Error Sources in Highly Precise GPS Positioning - Modelling and ...

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


Site specific errors

Contents

Multipath

Antenna phase centre offsets and variations

Calibartion of GPS antennas


Multipath



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


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


Phase difference between direct and reflected signal


ε⋅λπ=⋅

λπ=Θ sin

H4D

2

Dependence of Θ on

- elevation angle ε

- height H = d


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


��

��

�

−=Ψ

aSb

arctand

)sin(cosAb)cos(cosAa

d

dΘ−π⋅φ⋅⋅α=Θ−π⋅φ⋅⋅α=


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


��

�

�

��

�

�

��

��

� 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


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



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



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


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 λ��

��

�

−α+λ�

�

��

�

−α+−=

22112 n11

2n

12

B λ��

��

� −−αα+λ�

�

��

�

−αα−=


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




WaSoft/Multipath: Studie SAPOS BW


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


2L,1L for 2,1idddddN)dTdt(cR ii,anti,multtropi,ionorbiii

=ε++++−+λ−−+=Φ

ii,ant

i,multtropi,ionorbiii

d

ddddNR

ε∆∇+∆∇+

∆∇+∆∇+∆∇−∆∇+∆∇λ−∆∇=∆Φ∇


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


( ) C2/

C

1122

1122

12

12

+πψλ−ψλ=∆

+φλ−φλ=∆

θ⋅λλ=θ

ii,anti,multiii ddNR ε∆∇+∆∇+∆∇+∆∇λ−∆∇≈∆Φ∇


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



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



Software WaSoft/MultipathExample (Wanninger & Wilde, AVN 1/97)


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)


Software WaSoft/MultipathResults: Multipath map for each processed station

0 ≤α<360°, 0≤z≤50°


< 5 mm5 mm – 15 mm

>15 mm

weakMedium

strong

.1

2

Multipath influence

MagnitudeSymbol


Software WaSoft/MultipathExamples


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 .

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az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384202A.map M= 27 .

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az 11111111112222222222333333 el 12345678901234567890123456789012345 .555555555555555555555555555555555555 .0384203A.map M= 33 .

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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)


Software WaSoft/MultipathExamples KARL PG1


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)


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



Antenna phase centre offsetsand variations


• „ 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


Trimble 22020 + Groundplane


Mechanical phase centre

Rotationaxis

ARP Lower edge pre-amplifier

Mean phase centre


Mechanical phase centre

ARP

L1-Phase centre

L2-Phase centre


Electrical phase centre

X

XXARP

Mean mechanicalphase centre

Mean electricalphase centre



X

XXARP

Mean mechanicalphase centre

L1-Phase centre

L2-Phase centre



X

XX ARP

N/S E/W

Up


X

XX

Variations of the electrical phase centre (PCV)

ARP

N/S E/W

Up

L2L1


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)


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


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


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


Processing of additional information: antenna

coordinatesmotions

accelerations?



Calibration of GPS antennas


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


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°


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]




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.



Individual calibration, Dorne Margolin T, L1



Individual calibration, Dorne Margolin T, L2



Individual calibration, Dorne Margolin T, L3, PCV(a)


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]



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]



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]



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]




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


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


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


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



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


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!


Remarks

Scale problems in extended networks using

absolute field calibration

and traditional GPS modelling

Improvement of GPS modelling


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



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


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?

Error Sources in Highly Precise GPS Positioning - Modelling and ...

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