Session on Calibration and Future Receiver Developments

Part I: Calibration

Yang Gao - Bias catalog, effect and calibration….Gerard Petit - Absolute receiver bias calibration, stability…..Stefan Schaer - IGS bias estimates, data format issue…

GNSS Biases, their Effect and Calibration

Yang GaoDepartment of Geomatics Engineering

The University of Calgaryygao@ucalgary.ca www.ucalgary.ca/~ygao

IGS Workshop 20082-6 June 2008, Miami Beach, Florida, USA

2/24IGS Workshop 2008, 2-6 June 2008

Outline

Catalog of GNSS BiasesEffect of Biases on IGS ProductsBias CalibrationBias Issue in PPPGNSS BiasesRecommendations/Actions for Discussions

3/24IGS Workshop 2008, 2-6 June 2008

Catalog of GNSS Biases

Hardware BiasSatellite related bias

Receiver related bias

Firmware BiasSatellite related bias

Receiver related bias

Bias in Code MeasurementsSatellite related bias

Receiver related bias

Bias in Phase measurementsSatellite related bias

Receiver related bias

4/24IGS Workshop 2008, 2-6 June 2008

GPS Biases in Observation Equations

)()()( 2222/2 PbbcddddtdTcP sP

rPLiontroporb ερ +−++++−+=

)()()( 1111/1 CbbcddddtdTcC sC

rCLiontroporb ερ +−++++−+=

)()()( 1111/1 PbbcddddtdTcP sP

rPLiontroporb ερ +−++++−+=

)()()( 111111/1 ΦελρΦ ΦΦ ++−+−++−+= NbbcddddtdTc srLiontroporb

)()()( '222'2'22/

'2 ΦελρΦ ΦΦ ++−+−++−+= NbbcddddtdTc sr

Liontroporb

)()()( 2222/2 CbbcddddtdTcC sC

rCLiontroporb ερ +−++++−+=

)()()( '2'2'22/

'2 PbbcddddtdTcP s

PrPLiontroporb ερ +−++++−+=

)()()( 222222/2 ΦελρΦ ΦΦ ++−+−++−+= NbbcddddtdTc srLiontroporb

Catalog of GNSS Biases

5/24IGS Workshop 2008, 2-6 June 2008

Catalog of GNSS Biases

Inter-Frequency Bias (IFB)Satellite IFBReceiver IFB

Differential Code Bias (DCB)Satellite DCBReceiver DCB

Differential Phase Bias (DPB)Satellite DPBReceiver DPB

Relative (fix a reference such as a ground receiver)

Inter-system Time System OffsetGPS/GLONASSGPS/GALILEOGPS/COMPASS

Inter-system Coordinate System Offset

GPS/GLONASSGPS/GALILEOGPS/COMPASS

Inter-System Biases (multi-constellations)

Biases are not estimable in absolute sense

6/24IGS Workshop 2008, 2-6 June 2008

Catalog of GNSS BiasesAbsolute receiver bias calibration

BIPM (see Petit’s slides)JPL (see below from Larry Young)

JPL had 4 generations of receiver calibration used since 1980.

1. SERIES (pretty much the same as for #4 below)

2. SERIES-X: codeless dual frequencyThis was calibrated by generating PN codes at 1.023 MHz and 10.23 MHz, and modulating both onto a L1 carrier, and the 10,23 MHz code onto the L2 carrier, and coupling them into the receiver data stream. An interesting featureis they were swept across the signal doppler range to measure phase shifts across each filter.

3. ROGUE This receiver used the CA, P1, and P2 codes, and was designed for ionospheric measurements, and so neededaccurate L1-L2 delay calibrations. There was a 'clever trick" which proved very accurate. The receiver was designedwith very symmetric paths for P1 and P2. For calibration, the operator used the L1 LO frequency to drive both L1 andL2 mixers, so the receiver tracked the P1 signal on both channels. This provided TEC calibrations to about 100 ps, which translates to a TEC error of about 0.3E-16 e-/m2.

