UTXAustin

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11/19/01 UTexas Austin Semin 1

“Global” Global PositioningSystem Measurements

Prof. Thomas HerringDepartment of Earth, Atmosphere and

Planetary Sciences

http://www-gpsg.mit.edu/~tah

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Overview

• Review of the development of the GPS

system and basics of its use and operation

• Selected regional applications

• Character of global measurements

• Origin of systematic effects in global results

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GPS Original Design

• Started development in the late 1960s as

NAVY/USAF project to replace Doppler

positioning system• Aim: Real-time positioning to < 10 meters,

capable of being used on fast moving

vehicles.• Limit civilian (“non-authorized”) users to

100 meter positioning.

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GPS Design

• Innovations:

– Use multiple satellites (originally 21, now ~28)

– All satellites transmit at same frequency– Signals encoded with unique “bi-phase, quadrature

code” generated by pseudo-random sequence

(designated by PRN, PR number): Spread-spectrum

transmission.– Dual frequency band transmission:

• L1 ~1.575 GHz, L2 ~1.227 GHz

• Corresponding wavelengths are 190 mm and 244 mm

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Latest Block IIR satellite

(1,100 kg)° Transmission array is

made up of 12 helical

antenna in two rings of43.8 cm (8 antennas) and

16,2 cm (4 antennas) radii

° Total diameter is 87 cm

° Solar panels lead to

large solar radiation

pressure effects.

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Measurements

• Measurements:– Time difference between signal transmission from

satellite and its arrival at ground station (called“pseudo-range”, precise to 0.1–10 m)

– Carrier phase difference between transmitter andreceiver (precise to a few millimeters) but initial valuesunknown (ie., measures change in range to satellites).

– In some case, the integer values of the initial phaseambiguities can be determined (bias fixing)

• All measurements relative to “clocks” in groundreceiver and satellites (potentially posesproblems).

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Measurement usage

• “Spread-spectrum” transmission: Multiple

satellites can be measured at same time.

• Since measurements can be made at same

time, ground receiver clock error can be

determined (along with position).

• Signal

V (t , x)=V osin[2π ( ft − k. x)+πC(t )]

C(t ) is code of zeros and ones (bi

Varies discretely at 1.023 or 10.

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Measurements

• Since the C(t) code changes the sign of the

signal, satellite can be only be detected if the

code is known (PRN code)• Multiple satellites can be separated by

“correlating” with different codes (only the

correct code will produce a signal)• The time delay of the code is the pseudo-

range measurement.

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Position

Determination(perfect

clocks).

• Three satellites

are needed for 3-D

position with

perfect clocks.

• Two satellites

are OK if height is

known)

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Positiondetermination:

with clock

errors: 2-D case• Receiver clock is

fast in this case, so

all pseudo-ranges are

short

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Positioning

• For pseudo-range to be used for positioningneed:

– Knowledge of errors in satellite clocks

– Knowledge of positions of satellites

• This information is transmitted by satellite

in “broadcast ephemeris”

• “Differential” positioning (DGPS)eliminates need for accurate satellite clock

knowledge.

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GPS Security systems

• Selective availability (SA) is no longer active butprior to 2000 “denied” civilian accuracy better

than 100 m• Antispoofing (AS) active since 1992, addsadditional encryption to P-code on L1 and L2.

• Makes civilian GPS receivers more expensive and

more sensitive to radio interference• Impact of AS and SA small on results presented

here.

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Satellite constellation

• Since multiple satellites need to be seen at

same time (four or more):

– Many satellites (original 21 but now 28)

– High altitude so that large portion of Earth can

be seen (20,000 km altitude —MEO)

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Current constellation

• Relative sizes

correct (inertial

space view)

• “Fuzzy” linesnot due to orbit

perturbations,

but due to

satellites beingin 6-planes at

55o inclination.

