2009年度GCOE地球惑星計測スクール

GPS Global Positioning System

東京海洋大学 高須 知二

GPS Global Positioning System

Part 2

Rev.A 2009/8/22

Outline: Part 1

• GPS/GNSS Basics and Principles

– GPS/GNSS Summary

– GPS Signal and Receiver Architecture

– Basic Observation Models– Basic Observation Models

– Navigation Processing

– Error Sources

– DGPS and SBAS

• Exercise: using GT 0.6.4

2

Outline: Part 2

• Precise Positioning with GPS/GNSS

– Time and Coordinate Systems

– Precise Measurement Models

– Relative Positioning– Relative Positioning

– Precise Point Positioning (PPP)

– Applications

• Exercise: PPP with GT 0.6.4

3

Time and Coordinate

4

Time and Coordinate

Systems

Time Systems

• Time Systems

– TAI: International Atomic Time

– UTC: Coordinated Universal Time

– Local Time (JST, EDT, ...)– Local Time (JST, EDT, ...)

– UT0, UT1, UT2: Universal Time

– GMST: Greenwich Mean Sidereal Time

– GPS Time

– GLONASS Time

– ...

5

Time System Conversion

)( TAIUTCtt TAIUTC −+=

)1(1 UTCUTtt UTCUT −+=

TAI to UTC:

UTC to UT1:

UT1 to GMST:

UTC-TAI (s)

-25 1990/1/1- -30 1996/1/1-

-26 1991/1/1- -31 1997/7/1-

-27 1992/7/1- -32 1999/1/1-

-28 1993/7/1- -33 2006/1/1-

-29 1994/7/1- -34 2009/1/1-

6

)(

'102.6'093104.0'812866.864018454841.24110

10110

36210

UThUTUTh

uuuUTh

ttrGMSTGMST

TTTGMST

−+=

×−++= −UT1 to GMST:

21511 '109.5'109006.5507950027379093.1 uu TTr −− ×−×+=

36525/'' uu dT = : number of days elapsed since 2000 Jan 1, 12h UT1ud '

GPS Time to UTC:))(( 10 otGPSTLSGPSTUTC ttAAttt −++−= ∆

GPS Time to TAI:stt GPSTTAI 19+≈

Coordinate Systems

• ECEF: Earth-Centered Earth-Fixed

– ITRF

– WGS 84: US (GPS)

– PZ90: Russia (GLONASS), ...

zReference

Pole Earth

Center

• ECI: Earth-Centered Inertial

– ICRF: International Celestial

Reference Frame

• ECI-ECEF Connection

– Precession/Nutation Model

– ERP: Earth Rotation Parameters

x

y

Reference

meridian ECEF

7

ITRF

• International Terrestrial Reference Frame

– A "Realization" of ITRS Maintained by IERS

– GPS, VLBI, SLR, DORIS Site Position/Velocity List

– ITRF2005, ITRF2000, ITRF97, ITRF96, ...

http://itrf.ensg.ign.fr/ITRF_solutions/2005/ITRF2005.php 8

ITRS: International Terrestrial Reference System

IERS: International Earth Rotation Service

VLBI: Very Long Baseline Interferometry

SLR: Satellite Laser Ranging

DORIS: Doppler Orbit determination and Radiopositioning Integrated on Satellite

ECEF to ECI Transformation

IRMO

Z

Y

0E

90E

90W

180E

ECEF

(ITRF) IRPCEP

X

X

YZ

yP

-xP

IRP

CEP

Z

O

Z

Y

Ecliptic of date

γ'γ

X

True equator

of date

Mean equator

of date

γ'

γ εA

εA+∆ε

∆ϕ

CEPP

εA

Mean of

Date

ZPJ2000(2)

