compatible with various triple-frequency ppp models estimating a … · 2019-01-31 ·...

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Estimating a set of IFCBs to make IGS ionospheric-free clock product

compatible with various triple-frequency PPP models

Presentation · December 2018

DOI: 10.13140/RG.2.2.13986.68807

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Lin Pan

Wuhan University

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Estimating a set of IFCBs to make IGS

ionospheric-free clock product compatible

with various triple-frequency PPP models

Lin Pan, Xiaohong Zhang, Jingnan Liu

School of Geodesy and Geomatics, Wuhan University

Benefit: formation of inter-frequency combinations with

good features; increased measurement redundancy

Challenge : satellite clock inconsistency

BDS-2: B1/B2/B3

BDS-3/3S: B1/B3/B1C/B2a/B2b

Galileo: E1/E5A/E5B/E5(A+B)/E6

GPS Block IIF: L1/L2/L5

GLONASS-K/GLONASS-M: G1/G2/G3

QZSS: L1/L2/L5

1. A newly emerging situation

Montenbruck et al. (2010) identified the presence of time-, signal- and

satellite-dependent line biases in carrier phase observations.

iiriri ddTItctcP ,dd

iviciriiri bbbNTItctc ,,,dd

)()(dd 2,2,121,1,1222,1211,1212, vvIF babadadatctc

Code and carrier-phase observations：

L1/L5 IF satellite clocks:

IGS satellite clocks (L1/L2 ionospheric-free (IF) satellite clocks):

IFCBd

)()(dd

12,

5,2,151,1,1552,1511,1515,

IF

vvIF

tc

babadadatctc

)( 2

2

2

1

2

11,12 fffa )( 2

2

2

1

2

22,12 fffa

)( 2

5

2

1

2

52,15 fffa )( 2

5

2

1

2

11,15 fffa

2. IGS satellite clocks

Kept consistent with Inter-Frequency Clock Bias (IFCB)

Satellite clock determination (Guo and Geng 2017): IF-PPP1 & UC-PPP

Least-squares adjustment (Montenbruck et al. 2012): IF-PPP1

Epoch-differenced (ED) strategy (Li et al. 2016): IF-PPP1

3. Mathematical conversion formula among various IFCBs

IF-PPP1：L1/L2 IF+L1/L5 IF

IF-PPP2：L1/L2/L5 IF (infinite number of combs.

with only two conditions)

UC-PPP：L1 UC+L2 UC+L5 UC

IFCB(IF-PPP1) IFCB(IF-PPP2) IFCB(UC-PPP)

Relationship?

The current IFCB estimation

approach should be modified

from time to time

Introduction of IFCB：

15,15,12,15, dd IFIFIFIF tctc

5,2,151,1,152,2,121,1,1215, vvvvIF babababa

),(DCB),(DCB 512,15212,12

52,1511,1522,1211,1215,

PPaPPa

dadadadaIF

Code-specific IFCB (CIFCB)：

Phase-specific IFCB (PIFCB)：

IFCB (IF-PPP1: L1/L2 IF+L1/L5 IF)


5151

2121

),(DCB

),(DCB

ddPP

ddPP

Triple-frequency GFIF (Geometry-Free and Ionospheric-Free)

carrier phase combinations:

PIFCB observation equation

GFIF,GFIF,GFIF15,

GFIF,GFIF,GFIF5,2,151,1,152,2,121,1,12

52,1511,1522,1211,12

)()(

)()(GFIF

crIF

crvvvv

bbN

bbNbabababa

aaaa

)(GFIF GFIF,GFIF,GFIF15, crIF bbN

)()(

)()(

)()(

5,2,151,1,152,2,121,1,12GFIF,

5,2,151,1,152,2,121,1,12GFIF,

52,1511,1522,1211,12GFIF

ccccc

rrrrr

babababab

babababab

NaNaNaNaN



Estimation process of PIFCB:

