Space-Based Satellite Antenna Maps;

Impact of Different Satellite Antenna Maps

on LEO & Terrestrial Results

Bruce Haines, Yoaz Bar-Sever, Willy Bertiger,

Shailen Desai, Aurore Sibois, Frank Webb and Larry Young

Jet Propulsion Laboratory

California Institute of Technology

June 3, 2008

IGS Workshop, Miami USA

June 3, 2008 BJH 2IGS Workshop, Miami FL

GRACE-Based Estimates of GPS Antenna Phase Variations

• Problem: Uncertainties in GPS antenna phase variations (APV) among the limiting sources of error in global, GPS-based geodesy.

• Solution: Use GRACE tandem mission (2002– ) as orbiting geodetic lab for recovering GPS transmitter APV maps.

• GRACE advantages:• Scale (mean height) can be determined at cm

level from dynamical POD constraint (GM).• Clean spacecraft and simple attitude laws

produce low multipath, and facilitate modeling of surface forces.

• Advanced “BlackJack” GPS receivers on two spacecraft separated by ~200 km.

• Long-duration measurements (2002–) with dense global coverage (89.5° inclination).

• 500 km altitude implies no troposphere to confound APV interpretation.

• 500 km altitude enables sampling of GPS antenna beam pattern away from Earth’s limb.

Gravity Recovery and Climate Experiment (GRACE)

GPS Block IIA Satellite

June 3, 2008 BJH 3IGS Workshop, Miami FL

GRACE Processing

• Daily precise orbit solutions for 2004–2006• One GRACE s/c at a time• Phase (LC) only (High rate 30-s) • Minimum arc length of 30 min

• Dynamical POD to preserve link between scale and GM

• CD and 1 cpr acc. reset every rev. per UT/CSR approach.

• GPS ephemeris and clock offsets fixed to precise, fiducial-free values (JPL/IGSAC)

• A priori offset of GPS s/c phase-center with respect to CG assumed to be zero.

• GRACE a priori antenna phase variation model from anechoic chamber:

• Postfit residuals binned according to az/el of transmitters.

• High rate (30-s) ionosphere-free phase (LC)

• Least-squares fit to antenna map

• Iterate until converged

–15 0 15mm

June 3, 2008 BJH 4IGS Workshop, Miami FL

GRACE-Based Antenna Phase Variations:Results for 3 GPS Satellite Blocks

Block II/IIA (1989–1997) Block IIR-A (1997–2003) Block IIR-B/M (2003–pr.)

RMS3.7 mm

RMS4.1 mm

RMS15.9 mm

June 3, 2008 BJH 5IGS Workshop, Miami FL

Recovery of Grace Multipath: A Closure Test

GRACE-A GRACE-B

–10 0 10mm

–10 0 10mm

–10 0 10mm

GRACEMultipath Simulator1 (X 0.5)

• Anechoic chamber measurements provide a-priori APV for GRACE choke-ring antennas.

• After recovery of GPS transmitter APVs, GRACE carrier-phase (LC) residuals depict multipath predicted by simulation:

1 Byun, S., G. Hajj and L. Young, Radio Science 37(6), 2002

June 3, 2008 BJH 6IGS Workshop, Miami FL

Block II/IIA LC Phase Center Offset (+Z)

June 3, 2008 BJH 7IGS Workshop, Miami FL

GPS Nadir (+Z) Phase Center OffsetsGRACE- Vs. Ground-based (IGS) Solutions

June 3, 2008 BJH 8IGS Workshop, Miami FL

TOPEX/POSEIDON and Jason-1 Tests:Antenna Offset Estimates as Proxy for Scale

• First demo of precise GPS in space • ~2 cm radial orbit accuracy from GPS• Low multipath (GPS antenna on 4-m boom)• Apparent 5-cm bias in radial position of antenna

• Reported early in mission (e.g., Bertiger et al., 1994)• Eluded explanation for over a decade

Jason-1 (2001–)• Successor altimeter mission to T/P• 1-cm radial orbit accuracy from GPS• Apparent 4–5 cm bias in radial antenna position

• Due to errors in modeling of GPS transmit antenna PCO.