O

Y

IRM

CEP

IRP

Ecliptic of date

γ'X

True equator

of date

GST

True of

Date O

Y

γJ2000γ

90°+zA

90°−ζA

θA

P

PJ2000

Mean equator

of date

mean equator

at epoch

J2000.0

Ecliptic at epoch

J2000.0

Ecliptic of

date

εJ2000

X ECI

(ICRF)

ecefPYPXZAXZAXAZAYAZ

ecefzeci

xyGSTz

GST

rRRRRRRRRR

WrPRr

)()()()()()()()()(

)(

−+−−=

−=

ε∆εϕ∆εθζ

W

P

: Nutation

: Precession

: Polar Motion

9(1)

(1)

(2)

(3)

(2)(3)

ΩΩ

εψ∆

2sin000063".0sin00264".0

cos

++

+= AGMSTGST

ERP: Earth Rotation Parameters

Polar Motion:

Xp, Yp

Earth Rotation Angle:

UT1-UTC

10

IERS C04 Series (1962/1/1-2009/8/11)Xp (mas)

Yp(m

as)

UT

1-U

TC

(ms)

1960 1970 1980 1990 2000

3m

Ellipsoid and Datum

Tr zyx ),,(=r

h

Ellipsoid:

)1( 2ea −

GRS 80 WGS 84

a (m) 6378137 6378137

f1/298.257222

101

1/298.257223

563

GM

(m3/s2)

3986005.000

x 108

3986004.418

x 108

=b

z

r

'φφ

'φφ

: Geocentric Latitude

: Geodetic Latitude

a

)1( ea −

h : Ellipsoidal Height

(m3/s2) x 108 x 108

x,y plane

++

+

+

=

−=

−=

φλφλφ

φ

sin))1((

sincos)(

coscos)(

sin1

)2(

2

22

2

he

h

h

e

a

ffe

rrλ : Longitude

Lat/Lon/Height to ECEF:

11

Geoid

Ellipsoid

Geoidh

H

ε

: Geodetic Height

+

+= ∑∑

∞

= =2 0

)(1),',(

n

n

m

nmsnmnmcnm

n

YSYCr

a

r

GMrV λφ

Geopotential:

EGM96 Geoid Model

12

Spherical Harmonics

λφ

λφ

mPY

mPY

YY

nmnms

nmnmc

cnn

sin)'(sin

cos)'(sin

00

=

=

=

Legendre function:

Spherical harmonic functions:

>+

−+=+

=

−

−+−−=

−−=

=

===

−−

−−

−

)0()!(

)!)(12(2

)0(12

)()1()()12()(

)()1)(12()(

,0)(

)(,1)(,

,2,1

1,12/12

,1

1000

mmn

mnn

mn

mn

xPmnxxPnxP

xPxnxP

xP

xxPxPPP

nm

mnmnnm

nnnn

nn

nmnmnm

Legendre function:

13

Coordinates Transformation

ABz

y

x

RR

RR

RR

D

T

T

T

z

y

x

−

−

−

++

=

1

1

1

)1(

12

13

23

3

2

1

Helmert Transformation (A to B):

- T1, T2, T3 : Translation along coordinate axis

14

Coordinates T1

(mm)

T2

(mm)

T3

(mm)

D

(10-9)

R1

(mas)

R2

(mas)

R3

(mas)A B

ITRF2005 ITRF2000

0.1 -0.8 -5.8 0.40 0.00 0.00 0.00

-0.2/y 0.1/y -1.8/y 0.08/y 0.00/y 0.00/y 0.00/y

- T1, T2, T3 : Translation along coordinate axis

- D : Scale factor

- R1, R2, R3 : Rotation of coordinate axis (rad)

(Epoch 2000.0)

Precise Measurement

15

Precise Measurement

Models

Carrier-Phase

Received Carrier Signal:

Reference Carrier:

Carrier Beat Signal:

)( ss tφ

)( rr tφ

sφ

16

φ

φ

φ

φ

λεφφλλφ

εφφλλ

εφφ

εφφφ

++−+−+−=

++−+−+−=

+++−+−+−+=

++−=

)()()(

)()()(

))(())((

)()(

00,

00,

000,0

sr

sr

sr

sr

sr

sr

sr

sr

sr

sr

sssrrr

sr

ssrr

sr

dTdtcttc

dTdtc

ttc

tdTtftdttf

tt

Carrier Beat Signal:srφ

))(),(( 0000, tt ssrr φφφφ ==

Carrier-Phase Model

ΦελρλφΦ ++++−−+=≡ sr

sr

sr

sr

sr

sr

sr

sr dBTIdTdtc )(

sr

sr

sr B +−= 00, φφ

Carrier-Phase Measurement Model:

sr : Integer Ambiguity

: Carrier-Phase Bias (cycles)

0,rφ : Receiver Initial Phases0φ : Satellite Initial Phase

17

( )relpw

senur

Tdisp

spcvpcvr

sr

Tspcoecefsat

senur

Tpcor

sr

dd

ddd

++

−+++−= → ,,,, ededEed

pcvrd ,

spcvd

dispd

pwd

reld

: Satellite Antenna Phase Center Offset

: Satellite Antenna Phase Center Variation

: Site Displacement

: Phase Wind-up Effect

: Relativistic Effect

0φ : Satellite Initial Phase

pcor ,d

spcod

: Receiver Antenna Phase Center Offset

: Receiver Antenna Phase Center Variation

Precise Ephemeris

• Precise Satellite Orbit and Clock

– By Post-Processing or in Real-time

– Observation Data of Tracking Stations World-Wide

• Format:• Format:

– Orbit: NGS SP3

– Clock: NGS SP3 or RINEX Clock Extension

• Contents:

– Orbit: ECEF-Positions of Satellite Mass Center

– Clock: Clock-biases wrt Time Scale Aligned to GPS Time

18

IGS: International GNSS Service

CODE

ESOC

NRCan

SIO

Analysis Centers (ACs)CDDIS

IGN

SIO

KASI

Global Data CentersData (GPS/GLONASS

Raw, Ephemeris,...)

ESOC

GFZ

JPL

NOAA

SIO

USNO

...

ACC

MIT

Regional DCs

Tracking Network

...

Oper. DCs

GNAACs

Products

(Satellite Orbit/Clock, Station

Pos/Vel, ERP, Atmos,...)

RNAACs

19

IGS Products Final

(IGS)

Rapid

(IGR)

Ultra-Rapid (IGU)Broadcast

Observed Predicted

Accuracy

Orbit ~2.5cm ~2.5cm ~3cm ~5cm ~100cm

Clock~75ps RMS

~20ps STD

~75ps RMS

~25ps STD

~150ps

RMS

~50ps STD

~3ns RMS

~1.5ns STD

~5ns RMS

~2.5ns STD~50ps STD

Latency 12-18 days17-41

hours3-9 hours realtime realtime

Updatesevery

Thursday

at 17 UTC

daily

at 03, 09,

15, 21 UTC

at 03, 09,

15, 21 UTC-

Sample

Interval

Orbit 15min 15min 15min 15min daily

ClockSat: 30s

Stn: 5min5min 15min 15min daily

(2009/8, http://igscb.jpl.nasa.gov/)

20

Interpolation of Satellite Orbit

)())...()((

))...()((...)(

))...()((

))...()((

)())...()((

))...()(()(

))...()((

))...()(()(

112111

213

132313

121

2123212

1311

113121

132

+++++

+

+

+

+

+

−−−−−−

++−−−−−−

+

−−−−−−

+−−−−−−

=

ns

nnnn

ns

n

n

s

n

ns

n

ns

ttttttt

ttttttt

tttttt

tttttt

ttttttt

ttttttt

tttttt

ttttttt

rr

rrr

Lagrange Interpolation:

Interpolation Error of 15-min Sample Orbit

21

Degree of

Polynomial

Position RMS Error (cm) Velocity RMS Error (cm/s)