)1(GFIF)(GFIF)1,(,15, tttt s

r

s

r

s

rIF

)1,(

1

)1,(

1

,15,15, )1,()1,()1,()1,(ttn

r

s

r

ttn

r

s

r

s

rIF

s

IF ttwttwtttt

40)1,(1

40)1,()1,(sin)1,(

ttel

ttelttelttw

s

r

s

r

s

rs

r

t

tj

s

IF

s

IF

s

IF jjtt1

15,015,15,

0

)1,()()(

Eliminating stable terms with

ED processing

A weighted average of solutions

over the entire network

The PIFCB at each epoch can be

obtained with an accumulation



Li et al. (2016): ED strategy

5,5,12,5,

2,2,12,2,

1,1,12,1,

dd

dd

dd

UCUCIFUC

UCUCIFUC

UCUCIFUC

tctc

tctc

tctc

0

0

),(DCB),(DCB

),(DCB

),(DCB

2,

1,

51212,125,

211,122,

212,121,

UC

UC

UC

UC

UC

PPPPa

PPa

PPa

DCB is used to compute the

L1, L2 and L5 UC CIFCB

Both L1 and L2 UC PIFCB equal

to 0, while an extra consideration of

L5 UC PIFCB is necessary

L1/L2 IF satellite clocks are converted into

uncombined (UC) satellite clocks with

estimated L1, L2 and L5 UC CIFCB and

PIFCB

IFCB (UC-PPP: L1 UC+L2 UC+L5 UC)


5,,55,5

,22,2

,1,1

5,2,52,121,522,125,5

2,2,121,121,1,122,2

2,2,121,2,121,12,1

d

d

d

])1()([d

])(2[d

]2)([d

UCEEEr

EEEr

EEEr

UCvvPPPUCEEr

vvEEr

vvEEr

NTItc

NTItc

NTItc

babagTItcP

baabaTItcP

babaaTItcP

2,52,121,2,1251,1255,5,5,5

2,22,121,2,1221,1222,2,2,2

2,2,121,2,121,1211,1,1,1

5,2,52,121,1,122,125

1,2,2,121,2,2,12

2,2,121,1,12,

)1()(

)1()(

2)(

)1()(

)()(

dd

rrcrE

rrcrE

rrcrE

rrrPPPUC

vvrrE

rrrEr

dadaadbbNN

dadaadbbNN

dadaadbbNN

ddadaag

bbaddaII

dadatctc

The UC triple-frequency

PPP observation equations

after applying the L1, L2

and L5 UC satellite clocks



5,2,52,121,251,125, )1()1( vvvUC bbaba

5,2,152,2,121,1,151,12

5,2,151,1,152,2,121,1,1215,

)( vvv

vvvvIF

bababaa

babababa

15,5,2,152,2,121,1,151,122,155, )( IFvvvUC bababaaa

2,1515,5, aIFUC

)( 2

2

2

1

2

11,12 fffa )( 2

2

2

1

2

22,12 fffa

)( 2

5

2

1

2

52,15 fffa )( 2

5

2

1

2

11,15 fffa

L1/L5 IF PIFCB:

Formulating the L5

UC PIFCB

The estimated L1/L5 IF

PIFCB can be converted

into L5 UC PIFCB

Coefficients for L1/L2 and

L1/L5 IF combinations



0

1

55221

521

eee

eee

)()(dd 5,52,21,1552211125, vvvIF bebebedededetctc

125,125,12,125, dd IFIFIFIF tctc

CIFCB

Theoretical

formula

Introduction of similar IFCBs

The combination coefficients

fulfill these two conditions

IFCB (IF-PPP2: L1/L2/L5 IF )


),(DCB),(DCB)(

)()(

515212,122

55221122,1211,12125,

PPePPae

dedededadaIF

Formulating the

L1/L2/L5 IF PIFCB

5,52,21,1

5,52,21,12,2,121,1,12125,

vvv

vvvvvIF

bcbcbc

bebebebaba

55

22,122

11,121

ec

eac

eac

0

0

55221

521

ccc

ccc

5

2

52

5

2

251

1

1

1

cc

cc

55,2,

2

51,

2

25

55,2,

2

51,

2

25

5,52,5

2

51,5

2

25125,

1

1

1

1

1

1

1

1

1

ebbb

cbbb

bcbcbc

vvv

vvv

vvvIF

2,15515,125, aeIFIF

Three combination

coefficients in L1/L2/L5

IF PIFCB

The estimated L1/L5 IF PIFCB can also be

converted into L1/L2/L5 IF PIFCB

Various L1/L2/L5 IF PIFCBs

are proportionally correlated

with each other

IFCB (IF-PPP2: L1/L2/L5 IF )


L1/L2-L1/L5IF PIFCB

(L1/L5)

UC PIFCB

(L5)

