An Empirical ModelSRP IGSWS2018-PS06 for the Orbit Normal … · 2019-01-02 · SRP accel....

1
Definition of -TBM ECOM - version with just 2 parameters covering SRP SRP due to SP: - can be ignored for short-arcs => β (T20, T30) ECOM TM - - SRP due to sat.-body may be absorbed by stochastic orbit parameters ( ) or by an a priori box model ECOM-TBMP Definition -TB of ECOM - SRP acceleration during ON described in TERM system as ... - ... by 9 parameters: SRP - β-dependency can be ignored for short-arcs => ECOM-T - stochastic orbit parameters (i.e., pulses or accelerations) can be added optionally => ECOM TBP - Introduction The Center for Orbit Determination in Europe ( ) is contributing to CODE the Multi- Extension ( ) since its start in 2012 with an IGS GNSS MGEX orbit and clock solution. `s ( ) product includes the CODE MGEX COM satellite systems , , Galileo, BeiDou2 ( 2), and GPS GLONASS BDS QZSS. GEO satellites are not included, so far. The ECOM2 solar radiation pressure model, used for all satellites ( ) SRP in the COM solution, has been designed for yaw-steering ( ) attitude. YS Consequently, the orbit quality was degraded for BDS2 and QZS-1 spacecrafts ( ) at times when operating under orbit-normal ( ) SC ON attitude, i.e., during or close to eclipse seasons. Here we introduce a family of empirical models taylored for the - SRP ON mode, which can either be used on top of an a priori model or as a SRP stand-alone model. International Service GNSS Workshop 2018 29 Oct. - 02 Nov. 18 Wuhan China 20 , , L . . Prange , R. Dach , G Beutler , A. Villiger , 1 1 1 1 S. Schaer , D. Arnold , A. Jäggi 2 1 1 1 Astronomical Institute, University of Bern, Switzerland 2 Federal Office of Topography swisstopo, Wabern, Switzerland An Empirical Model SRP for the Orbit Normal Mode Poster compiled by , L. Prange October 2018 Astronomical Institute, University of Bern, Switzerland @aiub.unibe.ch lars.prange IGSWS2018-PS06 Contact address Lars Prange Astronomical Institute, University of Bern Sidlerstrasse 5 3012 Bern (Switzerland) [email protected] Posters and other publications from the Satellite Geodesy Group: AIUB http://www.bernese.unibe.ch/publist Attitude Modes Most SCs are oriented with attitude. Some GNSS YS BDS QZS ON 2 satellites and -1 switch to attitude for small elevation angles of the Sun w.r.t. the orbital plane. β All spacecrafts maintain the attitude GEO ON permanently. Du Du b Z Z Z Y Y Y Y X X Spacecraft-fixed reference frame ( aw- teering attitude): Y S X X SPN = D Fig. 1: Satellite-fixed ref. frames under - and -mode. YS ON ECOM SRP Model Frames During -mode the co-rotating decomposition YS ECOM is practical ( due to solar panels absorbed by one SRP coeff.; Y=0). For -mode non-rotating frames are better ON suited (e.g., frames fixed to local orbit or orbital plane). We use the Terminator System Decomposition ( ). TERM Du Du b Z Z Z X X Spacecraft-fixed reference frame ( rbit- ormal attitude): O N X X Y = W SPN D Y = W Y = W Y = W Du Du b = D T3 = D T3 = D T3 = D T2 Terminator line T1 T1 T1 T2 T2 T2 TERM T ( erminator) frame: T1 Fig. 2: model frame definition. SRP SRP YS ON in - and -modes Features of the attitude mode are: YS - solar panel ( ) plane is always parallel to the terminator plane and SP normal to the vector Sun => satellite ( ) D - C`sY-sides are never illuminated (Y=0, apart fromY-bias) S - ody (+Z, -Z, +X panels) causes an signal, which is periodic SCb SRP w.r.t. the argument of latitude difference betw. SC and Sun ( ) Δu - rapid noon/midnight turns for small elevation angles ( ) of the Sun w.r.t. β the orbital plane Features of the attitude mode are: ON - no noon and midnight turns - SP-normal ( ) deviates from the vector D by -angle SPN the β - power generation is reduced compared to the -mode YS - due to SP can be absorbed by 2 parameters, which are constant SRP SRP w.r.t. u, but not w.r.t. Δ β - all panels of body can be illuminated - causing periodic signals SP SRP w.r.t. u and Δ β SRP ON Simulation for Simulations based on released meta data of -1 have been QZS performed separately for SP and SC body. Simulated SRP acceleration has been projected into the terminator reference frame ( TERM, Fig. 2). Coefficients of significant size have been selected for ( u) and ( u, )- ECOM-T ECOM-TB Δ Δ β empirical SRP models for the ON-mode. -100 -50 0 50 100 Beta [deg] -20 -15 -10 -5 0 5 10 15 20 SRP accel. [nm/s**2] SRP coeff: TERM 0010 T20 for QSP -100 -50 0 50 100 Beta [deg] -120 -100 -80 -60 -40 -20 0 SRP accel. [nm/s**2] SRP coeff: TERM 0010 T30 for QSP Fig. 3: Simulated due to in system. SRP SP TERM 0 50 100 150 200 250 300 350 400 du [deg] -60 -55 -50 -45 -40 -35 -30 -25 -20 SRP T3 [nm/s**2] Simulated SRP acceleration, QBX 0 50 100 150 200 250 300 350 400 du [deg] -15 -10 -5 0 5 10 15 SRP T2 [nm/s**2] Simulated SRP acceleration, QBX 0 50 100 150 200 250 300 350 400 du [deg] -6 -4 -2 0 2 4 6 SRP T1 [nm/s**2] Simulated SRP acceleration, QBX Fig. 4: Simulated due to box in system. Colors SRP SC TERM represent following -angles: , , β green, dotted: -80° cyan: -30° red: 0°, , . blue: +30° green, solid:+80° Validation -1 of QZS - Simulated and estimated SRP coefficients have comparable characteristics (apart from singularities) and show little variations from day to day: - clear improvement of QZS-1 orbits and clocks: - agreement with external QZF orbit solution improves: Validation 2 of BDS - smallest deviation of SRP coefficients from assumed values observed for MEOs, shorter orbit arcs, and ECOM-TBM(P) - for IGSOs the periodic SRP coefficients are not well enough determined to represent the orbit over longer periods, which affects the remaining parameters: - consequently, the orbits are degraded as well in case the full ECOM-TB is used for long-arc POD of BDS2 IGSOs: Reference to products COM Prange, L.; Arnold, D.; Dach, R.; Schaer, S.; Sidorov, D.; Stebler, P.; Villiger, A.; Jäggi, A. (2018). CODE product series for the project IGS MGEX . Published by Astronomical Institute, University of Bern. URL CODE MGEX : http://www.aiub.unibe.ch/download/ _ ; DOI: 10.7892/boris.75882.2. Validation-Summary and Conclusions - is a suitable stand-alone SRP model QZS-1: ECOM-TB - : addition of pulses (=> ) or of an a BDS2 MEO ECOM-TBP priori box model is recommended - : periodic SRP coefficients cannot be estimated BDS2 IGSO for long-arc orbits with current network and orbit model (=> use or ECOM-TBM + an a priori box model) ECOM-TBMP Possible reasons for reduced performance of ECOM-TB for BDS2: - sampling problem for periodic SRP coefficients due to poor observation coverage over East Asia (affecting IGSOs more than globally observed MEOs; see Fig. 