TOPEX/Poseidon (1992–2005)

• Enable estimation of mean (daily) antenna phase center offset wrt vehicle CM• Serves as proxy for errors in the TRF (scale) realized by GPS• Exposes errors in the transmitter phase-center locations• Use ionosphere-free phase (LC) alone in dynamic POD soln.

Specialized Dynamic POD Tests

June 3, 2008 BJH 9IGS Workshop, Miami FL

GPS Transmitter APV Maps Explain Anomalous Estimated Radial Antenna Offsets for T/P and Jason-1

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Time Series of T/P and Jason-1 Radial Antenna Offset EstimatesNoneIGSJPLBCDBCD

Nominal (Gipsy) ModelGRACE-Based GPS PCV Maps

mm

ppb

Year

TOPEX/Poseidon Jason-1

GRACE Data SpanUsed In

PCV Maps

D

-8.2953701Minimum

8.5058155Maximum

0.60300648Sum

19Points

0.031737183Mean

1.1129774Median

4.6419038RMS

4.7689914Std Deviation

22.743279Variance

1.0940817Std Error

-0.039184551Skewness

-0.92282638Kurtosis

Slope = +3.7 ± 0.1 mm/yr

Slope = +0.1 ± 0.1 mm/yr

Bias = +55.6 ± 0.8 mm

B

48.259182Minimum

60.715157Maximum

1056.7383Sum

19Points

55.617803Mean

55.645386Median

55.716286RMS

3.4020173Std Deviation

11.573722Variance

0.78047629Std Error

-0.39930782Skewness

-0.57790671Kurtosis

Bias = +0.0 ± 1.1 mm

June 3, 2008 BJH 10IGS Workshop, Miami FL

GPS Transmitter APV Maps Explain Anomalous Estimated Radial Antenna Offsets for Jason-1

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4

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12

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Time Series of Jason-1 Radial Antenna Offset Estimates(Jason Yaw Steering, JPL IGSAC "Flinn" Orbits and Clocks)

NoneIGSJPLBCD

PPB

PPB

PPB

mm

ppb

Year

SVN45

SVN47

SVN59

SVN60

SVN61

SVN56

SVN53

ppb/yrmm/yrppbmmAPPROACH

+0.5+3.7+5.7 +44 NONE (Gipsy Nominal)+0.0+0.1–2.4 –19 GRACE-Based Map (JPL)+0.3+2.4–4.0 –31 Ground-Based Map (GFZ+TUM)

BIAS (2004.5) DRIFT

y = m1 + m2*(M0-2004.5)

ErrorValue

0.09989344.073m1

0.0793083.6713m2

NA13240Chisq

NA0.80499R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.099305-31.07m1

0.0788412.4847m2

NA13085Chisq

NA0.67854R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.098676-18.635m1

0.0783410.10805m2

NA12919Chisq

NA0.040391R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.0129735.7237m1

0.01030.47679m2

NA223.31Chisq

NA0.80499R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.012897-4.035m1

0.0102390.32269m2

NA220.69Chisq

NA0.67854R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.012815-2.4201m1

0.0101740.014032m2

NA217.9Chisq

NA0.040391R

June 3, 2008 BJH 11IGS Workshop, Miami FL

Sampling of GPS Transmitter Beam Pattern:Effect of Ground vs LEO Data Distribution on IIR-B/M Phase Center Estimate

0

5

10

15

0 4 8 12 16

Sampling of GPS Transmitter Beam Pattern

TERRESTRIAL NETWORK

GRACE (500 km)

JASON (1300 km)

% Obs.

Nadir Angle (Deg.)

