .1.... . ..1..... ........1 41 .... . ....1..... ........1 39 .... ............ ........1 37 ..........................1 35 ..... ............. ....... 33 ..... ............. ....... 31 .11.. ............. . ..... 29 .111....................... 27 ............................. 25 2.....................2...... 23 22................... 2...... 21 22.2................. 2.....2 19 2..2. ................2.2...2. 17 .2......... ............22...22 15 .2......... ............2.....2 13 22....2.... ............2.....2 11 222...2 ... ............. ....2 9 .2.... .2.. ........ .. ..... 7 .. . .. . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL207A.map M= 8 .
1..... .. ....... 11..... 49 1..... .......... 1.. ... 47 .1.. ... ......... ... .... 45 .1.... . ............. .... 43 .1.... . ....2... ......... 41 .1.. . ......2... ......... 39 .1.. ........2... ......2.. 37 .............22...2.2....2. 35 12... .......22...2 2....2. 33 122.. .......22...2 2...... 31 1.2.. .......22...2 2 ..... 29 ..2..........12...2.22..... 27 .2............1.....222...... 25 .2....................2...2.2 23 .2................... 2...2.2 21 22.2............2.... 2.2.2.2 19 .2222 ......2...2.....2.2.2.2. 17 ..22.22.... .2...2.......2...22 15 2.22..2.... .2...2............2 13 2..2..2.... .2................2 11 ....2...... ............... ... 9 ....2 .... ......... ..... ... 7 ... . . . . 5 3 1
az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .KARL208A.map M= 15 .
Good station (Karlsruhe)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Multipath mitigation
Pseudorange multipath
- new reciever technology: narrow correlators
Carrier phase multipath
- Chokering antenna
- Ground plane
- Postprocessing evaluation:
– Processing of several daily data sets
– Exclude GPS data from satellites at low elevation
– Detection of disturbed data
Problems: RTK measurements
Separation from PCV and antenna imaging effects
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Site specific errors
Antenna phase centre offsetsand variations
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
• „ direction“ : - slant height → Reduction
- true vertical
• Means: - Trimble rod
- Height Hook
-
• Reference point at Trimble 22020 + GP:
- upper edge ground plane
- lower ground plane Notches
- lower edge pre-amplifier (ARP)
•Aim: determination of the coordinates of the ground point
Measurement of antenna height
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Trimble 22020 + Groundplane
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Mechanical phase centre
Rotationaxis
ARP Lower edge pre-amplifier
Mean phase centre
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Mechanical phase centre
ARP
L1-Phase centre
L2-Phase centre
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Electrical phase centre
X
XXARP
Mean mechanicalphase centre
Mean electricalphase centre
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Electrical phase centre
X
XXARP
Mean mechanicalphase centre
L1-Phase centre
L2-Phase centre
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Electrical phase centre
X
XX ARP
N/S E/W
Up
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
X
XX
Variations of the electrical phase centre (PCV)
ARP
N/S E/W
Up
L2L1
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Phase Centre Variations
0
40 80
120
160
200
240
280
320
3600 15
30
45
60
75
90-0,012-0,010-0,008-0,006-0,004-0,0020,0000,0020,0040,0060,008
[m]
Azimut [°]Elevation [°]
PCV L1 Leica AT 503 (3046)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Antenna - Model
How are the electrical phase centres fixed?• Mean offset in N/S, E/W- and Up
Alignment to north is compelling
• Phase centre variations
- purely elevation dependent
- dependent on elevation and azimuth
TRIMBLE 4000SSI 0 999999 1 0.0015 -0.0012 0.0751TRM22020.00+GP 2 -0.0011 0.0017 0.0692
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
How are the electrical phase centres fixed?
Antenna - Model
A\Z 0 5 10 15 ... 75 80 85 90
L1 0 0.00 1.80 4.60 ... 7.90 8.20 8.20 8.20L2 0 0.00 0.30 0.90 ... 1.20 0.10 0.10 0.10
Mean offset in N/S, E/W- and UpAlignment to north is compelling
• Phase centre variations
- purely elevation dependent
- dependent on elevation- and azimuth
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Dependency of phase centre
• Frequency
• Elevation
• Azimuth
• Manufacturer (Trimble, Leica, ...)
• Antenna type (AT 502, AT 503, ...)
• Production series
• External influences (ground plane, radom, ...)
Everyantenna
is unique++
1
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Processing of additional information: antenna
coordinatesmotions
accelerations?
