8/3/2019 Gpsdp Gage
1/219
1Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyan
dGeomatics
TechnicalUniversityofC
atalonia,
Barcelona,
Spain
GPS Data processing:Code and Phase
http://gage1.upc.es
Hernndez-Pajares M., Juan M., Sanz J,
Salazar D., and Ramos P.gAGE/UPC,
Barcelona, Spain
8/3/2019 Gpsdp Gage
2/219
2Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyan
dGeomatics
TechnicalUniversityofC
atalonia,
Barcelona,
Spain
"This document has been produced with the"This document has been produced with thefinancial assistance of the European Union.financial assistance of the European Union.
The contents of this document are the soleThe contents of this document are the sole
responsibility of the authors and can under noresponsibility of the authors and can under no
circumstances be regarded as reflecting thecircumstances be regarded as reflecting the
position of the European Union".position of the European Union".
8/3/2019 Gpsdp Gage
3/219
3Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyan
dGeomatics
TechnicalUniversityofC
atalonia,
Barcelona,
Spain
This course is based on the book edited bygAGE/UPC:
GPS data processing: code and phase.
Algorithms, techniques and recipes.
(available at http://gage1.upc.es)
These slides show some exercises and exampleswhose data fi les (w ith actual GPS data) andcorresponding software (w ith source code) are
provided in the book.
8/3/2019 Gpsdp Gage
4/219
4Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyan
dGeomatics
TechnicalUniversityofC
atalonia,
Barcelona,
Spain
Summary Introduction
GPS measurements and their combinations The RINEX files
Ionospheric combination
Ionosphere-Free combination
Wide-lane and Narrow-lane combinations
Satellite coordinates
The model
Navigation equations Code and phase differential positioning.
Floating versus fixing ambiguities
Introduction
GPS measurements and their combinations
The RINEX files Ionospheric combination
Ionosphere-Free combination
Wide-lane and Narrow-lane combinations
Satellite coordinates
The model
Navigation equations Code and phase differential positioning.
Floating versus fixing ambiguities
8/3/2019 Gpsdp Gage
5/219
5Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
8/3/2019 Gpsdp Gage
6/219
6Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Specific Objectives:
To learn about GPS observables (code and phase), theircharacteristics, properties, combinations and applications.
To learn how to calculate satellites orbits and clocks fromnavigation message. To know the achievable precision.
To learn how to model pseudodistance for code and phasemeasurements. This includes calculation of: 1) Coordinates atemission epoch, 2) Ionospheric delay (Klobuchar model), 3)Tropospheric delay, 4) relativistic correction, 5) clocks offsets and
satellite instrumental delays, 6) phase wind-up, etc.
To learn how to set and solve the navigation equation systemusing least-squares or Kalman filter (algorithm level).
To know how to use phase differential positioning: Floating andfixing ambiguities.
To get tools and skil ls to process and analize GPSdata. Implement algorithms defined in GPS/ SPS-SS
To get tools and skil ls to process and analize GPSdata. Implement algorithms defined in GPS/ SPS-SS
8/3/2019 Gpsdp Gage
7/219
7Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Techni
calUniversityofCatalonia,
Barcelona,
Spain
Introduction
8/3/2019 Gpsdp Gage
8/219
8Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
Techni
calUniversityofCatalonia,
Barcel
ona,
Spain
A ship determ ines its location from a set on lighthouses thatsend an acoustic signal at a know n time.
Know ing the emission timet0 in the lighthouse andthe reception time t1 inthe ship, the traveling time
t1-t0, and the geometricrange =v(t1-t0) may becomputed.
Know ing the emission timet0 in the lighthouse andthe reception time t1 inthe ship, the traveling time
t1-t0, and the geometricrange =v(t1-t0)may becomputed. =v(t1-t0)With only one lighthouse
there is a whole circumferenceof possible locations
With only one lighthouse
there is a whole circumferenceof possible locations
8/3/2019 Gpsdp Gage
9/219
9Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
A ship determ ines its location from a set on lighthouses thatsend an acoustic signal at a know n time.
With two lighthouses thereare two possible solutions.
But, one of them is not onthe sea!
With two lighthouses thereare two possible solutions.
But, one of them is not onthe sea!
8/3/2019 Gpsdp Gage
10/219
10Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
A ship determ ines its location from a set on lighthouses thatsend an acoustic signal at a know n time.
With three lighthouses asingle solution is found
With three lighthouses asingle solution is found
8/3/2019 Gpsdp Gage
11/219
11Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Errors in the clocks (lighthouses and ship) synchronism affects the accuracy
The ranges are measured by means thetraveling time of the acoustic signal fromthe lighthouses to the ship.
Thence, the synchronism errors between
the lighthouses and ship clocks will degradethe positioning accuracy.