IF PIFCB

(L1/L2/L5)

transformation

Estimation

DCB products

IF satellite clocks

（ L1/L2, L1/L5）

UC satellite clocks

（L1、L2、L5）

IF satellite clocks

（L1/L2/L5）

IF triple-

frequency users

（ L1/L2, L1/L5 ）

UC triple-

frequency users

（ L1、L2、L5 ）

IF triple-

frequency users

（ L1/L2/L5 ）

Estimation Service User

IGS satellite clocks

Satellite clocks for various triple-frequency PPP models


transformation

PIFCB estimates for UC-PPP, IF-PPP2 and IF-PPP1 on

April 8, 2017

4. Results

PIFCB estimates

-0.15

0

0.15

-0.15

0

0.15

-0.15

0

0.15

Inte

r-F

requency C

lock B

ias (

m)

-0.15

0

0.15

-0.15

0

0.15

0 4 8 12 16 20

-0.15

0

0.15

Time (hour)

0 4 8 12 16 20 24

Time (hour)

IF-PPP1

IF-PPP2

UC-PPP

G01 G03

G06 G08

G09 G10

G24 G25

G26 G27

G30 G32

Amplitude:

4–16 cm

Positioning accuracy

0

0.02

0.04

0.06

0.08

0.10

East

(m)

0

0.02

0.04

0.06

0.08

0.10

Nort

h (

m)

0 2 4 6 8 10 12 14 16 18 20 22 240

0.02

0.04

0.06

0.08

0.10

Up (

m)

Time (hour)

Without PIFCB

With PIFCB

0

0.02

0.04

0.06

0.08

0.10

East

(m)

0

0.02

0.04

0.06

0.08

0.10N

ort

h (

m)

0 2 4 6 8 10 12 14 16 18 20 22 240

0.02

0.04

0.06

0.08

0.10

Up (

m)

Time (hour)

Without PIFCB

With PIFCB

0

0.02

0.04

0.06

0.08

0.10

East

(m)

0

0.02

0.04

0.06

0.08

0.10

Nort

h (

m)

0 2 4 6 8 10 12 14 16 18 20 22 240

0.02

0.04

0.06

0.08

0.10

Up (

m)

Time (hour)

Without PIFCB

With PIFCB

Epoch-wise RMS values of UC-PPP (left), IF-PPP2 (middle) and

IF-PPP1 (right) positioning errors without and with PIFCB

consideration for different observational lengths

8->5 (38%)

6->4 (33%)

13->9 (31%)

8->4 (50%)

5->3 (40%)

13->10 (23%)

6->4 (33%)

4->3 (25%)

12->10 (17%)

4. Results

Distribution of convergence time for 24-h UC-PPP solutions

0

2

4

6

8

10EastP

erc

enta

ges (

%)

North Up

0 30 60 900

2

4

6

8

0 30 60 90

Convergence Time (min)

0 30 60 90 120

Without PIFCB

With PIFCB

Mean: 24.5 min

Mean: 20.3 min

Mean: 8.1 min

Mean: 8.0 min

Mean: 30.1 min

Mean: 23.5 min

Improvement :

17%、1%、22%

4. Results

Convergence time

Phase observation residuals for UC triple-frequency PPP at

stations AJAC and CEBR on April 2, 2017

4. Results

Phase observation residual

Epoch-wise satellite EWL UPD estimates without (left) and

with (right) PIFCB consideration on April 2, 2017

4. Results

Extra-Wide-Lane (EWL) UPD estimates

0 4 8 12 16 20 24-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

GPS Time (hour)

Extr

a-W

ide-L

ane U

PD

(cycle

)

0 4 8 12 16 20 24-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

GPS Time (hour)E

xtr

a-W

ide-L

ane U

PD

(cycle

)

1All the new-generation GNSS satellites are designed to

transmit signals on three or more frequencies. The

satellite clock consistency must be ensured.

2The mathematical conversion formula among the

PIFCBs of different triple-frequency PPP models is

rigorously derived.

3After applying the PIFCB corrections, the positioning

accuracy, convergence time, phase observation residuals,

and EWL UPD estimates are significantly improved.

5. Conclusions

Thank You for Your Attention!

More details refer to our recently published paper:

Pan L, et al. 2018. Journal of Geodesy.

doi:10.1007/s00190-018-1176-5View publication statsView publication stats

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