Block IIR-B/M

June 3, 2008 BJH 12IGS Workshop, Miami FL

GPS Global Network Data ReanalysisHighlights of Long-arc POD Strategy

• Reprocess 6-yrs of data from 2002–2007 (inclusive)• 60 stations

• Reprocess 25-d of data in 1995 (AS-free period from April–May)• Support selected TOPEX/Poseidon POD tests• Obtain snapshot of TRF scale realized from older GPS data set (fewer stations)

• Use 3-day solution arcs, shifted by 1 day.• Use fiducial-free strategy

• TRF realized by GPS alone (large rotations possible, but scale well determined).

• Use GRACE-based APV maps • Block averages of GRACE maps for GPS transmit antennas• Robot/anechoic maps for ground antennas (igs05_1455, Schmid et al., 2007).

• Employ POD strategy that capitalizes on dynamical constraints.• 1-cpr empirical accelerations in along, cross track (random walk w/ 12 hr update)• Y bias and solar radiation pressure coefficient (bias parameters)• Extra stochastics on eclipsing satellites (2-hr update)• Model planetary radiation pressure (albedo)• Apply second-order ionosphere correction (Kedar et al., 2003)• Use GMF troposphere mapping function (Boehm et al., 2006)• Use bias fixing

• Internal (GPS) TRF compared to ITRF via 7-parameter transformation

June 3, 2008 BJH 13IGS Workshop, Miami FL

TRF Scale from GPS Alone (2002–2007):Agreement with ITRF2005

Annual Cycle RemovedSee also Ge et al. (GRL, 2005)

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40

60

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2

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2002 2003 2004 2005 2006 2007 2008

mm

ppb

Years

+0.01 ppb/yr

–0.21 ppb/yr

–0.37 ppb/yr

This Study vs. ITRF2005IGT05

Legacy vs. ITRF2005IGT05

Legacy vs. ITRF2000JPL00

June 3, 2008 BJH 14IGS Workshop, Miami FL

TRF Scale from GPS Alone (2002–2007):Agreement with ITRF2005

Annual Cycle RemovedSee also Ge et al. (GRL, 2005)

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20

40

60

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-2

0

2

4

6

8

2002 2003 2004 2005 2006 2007 2008

mm

ppb

Years

+0.01 ppb/yr

–0.37 ppb/yr

This Study (w/ GRACE Maps) vs. ITRF2005

IGT05

Legacy vs. ITRF2005IGT05

Legacy vs. ITRF2000JPL00

This Study (w/ IGS Maps) vs. ITRF2005

IGT05–0.21 ppb/yr

June 3, 2008 BJH 15IGS Workshop, Miami FL

Alternative Choke Ring APV ModelReduces Scale Difference to 1 ppb

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3

Scale vs. ITRF2005/IGT0572-hr Global Network Solution for 22-Feb-200557 sites, all with choke rings, no fiducials

ppb

cm

IGS1

IGS1

GRACE2

IGS1

GRACE2

JPL3

Xmit1

Rcvr1

1 igs05_1472 ( Schmid et al ., 2008)2 GRACE-based (Haines et al ., 2007)3 JPL Antenna Range ( Young and Dunn , 1992)

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TurboRogue Choke RingAnt. Phase Variation (LC, mm)

Robot (Menge et al., 1998; 2003)Test Range (Young and Dunn, 1992)Test Range X 1.91

mm

Elevation (deg)

Y = M0 + M1*X

0.18968M0

1.9102M1

0.97503R

June 3, 2008 BJH 16IGS Workshop, Miami FL

Ensemble Ground Multipath?1 Month of Stacked LC residuals (60 stations) from Global Net. Soln.