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Global GPS analysis• GPS phase measurements at L1 and L2 from a global

distribution of station used

• Analysis here is “un-constrained”

– All site positions estimated– Atmospheric delay parameters estimated

– “Real” bias parameters for each satellite global, integervalues for regional site combinations (

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Global GPS analysis

• Data used between 1992-2001

• Full analysis has ~600 stations (analysis

here restricted to ~100 sites that have morethan 5 years of data

• Large density of sites (~300) in California

• Total data set has > 2 billion phasemeasurements

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GPS Antennas (for precise positioning)

• Rings are

called

choke-rings

(used to

suppressmulti-path)

Nearly all antennas are patch antennas (conductingpatch mounted in insulating ceramic).

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Global IGS Network (~150 stations)

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Specific sites analyzed

• Total of 100 sites analyzed of which 50 were used

to realize coordinate system

• Since analysis has little constraint, it is:– Free to rotate

– Possibly free to translate (explicit estimation)

– Possibly free to change scale (explicit estimation)

• Latter too effects should not be present but these

we will explore here.

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Network used in analysis

Black: Frame sites; Red other sites

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Results from analysis

• Examples of time series for some sites

– “Common Mode” error, example of regional

frame definition

• Satellite phase center positions

• Scale and Center of Mass (CoM) variations

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Example of motions measured in

Pacific/Asia region• Fastest motions are

>100 mm/yr

• Note convergencenear Japan

More at http://www-gpsg.mit.edu/~fresh/index2.html

http://bowie.mit.edu/~fresh/index2.htmlhttp://bowie.mit.edu/~fresh/index2.html

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11/19/01 UTexas Austin Semin 23Ψεαρ

Αϖεραγε ΡΜΣ 5 µµ-40

-20

0

20

40

1994 1995 1996 1997 1998 1999 2000 2001 2002

∆ΧΑΤ1 Εαστ (µµ) −40.1 µµ/ψρ

∆ΧΗΙΛ Εαστ (µµ) −36.1 µµ/ψρ

∆ΗΟΛΧ Εαστ (µµ) −31.5 µµ/ψρ

∆ϑΠΛ Εαστ (µµ) −36.7 µµ/ψρ

∆ΥΣΧ1 Εαστ (µµ) −38.3 µµ/ψρ

California East residuals (trends removed)

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11/19/01 UTexas Austin Semin 24Ψεαρ

-30

-20

-10

0

10

20

30

1994 1995 1996 1997 1998 1999 2000 2001 2002

∆ΧΑΤ1 Εαστ (µµ)

∆ΧΗΙΛ Εαστ (µµ)

∆ΗΟΛΧ Εαστ (µµ)

∆ϑΠΛ Εαστ (µµ)

∆ΥΣΧ1 Εαστ (µµ)

East position residuals (California)

E l f “ i l” f d fi i i

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Example from “regional” frame definition

Ψεαρ

Ηεχτορ Μινε Εαρτηθυακε

-10

-5

0

5

10

1995 1996 1997 1998 1999 2000 2001

∆ΧΑΤ1 Ρεγ (µµ) ΡΜΣ 0.9 µµ

∆ϑΠΛΜ Ρεγ (µµ) ΡΜΣ 1.4 µµ

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“Desert” California site

Year

RMS

0.7 mm

0.6 mm

2.9 mm

-30

-25

-20

-15

-10

-5

0

5

2000 2000.2 2000.4 2000.6 2000.8 2001

BULL North (mm)BULL East (mm)BULL Height (mm)

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Origin of “common” mode errors

• Unknown at the moment, but clearly scaleswith distance (172 of 500 sites in

S.California have sub-mm daily horizontalscatter, 2-3 mm vertical)

• Possible effects from satellite transmissionsystem.

• Example of estimating corrections to phasecenter position (wrt CoM) of satellites

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Phase center offsets

a

δρ = dh cos γ ; sin γ = (R/a) sin ψ ; (R/a) = 0.24

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Elevation angle dependence

Ελεϖατιον ανγλε (δεγ)

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 60 80

δρ − 1

0.03 Ηειγητ ερρορ

Full estimation effects

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Full estimation effects

TextEnd

0

5

10

15

20 6065

7075

8085 90

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Max ElevMin Elev

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Effects of phase center position

changes• A unit change in the radial phase center

position will change the range to the

satellite by a constant plus up to 0.03 units.• For 1 meter change; range change about 5

parts-per-billion

• If different models of satellites havedifference phase center positions, scalecould change with time.