4 Turborogue: Codeless or semicodeless tracking CA, P(Y)1, and P(Y)2 The calibrator generated a GLONASS code at 10.23 MHz, and mixed that with the sum of L1 and L2 LOs in a single mixer. The modulated L1 and L2 carriers were cupled into the receiver signal path near the antenna. This provided ~200 ps to 300 ps L1 - L2 calibration accuracy when it worked, but there were problems with some of the directional couplers which added differential delay to the calibration signal.

Lesson: It is not easy to get better than 1 ns calibration!

7/24IGS Workshop 2008, 2-6 June 2008

IGS Product Convention and Bias Effect on IGS products

Effect of Biases on IGS Products

)()()(22

21

22

212

1IF

sIFP

rIFPtroporbIF PbbcdddtdTc

ffPfPfP ερ +−+++−+=

−⋅−⋅

=

)( )()(22

21

22

212

1IFIFIF

sIF

rIFtroporbIF NbbcdddtdTc

ffff ΦελρΦΦΦ ΦΦ ++−+++−+=

−⋅−⋅

=

)()]()[(22

21

22

212

1IFtroporb

sIFP

rIFPIF PddbdtbdTc

ffPfPfP ερ ++++−++=

−⋅−⋅

=

)( )]()[(22

21

22

212

1IFIFIFtroporb

sIF

rIFIF NddbdtbdTc

ffff ΦελρΦΦΦ ΦΦ +++++−++=

−⋅−⋅

=

)()]()[(22

21

22

212

1IFtroporb

sIFP

rIFPIF PddbdtbdTc

ffPfPfP ερ ++++−++=

−⋅−⋅

=

)( )]()[(

)]()[(22

21

22

212

1

IFIFIFsIFP

sIF

rIFP

rIF

troporbsIFP

rIFPIF

Nbbbbc

ddbdtbdTcffff

Φελ

ρΦΦΦ

ΦΦ ++−+−+

+++−++=−

⋅−⋅=

8/24IGS Workshop 2008, 2-6 June 2008

GPS Observation Equations using IGS Products

)( 111/1 PcbcTddcdTP rPgdLiontrop ερ ++++++=

)()( 111/11/1 CcbDCBTcddcdTC rCCPgdLiontrop ερ +++++++=

)( 222/2 PcbTcddcdTP rPgdLiontrop εγρ ++++++=

)( '2'21/12/

'2 PbDCBcTcddcdTP r

PCPgdLiontrop εγρ ++⋅+++++=

)()( 111111/1 ΦελρΦ ΦΦ ++−++−++= NbbbcddcdT srsIFPLiontrop

)()( 222222/2 ΦελρΦ ΦΦ ++−++−++= NbbbcddcdT srsIFPLiontrop

)()( 222/22/2 CcbDCBTcddcdTC rCCPgdLiontrop ερ +++++++=

Bias Calibration

)()( '222'2'22/

'2 ΦελρΦ ΦΦ ++−++−+++= NbbbcdddcdT srs

IFPLiontroporb

9/24IGS Workshop 2008, 2-6 June 2008

22

21

22

212

1

ffbfbfb

sP

sPs

IFP −−

=

γγ −=

−−

=11

2/112s

PPsP

sP

gdDCBbbT

DCB (P1, P2) and Tgd

Bias Calibration

2

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛=

ffγ

gds

PP TDCB )1(2/1 γ−=

DCB (C1, P1)

sC

sP

sPC bbDCB 111/1 −=

⎪⎪⎩

⎪⎪⎨

⎧

−=−

−=

−=−

−=

gdsIFP

sPP

sIFP

sP

gdsIFP

sPP

sIFP

sP

TbDCBbb

TbDCBbb

γγ

γ

γ

2/12

2/11

11

11

IGS bias estimates (see Schaer’s slides)