Pseudorange or
apparent distancedue to the error clocks
True range or
Geometric range
8/3/2019 Gpsdp Gage
12/219
12Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
SUMMARY: The positioning system is based on:
To know the coordinates of the lighthouses
To know the ranges from the ship to the lighthouses To solve a geometric problem.
SUMMARY: The positioning system is based on:
To know the coordinates of the lighthouses
To know the ranges from the ship to the lighthouses To solve a geometric problem.
NOTE: the ranges are measured by meansthe traveling time of the acoustic signalfrom the lighthouses to the ship.
Thence, the synchronism errors between
the lighthouses and ship clocks will degradethe positioning accuracy.
NOTE: the ranges are measured by meansthe traveling time of the acoustic signalfrom the lighthouses to the ship.
Thence, the synchronism errors between
the lighthouses and ship clocks will degradethe positioning accuracy.
Pseudorange or
apparent distancedue to the error clock.
True range or
Geometric range
8/3/2019 Gpsdp Gage
13/219
13Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Satellites broadcastSatellites broadcastorbit and clock dataorbit and clock data
Satellite coordinatesSatellite coordinates
and clock offsetand clock offset
Receiver measuresReceiver measurestraveling time fromtraveling time fromsatellite to receiversatellite to receiver PseudorangePseudorange (P)(P)
PP
Thence, the receiver coordinates are found solving ageometrical problem: from sat. coordinates and ranges
Thence, the receiver coordinates are found solving ageometrical problem : from sat. coordinates and ranges
Lighthousescoordinates
Lighthouses-shipranges.
How GPS Works
8/3/2019 Gpsdp Gage
14/219
14Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
How GPS Works
One of the solutions is noton the Earth surface.
8/3/2019 Gpsdp Gage
15/219
15Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityof
Catalonia,
Barcelona,
Spain
Receiver
location
How GPS Works
8/3/2019 Gpsdp Gage
16/219
16Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
TechnicalUniversityof
Catalonia,
Barcelona,
Spain
Measurements:
Ranges Pseudoranges arecomputed from thetraveling time sat-rec
Several error sourcesaffect thesemeasurements
Receiver
location
How GPS Works
Lesson 3:GPS measurementsand its combinations
8/3/2019 Gpsdp Gage
17/219
17Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
TechnicalUniversityof
Catalonia,
Barcelona,
Spain
Receiver
location
Satellite location
Satellite coordinates
and clock offsets arecomputed from thenavigation message:(orbit.f)
Measurements:
Ranges Pseudoranges arecomputed from thetraveling time sat-rec
Several error sourcesaffect thesemeasurements
How GPS Works
Lesson 4:GPS Orbits and
clocks
8/3/2019 Gpsdp Gage
18/219
18Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
TechnicalUniversityof
Catalonia,
Barcelona,
Spain
MODEL:
Atmospheric propag.,relativistic effects,clocks and instrum.
delays are modeledand removed.
And the navigationequations are built
Receiver
location
Satellite location
Satellite coordinates
and clock offsets arecomputed from thenavigation message:(orbit.f)
Measurements:
Ranges Pseudoranges arecomputed from thetraveling time sat-rec
Several error sourcesaffect thesemeasurements
How GPS Works
Atmospheric propagation: IONO, TROPO
Relativistic effects
Lesson 5:GPS measurements
modeling (code)
8/3/2019 Gpsdp Gage
19/219
19Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
MODEL:
Atmospheric propag.,relativistic effects,clocks and instrum.
delays are modeledand removed.
And the navigationequations are built
Navigationequations
The geometricproblem is linearized,and Weighted LeastMean Squares orKalman filter areused to compute thesolution.
Satellite location
Satellite coordinates
and clock offsets arecomputed from thenavigation message:(orbit.f)
Measurements:
Ranges Pseudoranges arecomputed from thetraveling time sat-rec
Several error sourcesaffect thesemeasurements
How GPS Works
Lesson 6:Solving thenavigation Equations
1 1
1
1 1 1
1 1 1 1
2 2 2
2 2 2 2
2 2 2
1
1
..................
io io io
io io ioio k
io io ioio k
io io io
n n n nn nio k
io io
n
io io
x x y y z z
P dt x x y y z z
P dt
P dt x x y y
+ +
= +
1
i
i
i
in
io
n n
io
x
y
z
cdtz z
i
i
i
i
cdt
z
y
x
........
2222
1111
=
+
++
n
k
nn
io
n
i
kioi
kioi
dtP
dtP
dtP
1 11
1 1 11 1 1 1
2 2 22 2 2 2
2 2 2
1
1
..................
io io io
io io io
io k
io io ioio k
io io io
n n n nn nio k
io io
n
io io
x x y y z z
P dt x x y y z z P dt
P dt x x y y
+ +
= +
1
i
i
i
in
io
n n
io
xy
z
cdtz z
i
i
i
i
cdt
z
yx
........
