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12.540 Principles of the Global
Positioning System
Lecture 17
Prof. Thomas Herring
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– Basic operation of antenna
–
– Phase center models for GPS ground antennas
–
–
Summary
? Finish propagation medium with discussion of
signal characteristics around GPS antennas
Ray approximation to effects of multipath
Phase center models for GPS satellite antennas
Use of signal strength (SNR) to assess multipath
1?
?
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Basic antenna operation
directions.
=
1
c
J(x')
e
-x'
x - x'
d
3
x'
B A E =
i
k
B
? Receiving and transmitting antennas are
identical: Time just flows in opposite
? Antenna problems are solved knowing the
current distribution J(x’) in the antenna and
using a vector potential
A(x)
ik x
úúú
= — ¥ — ¥
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Basic Antenna theory
l
– The near (static zone) d<<r<<l
– d<<r~l
– The far radiation zone: d<<l<<r
? Basic problem with using these equations is
that the propagating EM field induces other
currents to flow in the antenna that must be
included in the integral.
? Generally three distance ranges are treated
with antennas for antenna size d <<
The intermediate (induction) zone
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?
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Simplest antenna
d/2
-d/2
q
n
f
I (z )e
- iwt
= I
0
(1-
2 z
d
)e
- iwt
dP
dW
=
I
0
32pc
(kd )
2
sin
2
q
x
y
z
radiated power
from the
antenna, with
current I
0
center fed into
antenna
? Short center-fed dipole
P is the
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Dipole antenna
? Notice that no power is transmitted in the direction of
the antenna; maximum power is perpendicular to the
antenna
? There is no f dependence to the power transmission.
? The received strength follows the same pattern; No
to it.
? The first civilian GPS antennas were of this form. But
how to mount the antenna?
gain along the antenna, maximum gain perpendicular
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Dipole antennas
horizontally
problem?
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Dipole over a ground plane
h
q
Ground
Plane
Additional
path
2h cosq
If the ground plane is
infinite, then antenna
acts like a point source,
in the ground plane
below the antenna.
Gain depends on h/l
In zenith h=l
maximum gain
? For GPS, you need to mount the dipole
? However, a simple dipole mounted this way
will see reflections from the ground just as well
as the direct signal from the satellite.
? This is called multipath (multiple paths that the
signal can travel to get to the antenna)
? How do you solve the ground reflection
? To solve reflection from ground problem: You
make your own, highly reflective ground.
/4 give
4?
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Polarization with dipole
90
o
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Other antenna styles
–
is good). Early T14100 antenna was of this design.
GPS II/III)
– Very common now.
Patch mounted close to ground plane embedded in
a dielectric.
–
inside dome) embedded in choke rings. Standard
global GPS tracking antenna.
? Since GPS signals are transmitted with right-
circular polarization, ideally an antenna should
receive RCP radiation
? This can be done with dipoles by having two
(horizontal) dipoles perpendicular to each
other and adding the output with the correct
phase shift (sets RCP or LCP)
? Macrometer (early MIT GPS receiver) antenna
worked this way. (Set height dipole was tricky
to get L1 and L2 tracking).
? Other styles of antenna commonly seen in
GPS applications:
Helical antenna (wire around styrofoam coffee cup
Some hand-held receivers use this style (Garmin
Microstrip patch antenna.
Dorne-Margollian element (4-patchs mounted
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GPS Antennas (for precise positioning)
called
choke-rings
(used to
suppress
multi-path)
Nearly all antennas are patch antennas
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ray-optics.
? Rings are
(conducting patch mounted in insulating ceramic).
Simple Multipath
? A simple approach to treating multipath is with
Approach should be valid for
reflectors that greater than one wavelength
from the antenna.
? It is important to note that all real antennas
have gain below the horizon (ie., zero
elevation angle) and will therefore see
reflections from the ground.
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?
?
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Surface reflections
E perpendicular to plane of incidence
E
r
E
i
=
ncosi - n'
2
-n
2
sin
2
i
ncosi + n'
2
-n
2
sin
2
i
E parallel to plane of incidence
E
r
E
i
=
n'
2
cosi - n n'
2
-n
2
sin
2
i
n'
2
cosi + n n'
2
-n
2
sin
2
i
n = me
refractive
index of
reflecting
medium
(m’=m)
? The amplitude of a reflected signal from a
surface depends on incidence angle and
refractive index of medium
Where n’ is
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? For normal incidence: the two cases reduce to
? Reflection strength will depend on dielectric constants:
e=1; water 80; Dry Sand 3-5; saturated sand 20-30; shale
5-15; silt/clay 5-40; Granite 4-6; Ice 3-4
E
r
E
i
=
2n
n'+n
E
r
E
i
=
n'-n
n'+n
Normal incidence reflection
– Air
– Reflected strength at least 30% of incident signal
Perpendicular
Parallel
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? The path length difference between the direct and
? When the reflector is close (d/l
? When reflector is distant (d/ l
rapidly and average to zero quickly.