Radial Along-Trk Cross-Trk Radial Along-Trk Cross-Trk

n=5 72.10 73.84 57.48 0.253 0.260 0.202

n=6 7.31 6.89 5.75 0.032 0.031 0.025

n=7 0.63 0.63 0.50 0.017 0.019 0.014

n=8 0.08 0.11 0.08 0.017 0.018 0.013

n=9 0.05 0.11 0.05 0.017 0.018 0.013

n=10 0.05 0.10 0.06 0.017 0.018 0.013

n=11 0.05 0.12 0.06 0.017 0.018 0.013

Interpolation of Satellite Clock

12

2112 )()()()()(

tt

tdTtttdTtttdT

sss

−−+−

=

Linear Interpolation:

Satellite Clock Stability:

)( 21 ttt <≤

22

Ionospheric Delay

22222 /30.4012/1/1 fffffn e −=−≈−=

Ionospheric Group Delay Model:

)(/11

)1(4)1(21

1 22

2

2

42

2 bandLffX

YiZX

Y

iZX

YiZ

Xn

LTT

−−=−≈

+−−

±−−

−−

−=

e

e

m

ef

02

22

4 επ= : plasma frequency

: Appleton-Hartree Formula

2162s ∫

23

Electron Density (Ne):

IRI-2007 model: 2009/7/31 0:00 Tokyo (http://modelweb.gsfc.nasa.gov/models/iri.html)

2162 /1030.40/30.40 fTECdlfI esr ×=≈ ∫ TEC: Total Electron Content

Solar Cycle

International Sunspot Number (ISN): 1700-2009

by SIDC (Solar Influences Data Analysis Center) in Belglum (http://sidc.oma.be)

23222120

24

Solar Cycle Prediction: Cycle 24

by NOAA SWPC (Space Weather Prediction Center) (http://www.swpc.noaa.gov/SolarCycle)

23 24 24

LC: Linear Combination

LCCoefficients Wave

Length

(cm)

Ionos

Effect

wrt L1

Typical

Noise

(cm)a b c d

L1 L1 Carrier-Phase 1 0 0 0 19.0 1.0 0.3

L2 L2 Carrier-Phase 0 1 0 0 24.4 1.6 0.3

),( 2221112121 φλΦφλΦΦΦ ==+++= dPcPbaC

25

LC/L3 Iono-Free Phase 0 0 - 0.0 0.9

LG/L4 Geometry-Free Phase 1 -1 0 0 - 0.6 0.4

WL Wide-Lane Phase 0 0 86.2 1.3 1.7

NL Narrow-Lane Phase 0 0 10.7 1.3 1.7

MW Melbourne-Wübbena 86.2 0.0 21

MP1 L1-Multipath 1 0 - 0.0 30

MP2 L2-Multipath 0 1 - 0.0 30

1/λλW 2/λλW−

1/λλ 2/λλ

1/λλW 2/λλW− 1/λλ 2/λλ

1C 2C

12 2 −C 22C−

12C− 12 1 −C

)/1/1/(1),/1/1/(1),/(),/( 212122

21

222

22

21

211 λλλλλλ +=−=−−=−= WfffCfffC

Single Layer Model

),,(1030.40

'cos

11030.402

16

2

16

pppptVTECfz

TECf

I λφ××

≈×

=

Satellite

IPP: Ionospheric

Pierce Point

Ionospheric Delay Model:

26

Receiver

Ionosphere

Earth

Pierce Point

z

z'

Re

Hion

pppp

pp

ione

e

Azαλλ

Azαα

z'zαHR

zRz'

Elπ/z

φ

φφφ

sinsinarcsin

)coscossinsinarcsin(cos

,sin

arcsin

2

+=

+=

−=+

=

−=

IPP Position/Slant Factor:

Ionospheric TEC Grid

2009/7/31 0:00 2009/7/31 2:00 2009/7/31 4:00 2009/7/31 6:00

27

2009/7/31 8:00 2009/7/31 10:00 2009/7/31 12:00 2009/7/31 14:00

2009/7/31 16:00 2009/7/31 18:00 2009/7/31 20:00 2009/7/31 22:00

(IGS TEC Final, GPS Time)

