3.2.1.2015 effects of interoperability of coordinates-icg 10.ppt · 2015-11-17 · galileo...

Yang Y, Qin X, Zeng A

1. China National Administration of

GNSS and Applications (CNAGA)

2. State Key lab of Geo-information

Engineering

Effects of Interoperability of GNSS Coordinate

System

2

Introduction1

2

3

4

IF of diff gravitational cons on ephemeris

IF of diff rotation rate on ephemeris

Effects of diff cons on positioning

Contents

5 Conclusions

3

� Background

� Multi GNSSs using

together should

provide better PNT

performance than

relying solely on

one system if the

systems compatible

and interoperable

GPS (31) GLONASS (24)

BDS (35) Galileo (27)

User

1. Introduction

4

1. Introduction

� Background

� Interoperable open signals can

� improve the observed geometry

� increase reference fame stations

� increase time keeping clocks

� compensate systematic errors

� compensate random errors

The requirements are compatibility and

interoperability!

5

� GPS---WGS 84

� GLONASS---PZ-90

� BDS---CGCS 2000 or BDC 2000

� Different geometrical reference ellipsoids

� Different gravitational constants

� Different rotation velocity

� Different reference frame

� Different updating period

� The status of GNSS coordinate references

1. Introduction

6

Broadcast ephemeris

Ground control system

Orbit & its prediction

Fitting of orbit parameters

Reference ellipsoid constants, reference frame,

gravitational constant and earth’ rotation velocity

Tracking stations Monitoring stations

2. Effects of Grav Cons on ephemeris

7

Original gravitational

constant of GPS

GM =3.986005××××10-14 GM=3.986004418××××10-14

Since 1994, the

gravitational constant

of GPS

Reduces about 1.2m

orbit radial errorExisting receivers

use the original GM

� Change of GPS gravitational constant


OrbitsReceivers ?

8

Gravitational cons GM

（（（（m3/s2））））

Rotation rate

（（（（rad/s））））

GPS 3.986005××××10-14 7.2921150××××10-5

GLONASS 3.986004418××××10-14 7.2921150××××10-5

Galileo 3.986004415××××10-14 7.2921151467××××10-5

BDS 3.986004418××××10-14 7.2921150××××10-5

IERS 3.986004418××××10-14 7.2921150××××10-5

� Gravitational constant and earth rotation rate

of GNSS

⊕ω


9

∆GM)

0

x

y

ω

z

y

x

(t2GM

1r∆ k ⋅

−

⋅+

⋅⋅=⊕

&

&

&

v

oek ttt −= (time starting from reference epoch)

[ ]Tzyxr &&&&v = (satellite velocity vector)

� Effect of ∆GM on orbit

Effects of ∆GM

changes with

Observation time tk

Satellite position

Satellite velocity


10

Effect of GM on Orbit of GPS03

� Effect of ∆GM on orbit

614 105.821083.98600441-3.986005∆GM ×=×= )(

� ΔΔΔΔGM=GMGM=GMGM=GMGM=GM

GPSGPSGPSGPS

----GMGMGMGM

IERSIERSIERSIERS

Effect of GM on all GPS orbits


11

� Different GM will result

in orbit error to 2m

� The effects of ∆GM on

the satellite orbits are

different for different

epochs

� The effects of ∆GM on

different satellite orbits

are different

� Analysis of Effect ∆GM on orbit


12

3. Effects of rotation velocity on orbits

⊕⋅⋅

−= ∆ωt

0

x

y

r∆ k

v

� Effects of rotational velocity on orbit⊕∆ω

� GPS starts its broadcast ephemeris according to the second

of GPS week, thus the biggest effect of the rotation rate on

the orbit appears at the last day of the GPS week

Effects of rotation

rate changes

Observation time tk

Satellite position⊕∆ω

13

ωGalileo – ωIERS=

-12-5 101.467 107.292115 - 677.29211514∆ω ×=×=⊕

)0(

Effects of ∆ω on GPS03

� Effects of rotational rate on orbit⊕

∆ω

⊕∆ω

Effects of ∆ω on all GPS sats

3. Effects of rotation rate on ephemeris

14

� Effect analysis of on Effect analysis of on Effect analysis of on Effect analysis of on