? l<<1.
This characteristic of antenna and is called phase
center model (needed when antenna types are mixed
Multipath characteristics
reflected signal determines the nature of multipath.
~1) multipath will be
slowly varying
>>1) multipath will vary
A class of multipath is what happens when d/
in high-precision applications).
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Receiving Antenna Phase center models
– Anechoic chamber measurements (absolute
calibration)
– In-situ relative measurements (one-antenna relative
to another)
–
–
antenna
? The specific characteristics of an antenna
need to be calibrated either with:
In-situ absolute calibration by antenna rotation
In-situ multipath calibration using a directional
8?
Phase center models
? First phase center models were made using
data from a chamber in which L1 and L2
signals were transmitted and antenna rotated
to measure phase difference between
transmitted and received signal.
? Signal strength also measured so that gain of
antenna can be measured (expect it to behave
like sin
2
(q) but with response for q>90 (back-
plane gain).
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Relative phase center models
? If an antenna with 0 phase center variation is
available, then phase center of another
antenna can be found by making differential
measurements between antenna on
monuments with known locations.
? National Geodetic Survey (NGS) has largest
setup: http://www.ngs.noaa.gov:80/ANTCAL/
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NGS Calibration set-up
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Typical Calibration results
?
?
TRM 36569.00+GP NGS ( 4) 01/10/12
.0 -.3 63.2
.0 .7 1.4 2.3 3.1 3.9 4.6 5.2 5.6 5.9 5.9 5.6
-.9 -.8 44.6
.0 -.9 -1.5 -1.9 -2.2 -2.4 -2.7 -3.0 -3.3 -3.6 -3.9 -4.0 -3.8 ..
4 MEASUREMENTS
.3 1.3 .1
.0 .1 .1 .1 .1 .2 .2 .2 .2 .1 .1 .1
.4 .6 .3
.0 .3 .5 .6 .7 .6 .6 .5 .5 .5 .5 .5
? Two types of information given:
“Phase center Position” relative to physical point on
antenna (ARP--normally base of pre-amplifier)
Elevation angle dependent deviations of phase:
13" Micro Centered with Ground Plane
5.0 ..
RMS mm (1 sigma)
.1 ..
.5 ..
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General results
?
free observable (LC)
? Positions can change by 10-cm when phase center
models used
? Phase residuals are systematic if wrong antenna type
used, but RMS is often less than 10 mm compared to
normal noise of ~5 mm
?
?
Typical phase variations are quite different at L1 and
L2 frequencies and the even larger in the ionospheric
Where do we get the “zero phase center antenna”?
The IGS has adopted the Dorne-Margolian Choke ring
as standard. What are its phase cenetr variations?
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Absolute calibration
? Hannover System:
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Original AOAD/M_T Choke Ring antenna, and antenna on the robot.
(Images courtesy of http://www.geopp.com/gnpcvdb/AOA_DM_T/.)
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L1 Results
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L2 Results
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The PCV vary for L1 over a range of approximately 20 mm.
The PCV vary for L2 over a range of approximately 14 mm.
Image courtesy of http://www.geopp.com/gnpcvdb/AOA_DM_T/calibDMT.html.
Image courtesy of http://www.geopp.com/gnpcvdb/AOA_DM_T/calibDMT.html.
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Absolute calibrations
? The Hanover results are similar to anechoic
chamber results although there are problems
with this type of measurement: As the antenna
is rotated, ground reflections have higher gain.
? Major problem at the moment: 10-cm height
changes (14-ppb scale change) in global GPS
when absolute models are used.
? Could be at satellite? Where are phase
centers on satellites?
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Satellite phase centers
? Satellites transmit from an array
? Figure at left gives some idea of
size.
? For current GPS precisions, we
need phase center to a few
centimeters
? See NGS ANTCAL site
? Currently adopted positions of
phase centers could be in error by
definitely wrong by this amount)
over 1 m. (Block IIR satellites are
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Use of Signal-to-noise ratio (SNR)
Cosine
Sine
Direct signal
Reflected signal
As path length changes
reflection rotated
Received
Signal
Phasor diagram
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SNR analysis
o
out-of-phase)
sign).
http://bowie.mit.edu/~tah/snrprog/
? One method of characterizing multipath at a
site is SNR analysis.
? Changing path length difference between
direct and reflected signals causes oscillating
signal amplitude and phase (90
? Analysis of signal strength variations can allow
prediction of phase errors (but ambiguous in
? Implemenation:
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Example HOLC California (LC)
Theoretical from SNR Measured Phase residuals
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scattering
centimeters
Summary
? Measurements at mm level require careful
evaluation of multipath and near-antenna
? Phase center variations can be many
? Probably largest problem is vegetation near
antennas since it changes with time and
allows transmission of GPS signals.
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