AIUB

IGSWS2018 – PS13International GNSS ServiceWorkshop 2018 29 Oct.-02 Nov. 2018, Wuhan, China

D. Arnold1, S. Schaer1,2, A. Villiger1, R. Dach1, A. Jäggi1

1Astronomical Institute, University of Bern, Bern, Switzerland2Swiss Federal Office of Topography, Wabern, Switzerland

Poster compiled by Daniel Arnold, October 2018Astronomical Institute, University of Bern, Berndaniel.arnold@aiub.unibe.ch

Undifference ambiguity resolution for GPS-based precise orbit determination of low Earth orbiters

using the new CODE clock andphase bias products

Introduction• GNSS-based Precise Orbit Determination (POD) of Low

Earth Orbiters (LEOs) has nowadays become a standard ap-plication for high-quality GNSS products as provided by theIGS, or its individual analysis centers. For many LEOs, e.g.,for altimetry missions, the centimeter absolute orbit preci-sion and accuracy achieved by carrier phase-based GNSSpositioning is mandatory and could hardly be obtained byother tracking data.

• Resolving carrier phase ambiguities to their integer valueshas been known to inherently stabilize solutions for param-eters since a long time and has been confirmed in many ap-plications.

• E.g., double-difference (DD) processing of space or space-ground baselines for relative LEO POD allows for ambiguityresolution (AR) without any dedicated GNSS products in ad-dition and is known to significantly enhance relative POD.

• In case of Precise Point Positioning, undifferenced or zero-difference ambiguity resolution (ZD AR) requires theknowledge of GNSS satellite phase biases which cancel outin forming baselines. Recently, the Center for Orbit Determi-nation in Europe (CODE) IGS analysis center has establishedthe generation of a high-quality signal-specific phase biasproduct and a fully consistent ambiguity-fixed clock prod-uct within its rapid and final IGS-related processing (moredetails in presentation Schaer et al. in session PY01).

• Using this new product, we demonstrate the benefit of ZDAR on the quality of LEO POD and compare its performanceto results obtained in double-difference processing (includ-ing AR).

MethodsReduced-dynamic and kinematic single-satellite orbits and base-line solutions are computed using the development version of theBernese GNSS Software (Dach et al., 2015). The following param-eters are estimated in a batch least-square adjustment:

• Reduced-dynamic POD: 6 initial conditions, 3 constant em-pirical accelerations in radial (R), along-track (T), and cross-track (N) direction, constrained 6-min. piecewise constantaccelerations (PCAs) in R,T,N direction, epoch-wise receiverclock correction, carrier phase ambiguities.

• Kinematic POD: 3-dimensional position and receiver clockcorrection at every observation epoch, carrier phase ambi-guities.

• For both the reduced-dynamic and kinematic baseline de-termination, the reduced-dynamic orbit of LEO A serves asreference orbit and relative parameters for LEO B are esti-mated. For the reduced-dynamic baseline determination thedifferential accelerations are relatively loosely constrained(1 · 10−8m/s2).

Satellite-specific phase center variation (PCV) maps are intro-duced (i.e., no relative PCV corrections). For the reduced-dynamicPOD GOCO03S up to degree and order 120 is used for the Earthgravity field model and non-gravitational forces are not explicitlymodeled.

AR strategy: For both ZD AR and DD AR in a first step, theMelbourne-Wuebbena linear combination of pseudo-range andcarrier phase observations is processed to resolve the widelaneambiguities. In a second step, the ionosphere-free linear combi-nation is processed to resolve the narrowlane ambiguities usingthe sigma strategy (Dach et al., 2015) and to solve for the parame-ters of the reduced-dynamic orbit. The same resolved ambiguitiesare then introduced in the subsequent kinematic POD.Data used: For GRACE, GPS and attitude data of April 2007 areprocessed. Sentinel-3A and -B are in formation with nearly iden-tical orbits and 30s separation since June 2018, thus allowing fordouble difference processing of baselines. Furthermore, the gen-eration of Sentinel-3 carrier phase data has recently been refined toavoid half-cycle ambiguities (Montenbruck et al., 2018), allowingfor proper integer AR. For this study, Sentinel-3 orbits and base-lines are computed for the month September 2018. In all cases,data sampling is 10 s.