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Site specific errors
Calibration of GPS antennas
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Calibration procedures
Differences: - Functional model
- Sample - Reference antenna
- Long time stability - Site
- Representativity -
IGSTypecalibration
Combination
Schupler, BallIndividualcalibration
Absolute chambercalibration
IfEIndividualcalibration
Absolute field calibration
NGS, obscampaign
Typecalibration
Relative field calibration
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Relative calibration at NGS
Procedure: Relative Type calibration in the field
short baseline (pillars)
Reference antenna: Dorne Margolin T
Problems: N/S-offset neglected per definition
E/W-offset neglected per definition
PCV(e, a) neglected per definition
Estimation: Mean offsets (N/S, E/W, h); PCV(e)
Problems: PCV (α) neglected
z ∈ [80°, 90°] neglected
Discontinuity at z = 0°
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Relative calibration at NGS
0
30 60 90
120
150
180
210
240
270
300
330
360
R 1
R 6
R 1 1
R 1 6
-0,008
-0,006
-0,004
-0,002
0,000
0,002
0,004
0,006
[m]
Azimut
Elevation
LEICA AT 502, SN 5120, L1
0
35 70
105
140
175
210
245
280
315
350 0
15
30
45
60
75
90-0,01200-0,01000-0,00800-0,00600-0,00400-0,002000,000000,002000,004000,006000,00800
[m]
Azimut [°]Elevation [°]
PCV L2 Leica AT 503 (3057)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Absolute calibration at IfE
Absolute Kalibrierung am IfE
Individual calibration on the basis of
daily differences for elimination of
station dependent error influences.
Elevation and azimuth dependent
PCV are determined by rotation and
tilt.
By this procedure e.g. the NGS
reference antenna can be
investigated.
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Absolute calibration at IfE
Individual calibration, Dorne Margolin T, L1
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Absolute calibration at IfE
Individual calibration, Dorne Margolin T, L2
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Absolute calibration at IfE
Individual calibration, Dorne Margolin T, L3, PCV(a)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
PCV of different antennae of the same series
0
40 80
120
160
200
240
280
320
3600 15
30
45
60
75
90-0,01200-0,01000-0,00800-0,00600-0,00400-0,002000,000000,002000,004000,006000,00800
[m]
Azimut [°]Elevation [°]
PCV L1 Leica AT 503 (3046)
0
40 80
120
160
200
240
280
320
360 0 15
30
45
60
75
90-0,01200-0,01000-0,00800-0,00600-0,00400-0,002000,000000,002000,004000,006000,00800
[m]
Azimut [°]Elevation [°]
PCV L1 Leica AT 503 (3049)
0
40 80
120
160
200
240
280
320
360 0 15
30
45
60
75
90-0,01200-0,01000-0,00800-0,00600-0,00400-0,002000,000000,002000,004000,006000,00800
[m]
Azimut [°]Elevation [°]
PCV L1 Leica AT 503 (3042)
0
40 80
120
160
200
240
280
320
3600 15
30
45
60
75
90-0,01200-0,01000-0,00800-0,00600-0,00400-0,002000,000000,002000,004000,006000,00800
[m]
Azimut [°]Elevation [°]
PCV L1 Leica AT 503 (3057)
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
PCV of different antennae of the same series
0
30 60 90
120
150
180
210
240
270
300
330
360
0
85-0,015
-0,010
-0,005
0,000
0,005
0,010
0,015
[m]
Aziumt
Elevation
LEICA AT 502, SN 5226, L2
0
25 50 75
100
125
150
175
200
225
250
275
300
325
350
0
65
-0,015
-0,010
-0,005
0,000
0,005
0,010
0,015
[m]
Azimut
Elevation
LEICA AT 502, SN 5133, L2
0
25 50 75
100
125
150
175
200
225
250
275
300
325
350
R 1
R 4
R 7
R 1 0
R 1 3
R 1 6
R 1 9
-0,015
-0,010
-0,005
0,000
0,005
0,010
0,015
[m]
Azimut
Elevation
LEICA AT 502, SN 5120, L2
0
25 50 75
100
125
150
175
200
225
250
275
300
325
350
R 1
R 4
R 7
R 1 0
R 1 3
R 1 6
R 1 9
-0,015
-0,010
-0,005
0,000
0,005
0,010
0,015
[m]
Azimut
Elevation
LEICA AT 502, SN 5076, L2
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Strongly disturbed L3-PCV
0
25 50 75
100
125
150
175
200
225
250
275
300
325
350
0
70-0,025
-0,020
-0,015
-0,010
-0,005
0,000
0,005
0,010
0,015
0,020
[m]
Azimut
Elevation
LEICA AT502, SN 5226, L3
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Remarks
Combining antenna information from different origin
- Relative and absolute calibration
- Different absolute procedures
- Different relative procedures
has to be avoided!
Reduction/transformation is necessary for comparison!
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Remarks
Scale problems in extended networks using
absolute field calibration
and traditional GPS modelling
Improvement of GPS modelling
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Satellite antenna calibration
• December 2000, NGS, Gerry Mader, Base line concept
• Necessary due to sparse information concerning the GPS satellite antenna
• L1 and L2 as well as L3 offsets
• Block IIA-Satellite
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Satellite antenna calibration
LK Northing[mm]
Easting[mm]
Up[mm]
L1 -3.2 19.2 530.0
L2 -4.8 4.7 191.1
L3 -6.8 -23.7 1053.7
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Satellite antenna calibration
Error Sources in Highly Precise GPS PositioningLecture Series UFPR Curitiba/Brasil, March 2004
Concluding remarks
• Cost-benefit-analysis
• influence of antenna modelling on highly precise
applications will increase
• Absolute calibration procedures as standard?
• Change of GPS modelling?
• Long term behaviour of antenna models
• GPS antenna calibration: standardizing?