Tropospheric Delay

H

pZHD

7108.22cos00266.01

0022768.0−×−−

=φ

Tropospheric Delay Model:

ZWDElmZHDElmT wh )()( +=

Zenith

Delay Slant

DelayElZWD

: Zenith Hydrostatic Delay (m)

: Zenith Wet Delay (m)

28

ElZWD : Zenith Wet Delay (m)

)(Elmh : Hydrostatic Mapping Function

)(Elmw : Wet Mapping Function

ZWD to PWV (Precipitable Water Vapor):

ZWD

T

k

m

mkkR

PWV

TT

md

vv

m

+−

×=

+=

312

5101

72.02.70

9644.28,0152.18

10754.3,98.71

,6.77,461

532

1

==

×==

==

dv

v

mm

kk

kR

Mapping Function

NMF, GMF, VMF1

cEl

bEl

aEl

c

b

a

Elm

++

+

++

+

=

)sin()sin(

)sin(

11

1

)( cba ,, : Mapping Function

Coefficients

29

NMF, GMF, VMF1

Hydrostatic

(2006/1/1-2007/12/31, TSKB, El=5°)

Wet

Tropospheric Gradient

Mapping Function with Horizontal Gradient:

( ))sin()cos()cot()()(),( 00 AzGAzGElElmElmAzElm E ++=

E GG , : North/East Gradient Parameters

PPP Solutions

with Gradient Estimation

PPP Solutions

without Gradient Estimation

302007/1/1-12/31, 24H-Static PPP, TSKB

with Gradient Estimation without Gradient Estimation

Antenna Phase Center 1

Choke-Ring Type

Antenna Phase Center Variation (PCV)

Antenna

Zero-Offset Type

Receiver Antenna

Phase Center:

31

L1

IGS Absolute Antenna Model (IGS05.PCV)

Antenna

Phase

Center

Antenna

Reference

Point (ARP)

z (U)

x (E)y (N)

Antenna Phase

Center Offset

L2

pcor ,d

pcvrd ,

Antenna Phase Center 2

Antenna Phase

Center

Mass Center of

Satellite

Antenna Phase

Center Offset

Nadir Anglesd

pcosd

Satellite Antenna

Phase Center:

32

Satellite Coordinate to ECEF:

zx

y

Sun

Satellite

xse

zsey

se

Nadir Angle

pcvsd

Earth

),,( zs

ys

xs

ecefsat eeeE =→

zs

ys

xs

szs

ss

zs

ys

ssun

ssun

ss

s

zs

eeeee

eee

rr

rre

r

re

×=×

×=

−

−=−=

,

,

Site Displacement

• Displacement of Ground-Fixed Receiver

– Solid Earth Tides

– Ocean Loading

– Pole Tide– Pole Tide

– Atmospheric Loading

• Tide Model

– IERS Conventions 1996/2003

– Ocean Loading: Schwiderski, GOT99.2/00.2, CSR 3.0/4.0,

FES99/2004, NAO99.b

– M2,S2,N2,K2,K1,O1,P1,Q1,M1,Mm,Ssa

33

Earth Tide

Earth Tide Model

34IERS Conventions 1996 + NAO99.b, 2007/1/1-1/31, TSKB

Phase Wind-up Effect

• Relative rotation between satellite and receiver antennas

effects to the measured phase of GPS RHCP (Right Hand

Circular Polarization) signal.

+

⋅×⋅= signd r

sss πλ 2/arccos))((

DDDDe

35

+

⋅×⋅= signd

rs

rr

ssrpw πλ 2/arccos))((

DD

DDDDe

sy

su

sx

su

su

sx

seeeeeeD ×−⋅−= )(

yrsrxr

sr

srxrr ,,, )( eeeeeeD ×+⋅−=

TTzr

Tyr

Txrenuecef ),,( ,,, eeeE =→

sre

: Dipole Vector of Satellite Antenna

: Dipole Vector of Receiver Antenna

: LOS Vector from Receiver to Satellite Antenna

: ECEF to ENU Transformation Matrix

: Integer Ambiguity

Relativistic Effects

• Satellite/Receiver:

– Frequency Shift by Earth Gravity (General Rel.)

