03/06/02 12.540 Lec 09 1
12.540 Principles of the Global
Positioning System
Lecture 09
Prof. Thomas Herring
03/06/02 12.540 Lec 09 2
Summary
?Review:
– Examined definitions of pseudorange and carrier
phase
– Looked at some actual raw measurements from a
RINEX file
? Today we look at:
– Combinations of range and phase measurements
– Simple differences between observed and rough
calculation of expected range and phase
measurements
– Sources of GPS data
03/06/02 12.540 Lec 09 3
Range and phase data
? As we have seen, with real data there are drops out of data
(missing data) and often associated with this cycle slips in the
phase data.
? The difference between the L1 and L2 range measurements
reflects noise and the ionospheric delay (grew by 5 meters in the
hour of data we looked at)
? Difference between L1 and L2 phase, when converted to
distance using standard frequencies and speed of light, also
reflects noise (much smaller than range) and ionospheric delay
but with opposite sign to range ionospheric delay.
? This difference can be used to check for cycles slips independent
of ionosphere and movement of receivers. Called the
Melbourne-Wubena Wide Lane
03/06/02 12.540 Lec 09 4
Melbourne-Wubena Wide Lane
? The difference between L1 and L2 phase with the L2
phase scaled to the L1 wavelenth is often called
simply the widelane and used to detect cycle slips.
However it is effected fluctuations in the ionospheric
delay which in delay is inversely proportional to
frequency squared.
? The lower frequency L2 has a larger contribution than
the higher frequency L1
? The MW-WL removes both the effects on the
ionspheric delay and changes in range by using the
range measurements to estimate the difference in
phase between L1 and L2
03/06/02 12.540 Lec 09 5
Melbourne-Wubena Wide Lane (MW-WL)
? Equation for the MW-WL. The term Rf/c are the range
in cycles (notice the sum due to change of sign
ionospheric delay)
?The ?f/Σf term for GPS is ~0.124 which means range
noise is reduced by a about a factor of ten.
? Because of phase and biases range biases, the ML-
WL should be integer (within noise) when data from
differerent sites and satellites (double differences) are
used. (Example shown later)
mw ?wl=φ
1
?φ
2
?
( f
1
? f
2
)
( f
1
+ f
2
)
R
1
f
1
/c+ R
2
f
2
/c
[]
03/06/02 12.540 Lec 09 6
Simple mathematical model
? We know examine as series of results based
on the results you are generating for
homework #1 and the rinex data collected at
the time.
? How closely can the observed ranges and
phases be matched with a simple calculation?
? Simplest calculation: At the time given in the
rinex data files, compute the position of
satellite and based on rinex header position
compute the range. How accurate is this?
03/06/02 12.540 Lec 09 7
Direct comparison
20000000
21000000
22000000
23000000
24000000
25000000
16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0
C1_07_(m)
Theory_(m)
C1_28_(m)
Theory_(m)
C1_26_(m)
Theory_(m)
C1_11_(m)
Theory_(m)
C1_02_(m)
Theory_(m)
Range (m)
Time_Hrs
03/06/02 12.540 Lec 09 8
Zoom of “jump” section
20000000
20500000
21000000
21500000
22000000
22500000
23000000
23500000
24000000
19.7 19.8 19.8 19.9 19.9 20.0 20.0 20.1
C1_07_(m)
Theory_(m)
C1_28_(m)
Theory_(m)
C1_26_(m)
Theory_(m)
C1_11_(m)
Theory_(m)
C1_02_(m)
Theory_(m)
Range (m)
Time_Hrs
03/06/02 12.540 Lec 09 9
C1 range to theory comparison
? Clearly the theoretical range and observed ranges are
“sort-of” tracking each other but there are large
differences.
? The “jump” with missing data seems to show the same
jump for all satellites (difficult to tell at this scale)
(Class notes have data files, so you can check).
? Pseudorange is difference of clock times, but we have
not taken into account the clocks.
? Examine the difference between observed and
theoretical range (omc).