Elosegui et al., 1995

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10

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Stacked LC ResidualsΔ ( – )APV Mdl Robot Test Range

( )LC Delay mm

( .)Elevation Angle deg

June 3, 2008 BJH 17IGS Workshop, Miami FL

Highlights

• GPS antenna phase variation (APV) maps developed from GRACE data• Describe complete phase correction with respect to s/c center-of-mass• No constraint to ITRF (use fiducial-free GPS orbit and clock products; derive scale from GRACE dynamics)• Individual maps for all GPS s/c flying in 2003–2006 time frame.• Using block averaged maps is viable option

• Basic validation of APV maps yields promising results• Inferred Block IIA nadir (Z+) offset (+1.8 m for LC) yields good agreement with recent robot test (+1.7 m;

Wubenna et al, 2007) and rooftop test (+1.7 m; Mader and Czopek, 2002)• Residual systematic errors (GRACE LC residuals) agree with multipath predicts.

• APV maps significantly reduce scale errors in kinematic LEO orbit solns (Jason-1, T/P)• Reduce Jason-1 scale rate (2002–06) from +0.48 to +0.01 ppb/yr (+3.7 to +0.1 mm/yr)• Reduce Jason-1 scale bias from +5.6 ppb to –2.4 ppb ( +43 to –19 mm)• Reduce T/P scale bias in 1995 test data from +7.3 to 0.0 ppb (+56 to 0.0 mm)• IGS transmitter maps also reduce LEO errors, but seem to be less effective, due in part to abundance of

LEO data outside 14o zenith angle represented by ground data (no map default to phase center offset.)

• APV maps significantly stabilize TRF scale realized in global network soln.• +0.01 ppb/yr wrt to ITRF2005 (2002-2007) using GRACE maps & IGS ground maps together.• Testifies to ability of GPS alone to determine TRF scale rate over 6-yr span.

• 6 ppb bias in TRF scale using GRACE maps & IGS ground maps together.• Consistent with smaller transmit PCO offsets (Z+) from GRACE-based technique.• Use of Choke ring APV from JPL antenna test range decreases bias to +1 ppb (< 1 cm).• Ground error sources (e.g., multipath, troposphere) should not be ruled out as potential cause of bias

discrepancy between GRACE- and ground-based APV estimates for GPS transmitters.

June 3, 2008 BJH 18IGS Workshop, Miami FL

• Backup

June 3, 2008 BJH 19IGS Workshop, Miami FL

GPS Transmitter X/Y Phase Center Offsets From GRACE Maps

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-0.20

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0.40

0 10 20 30 40 50 60 70

X OffsetY Offset

Offset (m)

GPS S/V Number

Block II/IIA

Block IIR

Prelaunch X Offset = 0.279 cm(e.g., Mader and Czopek, 2002)

June 3, 2008 BJH 20IGS Workshop, Miami FL

GPS S/C Orbit Solution Differences: (Long Arc vs. IGS Combined)

Bias 6.78Drift 0.21Pfit 0.56

Bias 0.20Drift -0.01Pfit 0.20

Bias 0.07Drift 0.00Pfit 0.19

Bias –0.28Drift 0.20Pfit 0.90

Median = 3.9 cm

June 3, 2008 BJH 21IGS Workshop, Miami FL

High Elevation SLR Passes Reveal Significant Reduction in Range Bias to GPS

-200-150

-100-50

050

100150200

2002 2003 2004 2005 2006 2007

GPS35Longarc Median = –1 mm, σ = 38 mmIGS_combined Median = –52 mm, σ = 24 mm

( )Bias mm

( )Time Year

High Elevation Passes from Graz, McDonald Observatory and Monument Peak

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050

100

150200

2002 2003 2004 2005 2006 2007

GPS36Longarc Median = –6 mm, σ = 32 mmIGS_combined Median = –52 mm, σ = 19 mm

( )Bias mm

( )Time Year

IGS_combinedBias_FLINN_R

-117.46651-170.1161Minimum

99.687126172.60152Maximum

-45308.56-1759.2187Sum

860860Points

-52.684373-2.0456031Mean

-52.463123-0.67453Median

56.10672832.26542RMS

19.3068732.219248Std Deviation

372.755231038.0799Variance

0.65835881.0986672Std Error

0.8225467-0.31972763Skewness

7.00535693.0727801Kurtosis

June 3, 2008 BJH 22IGS Workshop, Miami FL

GPS Orbit & TRF Scale (ppb)

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IMPLICATIONS OF LONGARC/GRACE ON SCALE(ORBIT VS IGS COMBINED, GROUND NETWORK VS IGT05)

Orbit ppb

Ground ppb

ppb

Legacy

("FlinnP")

Legacy +

Gr. Off.