10/24IGS Workshop 2008, 2-6 June 2008

CODE DCB(P1, P2) and broadcast Tgd

( ) 070.11 2,1 ≠=−− sPPDCBTgdγ

Bias Calibration

11/24IGS Workshop 2008, 2-6 June 2008

P2-C2 of PRN 12

-1. 2

-0. 8

-0. 4

0

0. 4

0. 8

1. 2

131280 149280 229560 309780 390150 408150 488370GPS Ti me (s)

P2-C

2 (m

)

P2- C2 of PRN 17

- 1. 2

- 0. 8

- 0. 4

0

0. 4

0. 8

1. 2

92040 129840 183630 221310 275070 312810 386340 440100 477780GPS Ti me ( s)

P2-C

2 (m

)

P2-C2 of PRN 31

-1. 2

-0. 8

-0. 4

0

0. 4

0. 8

1. 2

92580 146580 183540 237090 274290 327810 364890 418410 490920GPS Ti me (s)

P2-C

2 (m

)

25.4-8.631

24.919.317

21.9-2.912

STD (cm)Mean (cm)PRN

Bias Calibration

DCB (C2, P2)

)()( 11111/1sC

sP

rC

rPPC bbbbDCB −−−=

12/24IGS Workshop 2008, 2-6 June 2008

Traditional model (Zumberge et al., 1997)Ionospheric-Free code and phase combinations

Bias Issue in PPP

Ambiguity term in the estimates

)()(22

21

22

212

1IFtrop

rIFPIF PdbdTc

ffPfPfP ερ ++++=

−⋅−⋅

=

)( )]()[(

)(22

21

22

212

1

IFIFIFsIFP

sIF

rIFP

rIF

troprIFPIF

Nbbbbc

dbdTcffff

Φελ

ρΦΦΦ

ΦΦ ++−+−+

+++=−

⋅−⋅=

Receiver clock term in the estimates

13/24IGS Workshop 2008, 2-6 June 2008

Bias Issue in PPPTraditional model (Zumberge et al., 1997)Ionospheric-Free code and phase combinations

