03/05/03 12.540 Lec 08 1
12.540 Principles of the Global
Positioning System
Lecture 08
Prof. Thomas Herring
Summary
? Review:
– Examined methods for measuring distances
– Examined GPS codes that allow a type of distance
measurement and phase to be measured
? Today:
– Examine how the range measurements are defined
and used
– Use of carrier phase measurements
– Examine RINEX format and look at some “raw” data
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Pseudorange measurements
? When a GPS receiver measures the time offset it
needs to apply to its replica of the code to reach
measuring?
? It is measuring the time difference between when a
signal was transmitted (based on satellite clock) and
when it was received (based on receiver clock).
? If the satellite and receiver clocks were synchronized,
this would be a measure of range
? Since they are not synchronized, it is called
Basic measurement types
maximum correlation with received signal, what is it
“pseudorange”
? Pseudorange:
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P
k
p
=(t
k
-t
p
)?c
p
k
is the pseudorange between receiver k and satellite
p; t
k
p
is the satellite transmit time;
and c is the speed of light
This expression can be related to the true range by introducing
t
k
=t
k
t
k
t
p
=t
p
t
p
t
k
and t
p
are true times; Dt
k
and Dt
p
are clock corrections
Where P
is the receiver clock time, t
corrections to the clock times
+D +D
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Basic measurement types
? r
k
p
P
k
p
= (t
k
-t
p
)+(Dt
k
t
p
)
[]
?c
P
k
p
=r
k
p
+(Dt
k
t
p
)?c+ I
k
p
Ionspheric
delay
{
+ A
k
p
Atmospheric
delay
{
? Substituting into the equation of the
pseudorange yields
is true range, and the ionospheric and
atmospheric terms are introduced because the
propagation velocity is not c.
-D
-D
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Basic measurement types
? The equation for the pseudorange uses the true range
because the propagation velocity is not the in-vacuum
value, c, 2.99792458x10
8
m/s
? To convert times to distance c is used and then
c. In RINEX data files, pseudorange is given in
distance units.
? The true range is related to the positions of the ground
receiver and satellite.
? Also need to account for noise in measurements
and corrections applied for propagation delays
corrections applied for the actual velocity not equaling
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Pseudorange noise
?
– Correlation function width:The width of the correlation is
inversely proportional to the bandwidth of the signal.
Therefore the 1MHz bandwidth of C/A produces a peak 1
msec wide (300m) compared to the P(Y) code 10MHz
bandwidth which produces 0.1 m
Rough rule is that peak of correlation function can be
determined to 1% of width (with care). Therefore 3 m for C/A
code and 0.3 m for P(Y) code.
Pseudorange noise (random and not so random
errors in measurements) contributions:
sec peak (30 m)
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Pseudorange noise
? More noise sources
– Thermal noise: Effects of other random radio noise in the
GPS bands
Black body radiation: I=2kT/l
2
where I is the specific intensity
in, for example, watts/(m
2
k
constant,1.380 x 10
-23
watts/Hz/K and l is wavelength.
Since P(Y)
code has narrower bandwidth, tracking it in theory has 10
times less thermal noise power (cut by factor of 2 because
less transmission power)
Thermal noise is general smallest effect
– Reflected signals (discussed later)
Hz ster), is Boltzman’s
Depends on area of antenna, area of sky seen (ster=ster-
radians), temperature T (Kelvin) and frequency.
Multipath:
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Pseudorange noise
? The main noise sources are related to reflected
? High quality receiver: noise about 10 cm
? Low cost receiver ($200): noise is a few meters
?
quality to P(Y) code ranges. C/A can use narrowband
? Precise positioning (P-) code is not really the case.
03/05/03 12.540 Lec 08 10
oscillators.
f=fDf is
signals and tracking approximations.
(depends on surroundings and antenna)
In general: C/A code pseudoranges are of similar
tracking which reduces amount of thermal noise
Phase measurements
? Carrier phase measurements are similar to
pseudorange in that they are the difference in
phase between the transmitting and receiving
Integration of the oscillator
frequency gives the clock time.
? Basic notion in carrier phase: t where
phase and f is frequency
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f
k
p
(t
r
)=f
k
(t
r
)-f
r
p
(t
r
)+N
k
p
(1)
f
r
p
(t
r
)=f
t
p
(t
t
)=f
t
p
(t
r
-r
k
p
/c)=f
t
p
(t
r
)-
˙
f
p
(t
r
)?r
k
p
/c
Phase measurements
? The carrier phase is the difference between
phase of receiver oscillator and signal
received plus the number of cycles at the
initial start of tracking
? The received phase is related to the
transmitted phase and propagation time by
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r
– Phase received at time t = phase transmitted at t-t
(riding the wave)
– Transmitter phase referred to ground time (used
later).
Phase measurements
? The rate of change of phase is frequency.
Notice that the phase difference changes as
/c changes. If clocks perfect and nothing
moving then would be constant.
? Subtle effects in phase equation
Also possible to formulate as transmit time.
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? Nominally phase can be measured to 1% of
wavelength (~2mm L1 and ~2.4 mm L2)
?