How to use CODE’s new clock and phase bias productsSince GPS week 2009 (July 2018) CODE produces a high-quality signal-specific phase bias product (the products for April 2007 have beengenerated for this study), see Fig. 1 . The corresponding OSB files can straightforwardly be introduced into GPSEST, the main parameterestimation program of the Bernese GNSS Software, which has been extended to allow for zero-difference ambiguity resolution, see Fig. 2.The new CODE rapid, final, and MGEX clock corrections are based on a fully consistent ambiguity fixing processing.

Bias SVN PRN Station name Obs yyyy mm dd hh mm ss yyyy mm dd hh mm ss Value (ns) RMS (ns)

*** **** *** ************* *** ******************* ******************* *********** ***********OSB G032 G01 C1C 2007 04 01 00 00 00 2007 04 02 00 00 00 0.52254 0.00610OSB G032 G01 C1W 2007 04 01 00 00 00 2007 04 02 00 00 00 -0.00000 0.00025OSB G032 G01 C2W 2007 04 01 00 00 00 2007 04 02 00 00 00 -0.00000 0.00025...OSB G032 G01 L1C 2007 04 01 00 00 00 2007 04 02 00 00 00 0.16431 0.00000OSB G032 G01 L1W 2007 04 01 00 00 00 2007 04 02 00 00 00 0.16431 0.00000OSB G032 G01 L2C 2007 04 01 00 00 00 2007 04 02 00 00 00 0.24524 0.00000OSB G032 G01 L2W 2007 04 01 00 00 00 2007 04 02 00 00 00 0.24524 0.00000OSB G032 G01 L2X 2007 04 01 00 00 00 2007 04 02 00 00 00 0.24524 0.00000...

Figure 1: Observation-specific bias (OSB) files generated by CODE, containingpseudo-range and phase biases for Integer-PPP (IPPP).

Figure 2: GPSEST, the main parameter estimation program of the BerneseGNSS Software, now allows for zero-difference ambiguity resolution.

Ambiguity resolutionFigure 3 shows the percentage of successfully resolved narrowlaneambiguities for both the ZD AR and DD AR in the GRACE andSentinel-3 processing. For GRACE, slightly less ambiguities areresolved in the DD processing compared to the ZD processing. InZD AR more ambiguities are resolved for GRACE-B (99.1%) thanfor GRACE-A (97.1%). The AR success rate for Sentinel-3 is in allcases close to 100%.

84.0

86.0

88.0

90.0

92.0

94.0

96.0

98.0

100.0

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

NL

AR

succe

ss r

ate

[%

]

Date in 2007

GRACE

Average: 97.1 %

99.1 %

92.2 %

GRACE-A ZDGRACE-B ZD

GRACE-A/B DD

97.0

97.5

98.0

98.5

99.0

99.5

100.0

01Sep

04Sep

07Sep

10Sep

13Sep

16Sep

19Sep

22Sep

25Sep

28Sep

NL

AR

succe

ss r

ate

[%

]

Date in 2018

Sentinel-3

Average: 99.0 %

99.2 %

98.8 %

Sentinel-3A ZDSentinel-3B ZD

Sentinel-3A/B DD

Figure 3: Percentage of resolved narrowlane ambiguities for GRACE (top) andSentinel-3 (bottom). Red: ZD AR for LEO A. Green: ZD AR for LEO B. Blue: DDAR for baseline.

K-Band validationGRACE offers the possibility to validate computed orbits, in par-ticular the along-track component, with the ultra-precise inter-satellite K-band measurements. Figure 4 shows the K-bandrange (KBR) residuals of reduced-dynamic ambiguity-float andambiguity-fixed GRACE orbits for one day, as well as the spec-tral analysis of the residuals. Both the ZD and the DD AR lead to asignificant reduction of KBR residuals, especially regarding longerperiods. Figure 5 shows the daily RMS values of K-band residu-als for the entire month for both reduced-dynamic and kinematicorbit and baseline solutions. For the reduced-dynamic and kine-matic solutions ZD AR and DD AR implies a reduction of the KBRresiduals by about a factor of 3-4 and 3-5, respectively.