)( )]()[(

)(22

21

22

212

1

IFIFIFsIFP

sIF

rIFCP

rIF

troprIFCPIF

Nbbbbc

dbdTcffff

Φελ

ρΦΦΦ

ΦΦ ++−+−+

+++=−

⋅−⋅=

Receiver clock term in the estimates

)()(1

)()(

)()(

22,12,12/

2222/2

PDCBDCBcbbcddbdTc

PbbccbddcdTP

sPC

rPC

sIFCP

sIFPLiontrop

rIFCP

sP

rP

sIFPLiontrop

εγγρ

ερ

+−−

+−+++++=

+−+++++=

)()(1

)()(

)()(

12,12,11/

1111/1

CDCBDCBcbbcddbdTc

CbbccbddcdTC

sPC

rPC

sIFCP

sIFPLiontrop

rIFCP

sC

rC

sIFPLiontrop

εγ

ρ

ερ

+−−

+−+++++=

+−+++++=

)(1

)( 1,1

22

21

22

212

1

IFCPs

PCtroprIFCP

IFCP

PDCBcdbdTc

ffPfCfP

εγ

γρ +−

−+++=

−⋅−⋅

=

must be calibrated

Ambiguity term in the estimates

based on C1 and P2

14/24IGS Workshop 2008, 2-6 June 2008

Bias Issue in PPP

UofC model (Gao and Shen, 2002)Average of code and phase + IF phase combination

( ) ( ) )(][5.0 2

1,1111111

111,1

ΦΦΦ

Φ

ελρ

Φ

Pss

Prr

PsIFPtrop

P

PNbbcbbccbdcdT

PP

+++−+++++=

+=

)(])()([

])()([)(

22

21

2222222

2

22

21

1111112

1

IF

sP

rP

sr

sP

rP

sr

troprIFPIF

ffNbbcbbcf

ffNbbcbbcfdddTc

Φελ

λρΦ

ΦΦ

ΦΦ

+−

+−−−−

−+−−−

++++=

( ) ( ) )(][5.0 2

2,2222222

222,2

ΦΦΦ

Φ

ελρ

Φ

Pss

Prr

PsIFPtrop

P

PNbbcbbccbdcdT

PP

+++−+++++=

+=

15/24IGS Workshop 2008, 2-6 June 2008

Bias Issue in PPP

UofC model (Gao and Shen, 2002)Average of code and phase + IF phase combination

( ) ( ) )(])(2[5.0 )( 2,2222222r

2,2 ΦΦΦΦ ελρ PsIFP

rIFP

ssP

rrPtropIFPP PNbbcbbcbbcdbdTcP ++−−+−+++++=

L1 ambiguity term in the estimates

L2 ambiguity term in the estimates

( ) ( ) )(])(2[5.0 )( 1,1111111r

1,1 ΦΦΦΦ ελρ PsIFP

rIFP

ssP

rrPtropIFPP PNcbbcbbcbbcdbdTcP ++−−+−+++++=

)(])(2)()([

])(2)()([)(

22

21

2222222

2

22

21

1111112

1

IF

sIFP

rIFP

sP

rP

sr

sIFP

rIFP

sP

rP

sr

troprIFPIF

ffNbbcbbcbbcf

ffNbbcbbcbbcfdddTc

Φελ

λρΦ

ΦΦ

ΦΦ

+−

+−−−−−−

−+−−−−−

++++=

( ) ( ) 222222 )(2 Nbbcbbcbbc sIFP

rIFP

ssP

rrP λΦΦ +−−+−+

( ) ( ) 111111 )(2 Ncbbcbbcbbc sIFP

rIFP

ssP

rrP λΦΦ +−−+−+

16/24IGS Workshop 2008, 2-6 June 2008

Receiver fractional phase biasZero-baseline approachReceiver fractional phase bias is not stableThe bias value changes after each power-cycle of receiver

)()( 22222/11111/21 NbbdNbbd srLion

srLion λλΦΦ ΦΦΦΦ +−+−−+−+−=−

( )22112121 )( NNbb rr ΔλΔλΦΦΔΔΔ ΦΦ −−−=−

( )22112121 )()( NNbb rr ΔλΔλΔΔΦΦΔ ΦΦ −+−=−

Bias Issue in PPP

17/24IGS Workshop 2008, 2-6 June 2008

Satellite fractional phase bias

Wide-lane phase bias value is stableNarrow-lane bias value is very hard to determine (noise std is 30 cycle and NL wavelength is only 10 cm)

Bias Issue in PPP

18/24IGS Workshop 2008, 2-6 June 2008

Challenges for integer ambiguity resolution in PPP

Ambiguity term in PPP is affected by many residual errors and biases including those due to satellite orbit/clock productsFloat ambiguity solutions usually not converge to a constant

Bias Issue in PPP

19/24IGS Workshop 2008, 2-6 June 2008

GNSS Biases

886849.63-50.461

9611911.6-50.7460

9026111.45-50.4557

850599.14-48.8356

7072610.38-53.7254

966089.3-54.8352

9395910-45.5651

720678.23-53.5650

810158.17-53.0248

1090838.3-50.3947

914237.21-53.4346

7270514.14-67.2145

644769.93-52.1543

1036589.65-62.1841

9586616.91-62.0638

EpochsSTD (cm)Bias (cm)PRN

GLONASS DCB (G1, G2)(zero-baseline)