orbitorbitorbitorbit

⊕∆ω

� If substitute Galileo’s rotational rate into GPS orbit

determination software , then will produce error

more than 10m on the GPS orbit

� It should be noted that Galileo system uses a different

earth rotation velocity from those of other GNSS, or

from IERS recommended value

⊕∆ω

3. Effects of rotation rate on ephemeris

15

Semi-major axis (m)))) FlattingFlattingFlattingFlatting

GPS 6378137.0 298.257223563

GLONASS 6378136.0 298.25784

Galileo 6378136.5 298.25769

BDS 6378137.0 298.257222101

IERS 6378137.0 298.2572221008827

� Ellipsoid geometrical constants of GNSS

(Cheng P et al 2009)

4. Effects of reference ellipsoid constants

16

� The semi-major axis of

GPS (WGS 84) and BDS

(CGCS 2000) ellipsoids are

the same, only the flatting is

different

� Different GNSS uses

different flatting of ellipsoid

� Effect of ellipsoid constants on GNSS positioning


� Difference of semi-major axis of the reference ellipsoid will

only affect the height and the latitude, not the longitude

17

⋅

−

−−−

−+

−

+

+

⋅

−+

+−

+

⋅

−+

+−

+

+−+

−+−

+

−+−

+

⋅

++−

++−

+−

=

df

da

f1

B)sinBsinBsineM(1B)sine(1

a

N00

f)H)(1(M

B)sinBcosBsineM(2

H)a(M

sinBcosBNe

m

BsinNeH)(N

0HM

sinBcosBNe

ε

ε

ε

0sLsinBcosBcoNenLsinBcosBsiNe

1tgBsinLHN

H)eN(1tgBcosL

HN

H)eN(1

0cosLHM

BsinNeH)(NsinL

HM

BsinNeH)(N

z

y

x

sinBconsBsinLcosBcosL

0H)cosB(N

cosL

H)cosB(N

sinLHM

cosB

HM

sinBsinL

HM

sinBcosL

dH

dL

dB

2222

222

22

2

z

y

x

22

22

2222

0

0

0

� Effects of

∆a, ∆f,

[x0, y0, z0],

(εx,εy,εz) as

well as the

scale m on

positions


18

� Latitude effects of diff ellipsoids


-100 -50 0 50 100

-0.00002

-0.00001

0.00000

0.00001

0.00002

Latitude(Degree)CGCS2000-0.002

-0.001

0.000

0.001

0.002GTRF -0.002

-0.001

0.000

0.001

0.002PZ90.11

-100 -50 0 50 100

-0.00002

-0.00001

0.00000

0.00001

0.00002

LatitudeCGCS2000-0.002

-0.001

0.000

0.001

0.002GTRF -0.002

-0.001

0.000

0.001

0.002PZ90.11

Effect btw GPS & BDS

-100 -50 0 50 100

-0.000010

-0.000005

0.000000

0.000005

0.000010

LatitudeCGCS2000-0.00010

-0.00005

0.00000

0.00005

0.00010GTRF-0.0004

-0.0002

0.0000

0.0002

0.0004PZ90.11

Effect btw GPS & GalEffect btw GPS & Glo

19

-100 -50 0 50 100

0.00000

0.00003

0.00006

0.00009

0.00012

Latitude(Degree)