10) - open questions regarding BDS orbit model (meta data!) -160 -155 -150 -145 -140 -15 -10 -5 0 5 10 15 SRP acceleration [nm/s**2] Beta [deg] T30C1b Estimated I1 Estimated I2 Simulated -30 -25 -20 -15 -10 -5 0 -15 -10 -5 0 5 10 15 SRP acceleration [nm/s**2] Beta [deg] T20S3b Estimated I1 Estimated I2 Simulated -150 -100 -50 0 50 100 150 0 50 100 150 200 250 300 SLR residuals [cm] DOY 2015 YS ECOM2 ON ECOM-TB 0 0.5 1 1.5 2 2.5 3 3.5 4 0 50 100 150 200 250 300 RMS of linear clock fit [ns] DOY 2015 YS ECOM2 ON ECOM-TB Fig. 5: vs. coefficients of ECOM-TB refer- Simulated estimated ring to different ON-periods and in 2015. I1 I2 Fig. 6: Orbit and CLK-valid. of 2015 or . ECOM2 ECOM-TB -180 -160 -140 -120 -100 -80 -60 -40 -20 0 -4 -3 -2 -1 0 1 2 3 4 SRP acceleration [nm/s**2] Beta [deg] T30C1b IGSO 1-day ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP -180 -160 -140 -120 -100 -80 -60 -40 -20 0 -4 -3 -2 -1 0 1 2 3 4 SRP acceleration [nm/s**2] Beta [deg] T30C1b IGSO 3-day ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP Fig. 8: SRP coefficient T30C1b of different ECOM-TB versions for BDS2 MEOs (top) and IGSOs (bottom) with 1- (left) vs. 3- day arcs -500 -400 -300 -200 -100 0 100 200 300 -10 -5 0 5 10 SLR residuals [cm] Beta [deg] BDS2 IGSO 1-day ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP -500 -400 -300 -200 -100 0 100 200 300 -10 -5 0 5 10 SLR residuals [cm] Beta [deg] BDS2 IGSO 3-day ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP Fig. 9: SLR- validation of BDS2 MEOs (top) and IGSOs (bottom) with 1- (left) vs. 3- day arcs (right). Fig. 10: Formal radial orbit error of QZS-1, BDS2 MEOs, and BDS2 IGSOs in early 2015 (YS and ECOM2 applied to all). Vali.-Method SLR, IQR [cm] CLK-fit, median [ns] OMC, median [cm] ORB-fit, med. [cm] Sat.-System BI BM Q1 BI BM Q1 BI BM Q1 BI BM Q1 ECOM2 20.5 21.0 62.0 1.72 1.61 1.43 55.9 29.2 42.4 23.0 10.1 14.1 ECOM-TB - - 15.2 - - 0.35 - - 14.2 - - 5.6 ECOM-TBP - 12.2 - - 0.69 - - 9.8 - - 6.8 - ECOM-TBMP 12.2 - - 0.72 - - 27.1 - - 44.0 - - Fig. 7: QZS-1 orbit comparison betw. COM and QZF ACs (screenshot taken from ) http://mgex.igs.org/analysis ECOM2 used for COM orbit ECOM-TB used for COM orbit Tab. 1: Results of orbit validation with SLR residuals (SLR), RMS of linear sat. clock fit (CLK), orbit misclosures (OMC), and 3-day long-arc fit ( )ORB-fit BI for BDS2 IGSO ( ), BDS2 MEO (BM), and QZS-1 (Q1) satellites with different SRP models during ON-periods in 2014 and 2015. -180 -160 -140 -120 -100 -80 -60 -40 -20 0 -4 -3 -2 -1 0 1 2 3 4 SRP acceleration [nm/s**2] Beta [deg] T30C1b MEO 1-day ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP -180 -160 -140 -120 -100 -80 -60 -40 -20 0 -4 -3 -2 -1 0 1 2 3 4 SRP acceleration [nm/s**2] Beta [deg] T30C1b MEO 3-day ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP -100 -50 0 50 100 -10 -5 0 5 10 SLR residuals [cm] Beta [deg] PRN C11 (MEO) 1-day ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP -100 -50 0 50 100 -10 -5 0 5 10 SLR residuals [cm] Beta [deg] PRN C11 (MEO) 3-day ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP Du Du b E3 = D E2 E1 E2 E2 E2 E1 E1 E1 ECOM C E O M ( mpirical rbit odel) frame: ODE E3 = D E3 = D E3 = D 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 39 40 41 42 43 44 45 Formal error radial [cm] Day of year 2015 BDS2 IGSO BDS2 MEO QZS-1