-8

-6

-4

-2

0

2

4

6

8

10

12

0 5 10 15 20

KB

R r

esid

uals

[m

m]

Hour of day 07/091

GRACE-A/B red.-dyn. KBR residuals

FloatZD ARDD AR

20 40 60 80 100 120 140 160 180Period [min]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Amplitu

de [m

m]

FloatZD ARDD AR

Figure 4: K-band range residuals for reduced-dynamic orbits and baseline solu-tions, as well as their spectral analysis for April 1, 2007.

0

1

2

3

4

5

6

7

8

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

KB

R r

esid

auls

[m

m]

Date in 2007

GRACE-A/B red.-dyn. KBR residuals

Average: 5.54 mm1.82 mm1.32 mm

FloatZD ARDD AR

0

2

4

6

8

10

12

14

16

18

20

22

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

KB

R r

esid

auls

[m

m]

Date in 2007

GRACE-A/B kin. KBR residuals

Average: 14.32 mm4.74 mm2.70 mm

FloatZD ARDD AR

Figure 5: Daily RMS values of K-band residuals for reduced-dynamic (left) andkinematic (right) orbit and baseline solutions. For the kinematic solution statisticsan outlier threshold of 10 cm was applied.

Reduced-dynamic vs. kinematic solutionsFigure 6 shows for GRACE-A the differences between thereduced-dynamic and kinematic single-satellite solutions for oneday. It can be observed that especially in along-track and cross-track direction the long-periodic differences are significantly re-duced by the ZD AR. Figure 7 shows the daily RMS values oforbit differences for April 2007. Figure 8 shows the correspond-ing statistics for Sentinel-3 for September 2018. In all cases a pro-nounced reduction can be observed in the ambiguity-fixed orbits.

-40

-20

0

20

40

0 5 10 15 20

Orb

it d

iffe

rences [m

m]

Hour of day 07/091

GRACE-A RD-KN (float vs fixed), radial

FloatFixed

-40

-20

0

20

40

0 5 10 15 20

Orb

it d

iffe

rences [m

m]

Hour of day 07/091

GRACE-A RD-KN (float vs fixed), along-track

FloatFixed

-40

-20

0

20

40

0 5 10 15 20

Orb

it d

iffe

rences [m

m]

Hour of day 07/091

GRACE-A RD-KN (float vs fixed), cross-track

FloatFixed Figure 6: Differences between reduced-

dynamic and kinematic GRACE-A or-bit for April 1, 2007 in radial (top left),along-track (top right), and cross-track(bottom) direction for the ambiguity-float(red) and the ZD ambiguity-fixed (green)solution.

6

8

10

12

14

16

18

20

22

24

26

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

RM

S o

f orb

. diff. [m

m]

Date in 2007

GRACE RD-KN (float vs fixed), radial

Average: 13.7 mm18.6 mm8.5 mm11.3 mm

GRACE-A floatGRACE-B float

GRACE-A ZDGRACE-B ZD

2

4

6

8

10

12

14

16

18

20

22

24

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

RM

S o

f orb

. diff. [m

m]

Date in 2007

GRACE RD-KN (float vs fixed), along-track

Average: 10.8 mm15.6 mm4.2 mm4.8 mm

GRACE-A floatGRACE-B float

GRACE-A ZDGRACE-B ZD

0

5

10

15

20

25

30

01April

04April

07April

10April

13April

16April

19April

22April

25April

28April

RM

S o

f orb

. diff. [m

m]

Date in 2007

GRACE RD-KN (float vs fixed), cross-track

Average: 8.9 mm14.3 mm2.3 mm2.9 mm

GRACE-A floatGRACE-B float

GRACE-A ZDGRACE-B ZD Figure 7: Daily RMS values of dif-

ferences between reduced-dynamic andkinematic orbit solutions for April 2007in radial (top left), along-track (top right),and cross-track (bottom) direction forGRACE-A and -B.