(~30m), atmospheric delays (3-30m).
?
need to be carefully accounted for with phase.
? Precise and consistent definition of time of events is
one the most critical areas
? In general, phase can be treated like range
offsets of oscillator phases.
Phase measurements
? When phase is used it is converted to distance
using the standard L1 and L2 frequencies and
vacuum speed of light.
? Clock terms are introduced to account for
difference between true frequencies and
nominal frequencies. As with range
ionospheric and atmospheric delays account
for propagation velocity
Precision of phase measurements
Again effected by multipath, ionospheric delays
Since phase is more precise than range, more effects
measurement with unknown offset due to cycles and
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GPS Data file formats
? Receivers use there own propriety (binary) formats but
programs convert these to standard format called
Receiver Independent Exchange Format (RINEX)
? teqc available at
http://www.unavco.ucar.edu/data_support/software/teqc/teqc.html is one
of the most common
? The link to the RINEX format is:
? ftp://igscb.jpl.nasa.gov/igscb/data/format/rinex2.txt
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2.00
teqc 1998Jul1
COMMENT
COMMENT
ETAB
tah MIT
7910
7910 TRM22020.00+GP
3711599.9580
1.0000 0.0000 0.0000
1 1
7 L1 L2 C1 P2 P1 D1 D2
15.0000 INTERVAL
COMMENT
COMMENT
COMMENT
2002 1 16 18 49 15.000000
Rinex header
OBSERVATION DATA G (GPS) RINEX VERSION / TYPE
Thomas Herring 20020117 06:28:28UTCPGM / RUN BY / DATE
Linux 2.0.30|PentPro|gcc|Linux|486/DX+
BIT 2 OF LLI FLAGS DATA COLLECTED UNDER A/S CONDITION
MARKER NAME
OBSERVER / AGENCY
TRIMBLE 4000SSE NP 7.19; SP 3.04 REC # / TYPE / VERS
ANT # / TYPE
-2225431.6719 -4676995.2141 APPROX POSITION XYZ
ANTENNA: DELTA H/E/N
WAVELENGTH FACT L1/2
# / TYPES OF OBSERV
SNR is mapped to RINEX snr flag value [1-9]
L1: 3 -> 1; 8 -> 5; 40 -> 9
L2: 1 -> 1; 5 -> 5; 60 -> 9
TIME OF FIRST OBS
END OF HEADER
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RINEX Data block
20
787986.44256 602246.12855 23296205.6024 23296215.6954
-1344.9694 -1048.0284
-2277471.81757 -1740781.13556 21398430.3444 21398436.5904
2700.6094 2104.3714
-1100283.16556 -822375.51955 23502290.7894 23502300.4844
1062.9224 828.2514
-1925082.16955 -1445658.56955 23293616.9844 23293626.4574
2176.8284 1696.2304
1016475.79056 786021.95356 21979554.0634 21979561.0984
-1782.8124 -1389.2054
-572573.66057 -446158.58357 20873925.7664 20873929.7624
446.3594 347.8134
20
? Phase in cycles, range in meters
1 16 18 49 15.0000000 6G 2G 7G11G26G27G28
1 16 18 49 30.0000000 6G 2G 7G11G26G27G28
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interval:
– Raw range data
– Raw phase data
– Differences between data
Examine Rinex file data
? Next set of plots will look at the contents of a
rinex file.
? Examples for one satellite over about 1 hour
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Raw range data
23200000
23400000
23600000
23800000
24000000
24200000
24400000
24600000
18.8 19.0 19.2 19.4 19.6 19.8
C1_range P2_range
C1_range (m)
Hrs
Drop out
Bad measurement
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Raw phase data (Note: sign)
-2000000
0
2000000
4000000
6000000
8000000
18.8 19.0 19.2 19.4 19.6 19.8
L1_phase L2_phase
Phase (cycles)
Hrs
Cycle slip at L2
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L2-L1 range differences
5
10
15
20
25
30
18.8 19.0 19.2 19.4 19.6 19.8
DP2-C1 (m)
D
P2-C1 (m)
Hrs
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L2-L1 phase differences
-5000
0
5000
10000
15000
20000
18.8 19.0 19.2 19.4 19.6 19.8
DL2*l
2
-L1*l
1
(m)
D
L2*
l
2
-L1*
l
1
(m)
Hrs
Cycle slip repaired approximately
Notice time to re-lock
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Zoomed L2-L1 phase
-20
-15
-10
-5
0
5
18.8 19.0 19.2 19.4 19.6 19.8
DL2*l
2
-L1*l
1
(m)
D
L2*
l
2
-L1*
l
1
(m)
Hrs
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Plot characteristics
? Data set plotted etab.plt.dat
? Notice phase difference is opposite sign to
range difference (discuss more in propagation
lectures)
? More manipulation can me made of data: How
about C1-L1*l
03/05/03 12.540 Lec 08 25
examine:
– Combination of range and phase that tell us more
things
–
data shown.
–
Summary
? Looked at definitions of data types
? Looked at data and its characteristics.
? Next class, we finish observables and will
How well with a simple model can we match the
Where do you get GPS data?
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