– Frequency Shift by Sun/Moon Gravity (General Rel.)

– Second-Order Doppler-Shift by Motion (Special Rel.)

• Signal Propagation:

– Sagnac Correction (Rotating Coordinates)

– Shapiro Time Delay Effect

– Lense-Thirring Drag

36

2

2

cd

ss

rel

vr ⋅−=

Satellite Clock Bias/Rate Correction

+ Periodic Term:

Relative Positioning

37

Relative Positioning

DD: Double Difference

Φελρ

φφφφλΦ

++++−−+=

−−−≡

ijub

ijub

ijub

ijub

ijub

ijub

ijub

jb

ju

ib

iu

ijub

dBTIdTdtc )(

))()((

ijub

jb

jb

ju

ju

ib

ib

iu

iu

ijub

jub

iub

ijub

ijb

iju

ijub

B

dTdTdTdtdtdt

=+−++−−+−−+−=

≈−==−=

)()()()(

0,0

00,00,00,00, φφφφφφφφ

DD Carrier-Phase Model:

38

Receiver u Receiver b

Satellite i Satellite j

iuφ

juφ

ibφ

jbφ

ubbbuubbuuub 00,00,00,00,

0,0,0 ≈−=≈−=≈−= jub

iub

ijub

jub

iub

ijub

jub

iub

ijub dddTTTIII (Short Baseline)

ΦελρΦ ++= ijub

ijub

ijub

Baseline

Relative Positioning

−

+−

+−

+−

=

=

,,

,,

,,

,,,

00

)(

),...,,(

12

111

11313

121212

11312

λ

λρρ

λρρ

λρρ

ΦΦΦ

L

M

mm

k

m

k

m

kk

kk

k

m

kkkk

Tss

ssub

sstb

sstu

ssub

sstb

sstu

ssub

sstb

sstu

t

Tsstub

sstub

sstubt

e

xh

y

TTt

Tt

Tt n

),...,,(11

yyyy =

Tssub

ssub

ssub

Tu

m ),...,,,( 11312rx =Parameter Vector:

Measurement Vector:

Nonlinear-LSE:

39

=

−

−

−

=

222

222

222

,

,

,

422

242

224

00

00

00

1

13

12

ΦΦΦ

ΦΦΦ

ΦΦΦ

σσσ

σσσσσσ

λ

λ

λ

L

MOMM

L

L

L

MOMMM

L

L

k

m

k

k

k

k

t

Tsstu

Tsstu

Tsstu

t

R

e

e

e

H

Meas Model, Design Matrix:

( )( )TT

tT

tT

t

TTt

Tt

Tt

n

n

HHHH

xhxhxhxh

,...,,

)(,...,)(,)()(

21

21

=

=

( )ntttblkdiag RRRR ,...,,

21=

Meas Error Covariance:

))(()(ˆ 0111

0 xhyRHHRHxx −+= −−− TT

Solution (Static/Float):

br : Fixed Base-Station Position

Integer Ambiguity Resolution

• Many Proposals for AR

– Simple Integer Rounding

– Wide-Lane + Narrow-Lane

– Coordinate Domain Search– Coordinate Domain Search

– Ambiguity Domain Search

– Shrink Search Space with Constraints

• Examples of AR Algorithms

– AFM, FARA, LSAST, LAMBDA, ARCE, HB-L3, Modified

Cholesy Decomposition, Null Space, FAST, OMEGA, ...