Transcript of An Empirical ModelSRP IGSWS2018-PS06 for the Orbit Normal … · 2019-01-02 · SRP accel....

Page 1: An Empirical ModelSRP IGSWS2018-PS06 for the Orbit Normal … · 2019-01-02 · SRP accel. [nm/s**2] SRP coeff: TERM 0010 T30 for QSP Fig. 3: Simulated due to in system.SRP SP TERM

Definition of -TBMECOM

- version with just 2 parameters coveringSRP SRP due to SP:

- can be ignored for short-arcs =>β (T20, T30)ECOM TM-

- SRP due to sat.-body may be absorbed by stochastic orbitparameters ( ) or by an a priori box modelECOM-TBMP

Definition -TBof ECOM

- SRPacceleration during ON described in TERM system as ...

- ... by 9 parameters:SRP

- β-dependency can be ignored for short-arcs => ECOM-T

- stochastic orbit parameters (i.e., pulses or accelerations) canbe added optionally => ECOM TBP-

Introduction

The Center for Orbit Determination in Europe ( ) is contributing toCODE

the Multi- Extension ( ) since its start in 2012 with anIGS GNSS MGEX

orbit and clock solution. `s ( ) product includes theCODE MGEX COM

satellite systems , , Galileo, BeiDou2 ( 2), andGPS GLONASS BDSQZSS. GEO satellites are not included, so far.

The ECOM2 solar radiation pressure model, used for all satellites( )SRP

in the COM solution, has been designed for yaw-steering ( ) attitude.YS

Consequently, the orbit quality was degraded for BDS2 and QZS-1spacecrafts ( ) at times when operating under orbit-normal ( )SC ON

attitude, i.e., during or close to eclipse seasons.

Here we introduce a family of empirical models taylored for the -SRP ONmode, which can either be used on top of an a priori model or as aSRPstand-alone model.

International ServiceGNSSWorkshop 201829 Oct. - 02 Nov. 18 Wuhan China20 , ,

L .. Prange , R. Dach , G Beutler , A. Villiger ,1 1 1 1

S. Schaer , D. Arnold , A. Jäggi2 1 1

1Astronomical Institute, University of Bern, Switzerland

2Federal Office of Topography swisstopo, Wabern, Switzerland

An Empirical ModelSRPfor the Orbit Normal Mode

Poster compiled by ,L. Prange October 2018Astronomical Institute, University of Bern, Switzerland

@aiub.unibe.chlars.prange

IGSWS2018-PS06

Contact address

Lars PrangeAstronomical Institute, University of BernSidlerstrasse 53012 Bern (Switzerland)[email protected]

Posters and other publications from theSatellite Geodesy Group:AIUB

http://www.bernese.unibe.ch/publist

Attitude Modes

Most SCs are oriented with attitude. SomeGNSS YSBDS QZS ON2 satellites and -1 switch to attitude forsmall elevation angles of the Sun w.r.t. the orbital plane.βAll spacecrafts maintain the attitudeGEO ONpermanently.

�u�u

Z

Z

Z

Y

Y

Y

Y

X

X

Spacecraft-fixed reference frame( aw- teering attitude):Y S

X

X

SPN = D

Fig. 1: Satellite-fixed ref. frames under - and -mode.YS ON

ECOM SRP Model Frames

During -mode the co-rotating decompositionYS ECOM

is practical ( due to solar panels absorbed by oneSRPcoeff.; Y=0). For -mode non-rotating frames are betterONsuited (e.g., frames fixed to local orbit or orbital plane). Weuse the Terminator System Decomposition ( ).TERM

�u�u

Z

Z

Z

X

X

Spacecraft-fixed reference frame( rbit- ormal attitude):O N

X

X

Y = W

SPN

D

Y = W

Y = W

Y = W

�u�u

= D

T3 = D

T3 = D

T3 = D

T2

Terminator

line

T1

T1

T1

T2

T2

T2

TERM T( erminator) frame:

T1

Fig. 2: model frame definition.SRP

SRP YS ONin - and -modes

Features of the attitude mode are:YS- solar panel ( ) plane is always parallel to the terminator plane andSP

normal to the vector Sun => satellite ( )D

- C`sY-sides are never illuminated (Y=0, apart fromY-bias)S- ody (+Z, -Z, +X panels) causes an signal, which is periodicSC b SRP

w.r.t. the argument of latitude difference betw. SC and Sun ( )Δu

- rapid noon/midnight turns for small elevation angles ( ) of the Sun w.r.t.βthe orbital plane