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Block IIR

-2.0 -1.5 -1.0 -0.5 0.0 0.5

1

23

45

6

7

8

910

13

1415

16

17

18

1921

22

23

2425

26

27

2930

31

GPS Satellite Antenna Phase Center offsets

X Offset (m)

Y Offset (m)

Z Offset (m)

Offset (m)-2.0 -1.5 -1.0 -0.5 0.0 0.5

1

23

45

6

7

8

910

13

1415

16

17

18

1921

22

23

2425

26

27

2930

31

GPS Satellite Phase Center Adjustments

Offset (m)

Total phase center position and adjustment to specified values

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Scale variations with time

Ψεαρ

Σχαλε ρατε οφ χηανγε −0.25 ππβ/ψρ

Γλοβαλ Ηειγητσ −1.6 µµ/ψρ

-10

-5

0

5

10

1992 1994 1996 1998 2000 2002

∆σχαλε (ππβ)

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Center of mass variations as well

Ψεαρ

Μεαν οφφσετ −120 µµ

-300

-200

-100

0

100

200

300

1994 1995 1996 1997 1998 1999 2000 2001 2002

∆Ζ (µµ) Σχαλε εστιµατεδδΖ (µµ) Σχαλεδ νοτ εστιµατεδ

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Conclusion• Regional GPS (e.g., California) yields sub-

millimeter results for “good” stations• Globally RMS increase to 2-3 mm for reasons that

are not clear

• Secular scale change -1.6 mm/yr in height

(Reference sites have 0.8 mm/yr average)• In GAMIT: -120 mm Z-offset in CoM for unknown

reasons

• Differences between generations of satellites might

explain some of these results.• Systematic nature suggests we might be able to

resolve

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Relativistic Corrections terms

• Propagation path curvature due to Earth’spotential (a few centimeters)

• Clock effects due to changing potential

• For e=0.02 effect is 47 ns (14 m)

"τ=2GM

c3

ln R

r +R

s+ρ

Rr +Rs−ρ

$%

'(

"τ=− GM

c2 e asinE

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Relativistic Effects

Time (hrs)

-50

-25

0

25

50

0 4 8 12 16 20 24

PRN 03 Detrended; e=0.02

Clock - trend (ns)GR Effect (ns)

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Tectonic Deformation Results

• “Fixed GPS” stations operate continuously

and by determining their positions each day

we can monitor their motions relative to aglobal coordinate system

• Temporary GPS sites can be deployed on

well defined marks in the Earth and themotions of these sites can be monitored

(campaign GPS)

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Motion after Earthquakes. Example from

Hector Mine, CA

Year

Hector Mine Earthquake(166 mm removed)

LDES Site Mojave Desert

-10

0

10

20

30

40

1999 1999.5 2000 2000.5 2001

Continued motion tells us about material characteristics

and how stress is re-distributed after earthquake

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Relativistic effects

• General relativity affects GPS in three ways– Equations of motions of satellite

– Rates at which clock run– Signal propagation

• In our GPS analysis we account for the

second two items• Orbits only integrated for 1-3 days andequation of motion term is considered small

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Clock effects

• GPS is controlled by 10.23 MHz oscillators

• On the Earth’s surface these oscillators are set to

10.23x(1-4.4647x10-10

) MHz (39,000 ns/day ratedifference)

• This offset accounts for the change in potentialand average velocity once the satellite is launched.

• The first GPS satellites had a switch to turn thiseffect on. They were launched with “Newtonian”clocks

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Propagation and clock effects

• Our theoretical delay calculations are made

in an Earth centered, non-rotating frame

using a “light-time” iteration i.e., thesatellite position at transmit time is

differenced from ground station position at

receive time.• Two corrections are then applied to this

calculation

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Effects of Selective Availability

Time (hrs)

-200

0

200

400

600

800

0 4 8 12 16 20 24

PRN 03 (June 14)

Clock SA (ns) 1999Clock NoSA (ns) 2000

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Conclusions• GPS dual-use technology: Applications in civilian world

widespread– Geophysical studies (mm accuracy)

– Engineering positioning (

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