rGGDCB 2/1Δ

20/24IGS Workshop 2008, 2-6 June 2008

GNSS Biases

887089.5420.1761

9618511.5320.8960

9028711.5719.1657

850799.0618.6856

7073710.4118.4354

966319.3120.5152

9398010.0216.0751

720988.2915.6550

810637.9819.1248

1091418.1721.1447

915437.2216.0746

7275914.1437.6945

645069.6919.9943

1037219.6432.5741

9589916.8732.3138

EpochsSTD (cm)Bias (cm)PRN

GLONASS G1-GPS C1(zero-baseline)

rGCDCB 1/1Δ

21/24IGS Workshop 2008, 2-6 June 2008

GNSS Biases

Timing System Difference

System time difference between GPS and GLONASS

22/24IGS Workshop 2008, 2-6 June 2008

Discussions IGS Convention and user guideline development

• Convention on observation combinations (modernized GPS signals, Galileo) and products (orbit/clock, iono/trop….)

• Convention on bias estimates (products)• User community need to understand the convention and proper use of IGS products• Increased user community participation should be considered• Stable or able to monitor reference should be established for bias estimates

Absolute receiver bias calibration is becoming increasingly important as the increase of GNSS signals along with biases

• Current effort should be continued and increased to develop standard and convention• In-receiver bias calibration should be investigated, long-term stability is more important if

removal is difficult• Firmware bias should be given special attention

Multi-constellation bias determination• GLONASS products (some confusion….)• Bias estimates for GLONASS• Inter-system bias/offset estimates

Actions should be taken to further improve IGS products to support demanding applications• These applications don’t tolerate current small systematic biases in IGS products• Basic research efforts are needed to understand better GNSS biases and develop new

modeling methodologies• Phase bias determination and real-time products should be investigated to support real-time

OTF PPP

23/24IGS Workshop 2008, 2-6 June 2008

Discussions

)()]()[(22

21

22

212

1IFtroporb

sIFP

rIFPIF PddbdtbdTc

ffPfPfP ερ ++++−++=

−⋅−⋅

=

)( )]()[(

)]()[(22

21

22

212

1

IFIFIFsIFP

sIF

rIFP

rIF

troporbsIFP

rIFPIF

Nbbbbc

ddbdtbdTcffff

Φελ

ρΦΦΦ

ΦΦ ++−+−+

+++−++=−

⋅−⋅=

)()]()[(22

21

22

212

1IFtroporb

sIFP

rIFPIF PddbdtbdTc

ffPfPfP ερ ++++−++=

−⋅−⋅

=

)( )]()[(

)]()[(22

21

22

212

1

IFIFIFsIFP

sIF

rIFP

rIF

troporbsIF

rIFIF

Nbbbbc

ddbdtbdTcffff

Φελ

ρΦΦΦ

ΦΦ

ΦΦ

++−+−+

+++−++=−

⋅−⋅=

Decoupling clock model (Collins, 2008)

Modeling issue for iono-free P1/P2

24/24IGS Workshop 2008, 2-6 June 2008

Modeling the effect of common signal (Gao et al., 2001)

Modeling issue for C1-P1 bias determination

[ ]{ })]()([)()()]()([)]()([ 1111,

11/,

11/1111 jPjCjPjCddjPjCjPjC kkiirkPCsat

riPCsat

kkii −−−+−=−−− −− εΔΔ

))j(P)j(C(S)j(dd

))j(P)j(C(SS)j(d)j(ddd)j(P)j(Ci

1i11P1C1P1C/rcv

i1P1C/sat

i1

i11P1C1P/rcv1C/rcv

i1P/sat

i1C/sat

i1

i1

−ε+++=

−ε+−+−+−=−

−−−

))()(()(

))()(()()(

)()(

1111/11/

111/1/1/1/

11

jPjCjdd

jPjCjdjddd

jPjC

iiPCrcv

iPCsat

iiPrcvCrcv

iPsat

iCsat

ii

−++=

−+−+−=

−

−− ε

ε

-1

-0.5

0

0.5

1

561600 581600 601600 621600 641600

GPS time (s)

Bia

s (m

)

Discussions