CGCS2000-0.04

-0.03

-0.02

-0.01

0.00GTRF -0.05

-0.04

-0.03

-0.02

-0.01

0.00PZ90.11

-100 -50 0 50 100

0.00000

0.00004

0.00008

0.00012

Latitude

CGCS20000.46

0.47

0.48

0.49

0.50GTRF0.960

0.975

0.990

1.005PZ90.11

-100 -50 0 50 100

-0.000010

-0.000005

0.000000

0.000005

0.000010

Latitude

CGCS20000.4980

0.4985

0.4990

0.4995

0.5000GTRF 0.996

0.997

0.998

0.999

1.000PZ90.11

Effect btw GPS & BDS Effect btw GPS & GalEffect btw GPS & Glo

�Height effects of diff ellipsoids


20

� Effects of GPS & BDS ellipsoids on both of the

latitude and Height are about 10-6s (or 0.1mm) . It

may be neglected

� However, different a btw GPS (or BDS) and Galileo

(GRTF) as well as GLONASS (PZ90) will result in

error of 0.001s (or 3cm) and 0.0015s (or 4.5cm) in

latitude respectively

� Height effects arrives at 0.5m and 1m respectively

� Effect analysis of ellipsoid constants


21

5. Effects of diff reference frames

� Effects of reference frames

� Differences of coordinate frames are usually reflected

in satellite orbits

� If CGCS2000 is selected as positioning system, the

corrections of the linearized GPS observation

equations will contain the effects of reference frames

and systematic orbit errors

� If single differencing positioning method is employed,

only the remain errors of reference frames affects the

positioning results

22

Error of satellite orbit

Errors of baseline vector

rij

rj

s Ratio of Ranging btw stations and btw

satellite and stations

� Coordinate system errors will be reduced by

differentiating the observations of near stations


� Effects of reference frames

Influence function

Frame errors orbit errors positioning errors

23


<5cm

� Effects of coordinate system offsets on single differential positioning

Influences of single differentiation positioning by the

coordinate offsets are 1m, 5m, 10m, 20m respectively

0 10 20 30 40 50 60 70 80 90 1000

0.01

0.02

0.03

0.04

0.05

基基线线 (km)

差差差差单单

(m)

星星星基卫卫MEO H=20000km

1 m

5 m

10 m

20 m

0 10 20 30 40 50 60 70 80 90 1000

0.01

0.02

0.03

0.04

0.05

基基线线 (km)

差差

差差

单单

(m)

星星星基卫卫GEO/IGSO H=36000km

1 m

5 m

10 m

20 m

Meo satellites with H=20000km GEO/IGSO satellites with H=36000km

Baseline length (km) Baseline length (km)

Single diff ra

nge erro

r (m)

Single diffe

range erro

r (m)

24

1. As broadcast ephemeris is related to the gravitational

constant GM and the rotation velocity ωωωω of the earth,

they should be consistent to those of ephemeris

2. Original GM of GPS and present one are different,

the orbit error more than 1m will be introduced

(Receiver and broadcast ephemeris still use the

original one for consistency)

3. Different rotational velocity affects satellite orbits.

The biggest error will arrive at several ten meters

4. Broadcast ephemeris is not related to semi-axis a, thus

different a does not affect user positioning

5. Summary

25

5. If GNSS positioning results need to be transformed to

geodetic ones, the parameters of different ellipsoids

should be used for different countries

6. The different frames of GNSS will result in satellite

orbit errors with several cm or dm, then systematically

affect the single point positioning results

7. The interoperability parameters should be introduced

into functional models; or using differential positioning

to reduce the effects

8. BDS coordinates connected to CGCS2000 by GPS

observations, thus additional errors are included

5. Summary

26

9. Coordinates updating strategies of BDS and GPS are

different. GPS updates them to every June 30, which

reduces deformation effects

10.Multi GNSS receivers should be used for

tracking stations. The plate moving information

from the ITRF and IGS should be used for

generating the interoperability parameters

5. Summary

The idealized reference coordinate system of GNSS

should be Interchangeable!

27

Thank you!

3.2.1.2015 effects of interoperability of coordinates-icg 10.ppt · 2015-11-17 · galileo...

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