Features of the attitude mode are:ON- no noon and midnight turns- SP-normal ( ) deviates from the vector D by -angleSPN the β- power generation is reduced compared to the -modeYS- due to SPcan be absorbed by 2 parameters, which are constantSRP SRP

w.r.t. u, but not w.r.t.Δ β- all panels of body can be illuminated - causing periodic signalsSP SRP

w.r.t. u andΔ β

SRP ONSimulation for

Simulations based on released meta data of -1 have beenQZSperformed separately for SP and SC body. Simulated SRPacceleration has been projected into the terminator referenceframe (TERM, Fig. 2). Coefficients of significant size havebeen selected for ( u) and ( u, ) -ECOM-T ECOM-TBΔ Δ βempirical SRP models for the ON-mode.

-100 -50 0 50 100Beta [deg]

-20

-15

-10

-5

0

5

10

15

20

SRP accel. [nm/s**2]

SRP coeff: TERM 0010 T20 for QSP

-100 -50 0 50 100Beta [deg]

-120

-100

-80

-60

-40

-20

0

SRP accel. [nm/s**2]

SRP coeff: TERM 0010 T30 for QSP

Fig. 3: Simulated due to in system.SRP SP TERM

0 50 100 150 200 250 300 350 400

du [deg]

-60

-55

-50

-45

-40

-35

-30

-25

-20

SR

P T

3 [n

m/s

**2]

Simulated SRP acceleration, QBX

0 50 100 150 200 250 300 350 400

du [deg]

-15

-10

-5

0

5

10

15

SR

P T

2 [n

m/s

**2]

Simulated SRP acceleration, QBX

0 50 100 150 200 250 300 350 400

du [deg]

-6

-4

-2

0

2

4

6

SR

P T

1 [n

m/s

**2]

Simulated SRP acceleration, QBX

Fig. 4: Simulated due to box in system. ColorsSRP SC TERM

represent following -angles: , ,β green, dotted: -80° cyan: -30° red:0°, , .blue: +30° green, solid:+80°

Validation -1of QZS

- Simulated and estimated SRPcoefficients have comparablecharacteristics (apart from singularities) and show littlevariations from day to day:

- clear improvement of QZS-1 orbits and clocks:

- agreement with external QZF orbit solution improves:

Validation 2of BDS

- smallest deviation of SRPcoefficients from assumed valuesobserved for MEOs, shorter orbit arcs, and ECOM-TBM(P)

- for IGSOs the periodic SRPcoefficients are not well enoughdetermined to represent the orbit over longer periods, whichaffects the remaining parameters:

- consequently, the orbits are degraded as well in case the fullECOM-TB is used for long-arc POD of BDS2 IGSOs:

Reference to productsCOM

Prange, L.; Arnold, D.; Dach, R.; Schaer, S.; Sidorov, D.;Stebler, P.; Villiger, A.; Jäggi, A. (2018). CODE productseries for the projectIGS MGEX . Published byAstronomical Institute, University of Bern.URL CODE MGEX: http://www.aiub.unibe.ch/download/ _ ;DOI: 10.7892/boris.75882.2.

Validation-Summary and Conclusions

- is a suitable stand-alone SRPmodelQZS-1: ECOM-TB

- : addition of pulses (=> ) or of an aBDS2 MEO ECOM-TBP

priori box model is recommended- : periodic SRPcoefficients cannot be estimatedBDS2 IGSO

for long-arc orbits with current network and orbit model (=>use or ECOM-TBM + an a priori box model)ECOM-TBMP

Possible reasons for reduced performance of ECOM-TB forBDS2:

- sampling problem for periodic SRPcoefficients due topoor observation coverage over EastAsia (affecting IGSOsmore than globally observed MEOs; see Fig. 10)

- open questions regarding BDS orbit model (meta data!)