03/06/02 12.540 Lec 09 10
Observed - Theory, Clock values from
broadcast ephemeris
-500000
-400000
-300000
-200000
-100000
0
100000
200000
300000
16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0
Clock_07_(m)
C1_07-Theory
Clock_28_(m)
C1_28-Theory
Clock_26_(m)
C1_26-Theory
Clock_11_(m)
C1_11-Theory
Clock_02_(m)
C1_02-Theory
Range (m)
Time_Hrs
Notice that omc is opposite to clock, Next plot satellite
clock corrections added
03/06/02 12.540 Lec 09 11
Observed - theory + satellite clock
-300000
-200000
-100000
0
100000
200000
16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0
C1_07-Theory+SV clock
C1_02-Theory+SV clock
C1_11-Theory+SV clock
C1_26-Theory+SV clock
C1_28-Theory+SV clockRange Residual (m)
Time_Hrs
03/06/02 12.540 Lec 09 12
Zoom of last plot
32000
32500
33000
33500
34000
34500
19.5 19.5 19.5 19.6 19.6 19.6 19.6
C1_07-Theory+SV clock
C1_02-Theory+SV clock
C1_11-Theory+SV clock
C1_26-Theory+SV clock
C1_28-Theory+SV clock
Range Residual (m)
Time_Hrs
03/06/02 12.540 Lec 09 13
Residuals
? After correcting for the satellites, the large
fluctuations can be removed with the receiver
clock. Once this is done the remaining
residuals are 10-100 meters.
? What needs to be corrected at this point?
03/06/02 12.540 Lec 09 14
Main model parts missing
? We already saw that L1-L2 range values change by up to 5m for
the short span we looked at Monday (next page shows longer
segment).
? Errors in station coordinates could add 5-10 m of error depending
on quality
? Atmospheric delays (and 3-10 m, especially for low elevation
satellites)
? Time the satellite position is calculated: We assumed the time tag
on the rinex file but clearly in error by 0.1 msec due to receiver
clock. A bigger error is the light propagation time (~7 msec).
? Satellites move in radial direction at ~1km/sec, therefore 7 ms
translates to about 7 meters of range change. Later in course you
will need to do this calculation
03/06/02 12.540 Lec 09 15
L1-L2 range for PRN 07
-18
-16
-14
-12
-10
-8
-6
-4
18.0 19.0 20.0 21.0 22.0 23.0 24.0
L1-L2 range (m)
L1-L2 range (m)
Time_Hrs
Missing data, should not be a jump in L1-L2
03/06/02 12.540 Lec 09 16
MW-WL (used for detecting cycle slips
and resolving phase ambiquities)
-25500000
-25000000
-24500000
-24000000
-23500000
18.0 19.0 20.0 21.0 22.0 23.0 24.0
MW_WL_07_cycles
MW_WL_07_cycles
Time_Hrs
Cycle slip
03/06/02 12.540 Lec 09 17
MW-WL Last part of data (plus PRN 28)
-23578705
-23578704
-23578703
-23578702
-23578701
-23578700
-23578699
-23578698
-23578697
-24380372
-24380371
-24380370
-24380369
-24380368
-24380367
-24380366
-24380365
-24380364
19.0 20.0 21.0 22.0 23.0 24.0
etab.07
MW_WL_07_cycles
MW_WL_28_cycles
MW_WL_07_cycles
MW_WL_28_cycles
Time_Hrs
03/06/02 12.540 Lec 09 18
MW-WL Characteristics
? In one-way form as shown the MW-WL does not need to be an
integer or constant
? Slope in one-way is common, but notice that both satellites show
the same slope.
? If same satellite-pair difference from another station (especially
when same brand receiver and antenna) are subtracted from
these results then would be an integer (even at this one station,
difference is close to integer)
? The MW-WL tells you the difference between the L1 and L2
cycles. To get the individal cycles at L1 and L2 we need another
techique.
? There is a formula that gives L1+L2 cycles but it has 10 times the
noise of the range data (Σf/?f) and generally is not used.
? Discuss more in the processing methods of the course
03/06/02 12.540 Lec 09 19
GPS Data availability
? Over 500 GPS sites from around the world are
available with latencies of 1-hour to a few days.
? The remainder of the lecture we look at these archives
starting from the following links:
– SOPAC http://sopac.ucsd.edu/
–CDDIS http://cddisa.gsfc.nasa.gov/cddis.html
– NGS/CORS http://www.ngs.noaa.gov/CORS/
– UNAVCO http://archive.unavco.ucar.edu/cgi-bin/dmg/pss
? There are more sites and many sites show results as
well as have data available