2222
1111
=
+
++
n
k
nn
io
n
i
kioi
kioi
dtP
dtPdtP
8/3/2019 Gpsdp Gage
20/219
20Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
Receiver
location
How GPS Works
Lesson 7:Code and phase
differential positioning.
Floating/fixing ambiguities
8/3/2019 Gpsdp Gage
21/219
21Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
Lesson 3GPS measurements and their
combinations: The RINEX files
8/3/2019 Gpsdp Gage
22/219
22Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
GPS SIGNAL STRUCTURE
P(Y)P(Y)
C/AC/A
P(Y)P(Y)
1227.6 MHz1227.6 MHz
L2L21575.42 MHz1575.42 MHz
L1L1
C/A-code for civilian users [C1(t)]
P-code only for military andauthorized users [P(t)]
Navigation message with satelliteephemeris and clock corrections[D(t)]
Two carriers in L-band: L1=154 fo=1575.42 Mhz L2=120 fo=1227.60 Mhzwhere fo=10.23 Mhz
1 1 1 1 1
2 2 2
( ) ( ) ( )sin( ) ( ) ( ) cos( )
( ) ( ) ( )sin( )
L t a P t D t f t a C t D t f t
L t a P t D t f t
= +
=
8/3/2019 Gpsdp Gage
23/219
23Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
GPS Pseudorange Measurements
1 1 1 1 1
2 2 2
( ) ( ) ( )sin( ) ( ) ( ) cos( )( ) ( ) ( )sin( )t a P t D t f t a C t D t f t
L t a P t D t f t = +=
From hereafter we will call: C1 pseudorange computed from C binary code (on frequency 1) P1 pseudorange computed from P binary code (on frequency 1)
P2 pseudorange computed from P binary code (on frequency 2)
From hereafter we will call: C1 pseudorange computed from C binary code (on frequency 1) P1 pseudorange computed from P binary code (on frequency 1)
P2 pseudorange computed from P binary code (on frequency 2)
P1= c t= c [trec(TR)-tsat(TS)]
C1,P1, P2C1,P1, P2
binary code P
8/3/2019 Gpsdp Gage
24/219
24Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
GPS Phase Measurements
1 1 1 1 1
2 2 2
( ) ( ) ( ) sin( ) ( ) ( ) cos( )
( ) ( ) ( ) sin( )
L t a P t D t f t a C t D t f t
L t a P t D t f t
= +
=
From hereafter we will call:
C1 pseudorange computed from C binary code (on frequency 1) P1 pseudorange computed from P binary code (on frequency 1)
P2 pseudorange computed from P binary code (on frequency 2)
L1 phase measur. computed from the carrier phase on frequency 1
L2 phase measur. computed from the carrier phase on frequency 2
C1,P1, P2C1,P1, P2
Carrier phase L
pseudorangesL1, L2 (containingunknown bias) can be alsomeasured from the carrier phasesL
1
(t), L2
(t) (integrated Doppler)L1, L2L1, L2
r e e
e
f f f c
fc c t t f
= =
= = +
&
&
8/3/2019 Gpsdp Gage
25/219
25Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
Phase and Code pseudorange measurements
P1P1
P1 is basically the geometric range ()
between satellite and receiver, plusthe relative clock offset.
The range varies in time due to thesatellite motion relative to the
receiver.
P120.000
clock offsetKm
+
P1 is an absolute measurement (unambiguous)
P1P1
8/3/2019 Gpsdp Gage
26/219
26Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
Phase and Code pseudorange measurements
Relative measurement
(shifted by the unknown ambiguity N)
1 L clock offset N + +
Each time that the receiver loose thephase lock, the unknow n ambiguitychanges by an integer number of
C d d h
8/3/2019 Gpsdp Gage
27/219
27Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
Code and phase measurements
Carrier Phase (ambiguous but precise)
Code (unambiguous but noisier)
Ambiguity
GPS t C d d Ph d
8/3/2019 Gpsdp Gage
28/219
28Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
GPS measurements: Code and Phase pseudoranges
1 1 1 1 1
2 2 2
( ) ( ) ( )sin( ) ( ) ( ) cos( )( ) ( ) ( )sin( )
L t a P t D t f t a C t D t f t L t a P t D t f t
= +=
Main
characteristics
noise(1% of ) [*]
Wavelength
(chip)GPS signal
2 mm
2 mm
30 cm
30 cm
3 m
24.45 cmL2
Precise
but ambiguous
19.05 cmL1
Phase measurements
30 mP2 (Y2): encrypted
30 mP1 (Y1): encryptedUnambiguous
but noisier
300 mC1Code measurements
[*] the codes can be smoothed with the phases in order to reduce noise(i.e, C1 smoothed with L1 50 cm noise)
Antispoofing (A/ S):The code P is encrypted to Y. Only the code C at
frequency L1 is available.