40

ILS: Integer Least Square

( )

)()(minarg

,,),(

1

,

HxyQHxyx

vBbAavHxy

BAHbax

RbZa

−−=

++=+=

==

−

∈∈y

T

TTT

mn

(

Strategy:

(1) Conventional LSE

Problem:

41

)ˆ()ˆ(minarg1

aaQaaaZa

−−= −

∈a

T

n

(

(1) Conventional LSE

11)(,

ˆ

ˆˆ −− =

==

= HQH

QQ

QQQyQHQ

b

ax y

T

bba

abaxy

Tx

(2) Search Integer Vector with Minimum Squared Residuals

)ˆ(ˆ 1aaQQbb((

−−= −aba

(3) Improve solution

LAMBDA

• ILS Estimation with:

– Shrink Integer Search Space with "Decorrelation"

Teunissen, P.J.G. (1995)

The least-squares ambiguity decorrelation adjustment: a method for fast GPS

integer ambiguity estimation. Journal of Geodesy, Vol. 70, No. 1-2, pp. 65-82.

– Shrink Integer Search Space with "Decorrelation"

– Efficient Tree Search Strategy

– Similar to Closest Point Search with LLL Lattice Basis Reduction

Algorithm

42

)ˆ()ˆ(minarg1

aaQaaaZa

−−= −

∈a

T

n

(

zZa

zzQzzz

ZQZQaZz

Zz

((

(

T

zT

aT

zT

n

−

−

∈

=

−−=

==

)ˆ()ˆ(minarg

,ˆˆ

1

Performance of LAMBDA

10

15E

xecu

tio

n T

ime

(m

s)

: with decorrelation

: without decorrelation

43

5 10 15 20 25 30 35 400

5

N : Number of Integer Ambiguities

Exe

cuti

on

Tim

e (

ms)

(Pentium 4 3.2GHz, Intel C/C++ 8.0)

Effect of Baseline LengthBL=0.3 km BL=13.3 km

RMS Error:

E: 0.2cm

N: 0.6cm

U: 1.0cm

Fix Ratio:

99.9%

RMS Error:

E: 2.2cm

N: 2.4cm

U: 10.6cm

Fix Ratio:

94.2%

44

BL=32.2 km BL=60.9 km

RMS Error:

E: 10.0cm

N: 12.0cm

U: 30.2cm

Fix Ratio:

64.3%

RMS Error:

E: 14.0cm

N: 14.8cm

U: 26.7cm

Fix Ratio:

44.4%

: Fixed Solution : Float Solution)(24 hr Kinematic

RTK-GPS

• Technique with Relative Positioning

– Real-time Position of the Rover Antenna

– Transmit Reference Station Data to Rover via Data Link

– OTF (On-the-Fly) Integer Ambiguity Resolution

45

– OTF (On-the-Fly) Integer Ambiguity Resolution

– Typical Accuracy: 1 cm + 1ppm x BL RMS (Horizontal)

– Applications:

Land Survey, Construction Machine Control, Precision

Agriculture etc.

Reference

Station

Rover

Receiver

Data Link

NRTK: Network RTK

• Extension of RTK-GPS

– RTK-GPS with Single Receiver

– Use Networked Reference Stations

– Generate Correction Messages with Interpolation of– Generate Correction Messages with Interpolation of

Sparse Station Data

– Provide Correction Messages via Mobile-Phone Network

– VRS, FKP, MAC, RTCM 2.3, RTCM 3.1

– NTRIP: Networked Transport of RTCM via Internet Protocol

• Commercial Services

46

Precise Point

47

Precise Point

Positioning (PPP)

Precise Point Positioning (PPP)

• Typical Strategy

– ZD (Zero-Difference) Measurement Equations

– Precise Ephemeris: IGS or Others

– Ionosphere: Eliminated by Dual-Freq LC– Ionosphere: Eliminated by Dual-Freq LC

– Troposphere: Estimated ZTD/ZWD + Mapping Function

– Antenna Model, Earth-Tide, Phase Wind-Up,...

• Integer Ambiguity Resolution

– Float Estimation

– Some Research propose PPP-AR with Satellite H/W Bias

Estimation

48

Applications

49

Applications

Exercise 2

PPP with GT 0.6.4

50

PPP with GT 0.6.4