Legacy+

Gr. Off +

Gr. APV

Legacy+

Robot

Legacy+

Gr. Off+

Robot

Legacy+

Gr. Off+

Gr. APV+

Robot

("AGU07")

Legacy+

IGS Off+

IGS APV+

Robot

("FlinnR")

June 3, 2008 BJH 23IGS Workshop, Miami FL

GPS Orbit & TRF Scale (cm)

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IMPLICATIONS OF LONGARC/GRACE ON MEAN HEIGHT(ORBIT VS IGS COMBINED, GROUND NETWORK VS IGT05)

Orbit cm

Ground cm

cm

Legacy

("FlinnP")

Legacy +

Gr. Off.

Legacy+

Gr. Off +

Gr. APV

Legacy+

Robot

Legacy+

Gr. Off+

Robot

Legacy+

Gr. Off+

Gr. APV+

Robot

("AGU07")

Legacy+

IGS Off+

IGS APV+

Robot

("FlinnR")

June 3, 2008 BJH 24IGS Workshop, Miami FL

Antenna Phase Variation (APV) Maps Reveal GPS Antenna Elements

GPS Block IIA Antenna Array GPS Block IIACarrier (LC) APV

(Mean Offsets Removed)

–10 0 10mm

Also Haines et al. (2004); Schmid et al. (2005)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Mader and Czopek (2002)

June 3, 2008 BJH 25IGS Workshop, Miami FL

GPS Transmitter PCV Maps Explain Anomalous Estimated Radial Antenna Offsets for Jason-1

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Time Series of Jason-1 Radial Antenna Offset EstimatesNoneIGSJPLBCD

PPB

PPB

PPB

mm

ppb

Year

ppb/yrmm/yrppbmmAPPROACH

+0.2+1.8+8.7 +67 NONE (Gipsy Nominal)+0.1+0.5+1.9 +15 GRACE-Based Map (JPL)–0.0–0.0–3.9 –30 Ground-Based Map (GFZ+TUM)

BIAS (2004.5) DRIFT

y = m1 + m2*(M0-2004.5)

ErrorValue

0.2589266.881m1

0.20561.8392m2

NA87960Chisq

NA0.25434R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.25221-30.4m1

0.20027-0.0011769m2

NA83457Chisq

NA0.00017277R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.301215.23m1

0.239170.52433m2

NA1.1902e+05Chisq

NA0.064318R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.0336278.6859m1

0.0267020.23886m2

NA1483.6Chisq

NA0.25434R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.032754-3.9481m1

0.026009-0.00015284m2

NA1407.6Chisq

NA0.00017276R

y = m1 + m2*(M0-2004.5)

ErrorValue

0.0391161.978m1

0.0310610.068095m2

NA2007.5Chisq

NA0.064318R

(14o Cutoff for Transmitter Nadir Angle)

June 3, 2008 BJH 26IGS Workshop, Miami FL

TRF Centering from GPS Alone (2002–2007): Agreement with ITRF2005

-75

0

75 X Slope = +0.3 ± 0.1 mm/yr ( σ = 4.6 )mm

mm

-75

0

75 Y Slope = +0.1 ± 0.1 mm/yr ( σ = 5.3 )mm

mm

-75

0

75

Z Slope = –5.3 ± 0.2 mm/yr ( σ = 13.9 )mm

mm

1500

2250 Zeta Slope = –50 km/yr

2002 2003 2004 2005 2006 2007 2008

km