-160

-155

-150

-145

-140

-15 -10 -5 0 5 10 15

SRP

acce

lera

tion

[nm

/s**

2]

Beta [deg]

T30C1b

Estimated I1Estimated I2Simulated

-30

-25

-20

-15

-10

-5

0

-15 -10 -5 0 5 10 15

SRP acceleration [nm/s**2]

Beta [deg]

T20S3bEstimated I1Estimated I2Simulated

-150

-100

-50

0

50

100

150

0 50 100 150 200 250 300

SLR residuals [cm]

DOY 2015

YS ECOM2 ON ECOM-TB

0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300

RMS of linear clock fit [ns]

DOY 2015

YS ECOM2 ON ECOM-TB

Fig. 5: vs. coefficients of ECOM-TB refer-Simulated estimatedring to different ON-periods and in 2015.I1 I2

Fig. 6: Orbit and CLK-valid. of 2015 or .ECOM2 ECOM-TB

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

-4 -3 -2 -1 0 1 2 3 4

SRP

acce

lera

tion

[nm

/s**

2]

Beta [deg]

T30C1b IGSO 1-day

ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

-4 -3 -2 -1 0 1 2 3 4

SRP

acce

lera

tion

[nm

/s**

2]

Beta [deg]

T30C1b IGSO 3-day

ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP

Fig. 8: SRPcoefficientT30C1b ofdifferentECOM-TBversions forBDS2 MEOs(top) andIGSOs(bottom) with1- (left) vs. 3-day arcs

-500

-400

-300

-200

-100

0

100

200

300

-10 -5 0 5 10

SLR

resi

dual

s [c

m]

Beta [deg]

BDS2 IGSO 1-day

ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP

-500

-400

-300

-200

-100

0

100

200

300

-10 -5 0 5 10

SLR

resi

dual

s [c

m]

Beta [deg]

BDS2 IGSO 3-day

ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP

Fig. 9: SLR-validation ofBDS2 MEOs(top) andIGSOs(bottom) with1- (left) vs. 3-day arcs(right).

Fig. 10: Formal radial orbiterror of QZS-1, BDS2 MEOs,and BDS2 IGSOs in early2015 (YS and ECOM2applied to all).

Vali.-Method SLR, IQR [cm] CLK-fit, median [ns] OMC, median [cm] ORB-fit, med. [cm]

Sat.-System BI BM Q1 BI BM Q1 BI BM Q1 BI BM Q1

ECOM2 20.5 21.0 62.0 1.72 1.61 1.43 55.9 29.2 42.4 23.0 10.1 14.1

ECOM-TB - - 15.2 - - 0.35 - - 14.2 - - 5.6

ECOM-TBP - 12.2 - - 0.69 - - 9.8 - - 6.8 -

ECOM-TBMP 12.2 - - 0.72 - - 27.1 - - 44.0 - -

Fig. 7: QZS-1 orbit comparison betw. COM and QZF ACs(screenshot taken from )http://mgex.igs.org/analysis

ECOM2 used for COM orbitECOM-TBused forCOM orbit

Tab. 1: Results of orbit validation with SLR residuals (SLR), RMS of linear sat. clock fit (CLK), orbit misclosures (OMC), and 3-day long-arc fit ( )ORB-fit BI for BDS2 IGSO ( ), BDS2 MEO (BM), and QZS-1 (Q1) satellites with different SRP models during

ON-periods in 2014 and 2015.-180

-160

-140

-120

-100

-80

-60

-40

-20

0

-4 -3 -2 -1 0 1 2 3 4

SRP

acce

lera

tion

[nm

/s**

2]

Beta [deg]

T30C1b MEO 1-day

ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

-4 -3 -2 -1 0 1 2 3 4

SRP

acce

lera

tion

[nm

/s**

2]

Beta [deg]

T30C1b MEO 3-day

ECOM-TB ECOM-TBP ECOM-TBM ECOM-TBMP

-100

-50

0

50

100

-10 -5 0 5 10

SLR

resi

dual

s [c

m]

Beta [deg]

PRN C11 (MEO) 1-day

ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP

-100

-50

0

50

100

-10 -5 0 5 10

SLR

resi

dual

s [c

m]

Beta [deg]

PRN C11 (MEO) 3-day

ECOM2 ECOM-TB ECOM-TBP ECOM-TBMP

�u�u

E3 = D

E2

E1

E2E2

E2

E1

E1

E1

ECOM CE O M( mpirical rbit odel) frame:ODE

E3 = D

E3 = D

E3 = D

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

39 40 41 42 43 44 45

Form

al e

rror

rad

ial

[cm]

Day of year 2015

BDS2 IGSO BDS2 MEOQZS-1