6

8

10

12

14

16

18

20

22

24

01Sep

04Sep

07Sep

10Sep

13Sep

16Sep

19Sep

22Sep

25Sep

28Sep

RM

S o

f orb

. diff. [m

m]

Date in 2018

Sentinel-3 RD-KN (float vs fixed), radial

Average: 15.1 mm15.6 mm8.9 mm9.3 mm

Sentinel-3A floatSentinel-3B float

Sentinel-3A ZDSentinel-3B ZD

2

4

6

8

10

12

14

16

18

20

22

01Sep

04Sep

07Sep

10Sep

13Sep

16Sep

19Sep

22Sep

25Sep

28Sep

RM

S o

f orb

. diff. [m

m]

Date in 2018

Sentinel-3 RD-KN (float vs fixed), along-track

Average: 11.6 mm12.1 mm4.1 mm4.3 mm

Sentinel-3A floatSentinel-3B float

Sentinel-3A ZDSentinel-3B ZD

2

4

6

8

10

12

14

16

01Sep

04Sep

07Sep

10Sep

13Sep

16Sep

19Sep

22Sep

25Sep

28Sep

RM

S o

f orb

. diff. [m

m]

Date in 2018

Sentinel-3 RD-KN (float vs fixed), cross-track

Average: 8.7 mm8.7 mm2.5 mm2.6 mm

Sentinel-3A floatSentinel-3B float

Sentinel-3A ZDSentinel-3B ZD Figure 8: Daily RMS values of dif-

ferences between reduced-dynamic andkinematic orbit solutions for September2018 in radial (top left), along-track (topright), and cross-track (bottom) directionfor Sentinel-3A and -3B.

SLR validationSatellite Laser Ranging (SLR) normal points from 12 laser stationswere used for orbit validation, residuals larger than 20 cm havebeen rejected and an elevation cutoff of 10◦ applied. No parame-ters were estimated. Table 1 shows the mean values and standarddeviations of SLR residuals, confirming the positive impact of ZDAR on the orbit quality.

Float ZD AROrbits red.-dyn. kin. red.-dyn. kin.GRACE-A +0.5/15.5 +1.5/16.6 +2.5/12.4 +2.6/12.0GRACE-B +0.9/12.1 -0.5/16.9 +3.8/8.5 +3.7/9.6Sentinel-3A -6.0/11.5 -6.5/14.7 -5.7/10.7 -5.4/11.9Sentinel-3B -2.9/12.4 -4.3/15.2 -3.5/10.4 -3.3/11.1

Table 1: Mean values and standard deviations in mm of SLR residuals over April2007 (GRACE) and September 2018 (Sentinel-3), respectively.

ConclusionsUsing CODE’s new observation-specific phase bias product, aconsistent ambiguity-fixed clock product and extensions of theBernese GNSS Software, zero-difference ambiguity resolution wasapplied to the GPS-based POD of the GRACE and Sentinel-3 satel-lites. Ambiguity fixing is shown to significantly improve the orbitquality in terms of the independent validation measures K-bandand SLR, as well as in terms of the internal consistency betweenthe reduced-dynamic and kinematic orbit solutions. The achiev-able relative orbit quality is comparable to what can be obtainedfrom a double-difference processing of space baselines employingambiguity fixing. All results confirm a high quality of the CODEclock and phase bias product.

ReferencesR. Dach, S. Lutz, P. Walser, and P. Fridez, editors. Bernese GNSS Software, Version

5.2. Astronomical Institute, University of Bern, Bern, Switzerland, November2015. ISBN 978-3-906813-05-9. doi: 10.7892/boris.72297. User manual.

O. Montenbruck, S. Hackel, and A. Jäggi. Precise orbit determination of theSentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase obser-vations. Journal of geodesy, 92(7):711–726, 2018.

Contact addressDaniel ArnoldAstronomical Institute, University of BernSidlerstrasse 53012 Bern (Switzerland)daniel.arnold@aiub.unibe.ch