Esci 203, Earth Structure and Deformation

Introduction to the global positioning system (GPS)

John Townend

EQC Fellow in Seismic Studies

john.townend@vuw.ac.nz

Recent events

Preliminary GPS displacement data (version 0.1) provided by the ARIA

team at JPL and Caltech. All Original GEONET RINEX data provided to

Caltech by the Geospatial Information Authority (GSI) of Japan.

Overview

• What is GPS– A space-based Global Positioning System

• How does it work?– Trilateration using very accurate timing

measurements

• What are some of its limitations?

• How can earth scientists use it?– General positioning, deformation monitoring…

What is GPS?

• Space segment, Navstar– 24 satellites orbiting at an

altitude of ~20,000 km

• Control segment– 5 ground stations

• User segment– Users with GPS receivers

Global

Positioning

System

Campaign and permanent GPS

Campaign (temporary) GPS station

Pu`u O`o, Kilauea, Hawai`i

Continuous (permanent) GPS station

Gisborne, New Zealand

Figures courtesy of Peter Cervelli, HVO, and Land Information New Zealand

The satellite signal

• Each satellite transmits low-power (20–50 W) signals on various frequencies– Civilian receivers listen at 1575.42 MHz

• The receiver determines the signal travel time from the satellite– With four or more satellites, the receiver

can determine its latitude, longitude, altitude, and internal clock error

Pseudo-random codes

• The signal emitted by each satellite is unique and extremely complex (“pseudo-random”)

• The receiver generates the same signal, and compares it with what it receives from the satellite to determine the travel time

Receiver

signal

Satellite

signal

t

Extra steps

• What is the time? – Each satellite carries an atomic clock but the

receiver’s internal clock is much less accurate– So, the receiver uses an extra satellite signal to

estimate the difference in time between it’s onboard clock and the standardised satellite time

• And where are the satellites exactly?– The control stations measure each satellite’s

ephemeris very precisely; this data is broadcast to the satellites and included in the GPS signal

Trilateration

distance = travel time speed of light

Sat1

Sat3

Sat2

Sat4

The receiver determines the distance (“pseudo-range”) to 4+

satellites, and calculates its position; it’s like locating an

earthquake in reverse!

Sources of error

• Ionospheric/tropospheric delays

• Multi-pathing

• Receiver clock errors

• Ephemeris errors

• Constellation geometry and weather

• Intentional signal degradation:– “selective availability”, which limited accuracy to

~6–12 m but has now been switched off

Selective availability

Figure courtesy of Peter Cervelli, HVO

Geometric dilution of precision

High GDOP; low confidence Low GDOP; high confidence

Differential GPS (“dGPS”)G

PS sign

al

GPS signal

dGPS correctionsignal

Satellite

Reference station Mobile receiver

Reference stations broadcast corrections to the satellites’

signals; typical dGPS accuracy is ~1–5 m

A typical permanent GPS installation

Geodetic velocities

We commonly make use of the east and north components of

velocity, vE and vN

The overall velocity vector v has a magnitude (length), v2 = vE

2 + vN2,

and an azimuth = atan (vE/vN)

vE

vN v

Measuring velocities

The velocity in each direction

(east, north, up) is just the gradient of the position time

series

Measuring velocities

The velocity in each direction

(east, north, up) is just the gradient of the position time

series

e.g. vN = n/t

t

n

Relative motion (1)

vplane-air

vair-ground

vplane-ground = vplane-air + vair-ground

Relative motion (2)

vA-B

vB-ref

vA-ref = vA-B + vB-ref

meaning that

vA-B = vA-ref – vB-ref = vA-ref + (– vB-ref)

Relative motion (3)

Site A

Site B

vA

vB

vA

vB

–vB

vA-B

Summary

• Points to revise– How GPS basically works– Key factors affecting position estimates– Measuring site velocities from GPS data

and relative velocities between sites

• Extra material online– http://ww2.trimble.com/gps_tutorial

Reading material

• Van der Pluijm and Marshak– Section 14.9

• Fowler (2005)– Sections 2.1 and 2.2

• Mussett and Khan– Section 20.5

• If you need to brush up on vectors, try “Mathematics : a simple tool for geologists”, by Waltham; this is in the library