Antispoofing (A/ S):The code P is encrypted to Y. Only the code C at
frequency L1 is available.
8/3/2019 Gpsdp Gage
29/219
29Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
RINEX measurement fi leRINEX measurement file
HEADER
MEASUREMENTS
8/3/2019 Gpsdp Gage
30/219
30Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
RINEX measurement fi leRINEX measurement file
8/3/2019 Gpsdp Gage
31/219
31Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
RINEX measurement fi leRINEX measurement file
Number of tracked satell ites
Measurement time
(receive time tags)
One satellite per rowEpoch flag 0: OK
8/3/2019 Gpsdp Gage
32/219
32Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
RINEX measurement fi leRINEX measurement file
S/ N indicators
Synthetic P2
(A/S=on)
Loss of lock indicator
Pseudorange model ing
8/3/2019 Gpsdp Gage
33/219
33Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomya
ndGeomatics
Techn
icalUniversityof
Catalonia,
Barce
lona,
Spain
sat sa t sat sat
rec rec rec recrel Trop Ion K K = + + + + +
Pseudorange model ing
( )
sat sat sat
rec rec rec P c dt dt = + +
P= c t= c [trec(TR)-tsat(TS)]
sat
recP Geometric range Clock offsets
Relativistic effectsTropospheric delay noiseInstrumental delaysIonospheric delay
8/3/2019 Gpsdp Gage
34/219
34Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
Techn
icalUniversityofCatalonia,
Barce
lona,
Spain
8/3/2019 Gpsdp Gage
35/219
35Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
Techn
icalUniversityofCatalonia,
Barce
lona,
Spain
8/3/2019 Gpsdp Gage
36/219
36Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
Techn
icalUniversityofCatalonia,
Barce
lona,
Spain
Exercise 1:
Exercise 1:
a) Using the file 95oct18casa___r0.rnx, generate the txt file
95oct18casa.a (with data ordered in columns).
b) Plot code and phase measurements for satellite PRN28 anddiscuss the results.
Resolution:
a)
b) See next plots:
cat 95oct18casa___r0.rnx| rnx2txt > 95oct18casa.a
An example of program to read the RINEX: rnx2txt
8/3/2019 Gpsdp Gage
37/219
37Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
Techn
icalUniversityofCatalonia,
Barce
lona,
Spain
rnx2txtRINEX file txt fi le
An example of program to read the RINEX: rnx2txt
cambiar
The RINEX file is convert to a columnar format to easily plot its
contents and to analyze the measurements (the public domain freetoolgnuplotis used in the book to make the plots).
sta Doy sec PRN L1 L2 C1/P1 P2
Code measurementsTh i
The geometry is
8/3/2019 Gpsdp Gage
38/219
38Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barce
lona,
Spain
+++++++=sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
staKKIonTropreldtdtcP 1111 )(
Code measurementsThe geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of
The geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of
P1P1
P1P1
Code measurementsSi il l t f d
Similar plot for code
8/3/2019 Gpsdp Gage
39/219
39Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
2 2 2 2( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta P c dt dt rel Trop Ion K K = + + + + + + +
Code measurementsSimilar plot for codemeasurements at f2.
Notice that
Ionosphere (Ion) and
Instrumental delays (K)
depend on frequency.
Similar plot for codemeasurements at f2.
Notice that Ionosphere (Ion) and
Instrumental delays (K)
depend on frequency.
P2P2
Code and Phase measurements
Code and Phase measurements
8/3/2019 Gpsdp Gage
40/219
40Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
+++++++=sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
staKKIonTropreldtdtcP 2222 )(
+++++++=sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
staKKIonTropreldtdtcP 1111 )(
1 1 1 1 1 1 1( )
sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
2 2 2 2 2 2 2( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
Code measurements: C1,P1,P2
Phase measurements: L1,L2
;1sat
staC
Code and Phase measurements
phase Ambiguit iesN1, N2 are integers
Wind Up
Frequency dependent
Phase measurementsThe geometry is
The geometry is
8/3/2019 Gpsdp Gage
41/219
41Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
1 1 1 1 1 1 1( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
The geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of .The curves are brokenwhen the receiver lossthe lock (cycle-slip).
The geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of .The curves are brokenwhen the receiver lossthe lock (cycle-slip).
When a cycle-slip happens,the phase measurement L
changes by un unknowninteger number of cycles (N)
Phase measurementsThe geometry is
The geometry is
8/3/2019 Gpsdp Gage
42/219
42Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroup
ofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
2 2 2 2 2 2 2( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
The geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of .The curves are brokenwhen the receiver lossthe lock (cycle-slip).
The geometry isthe dominant term in
the plot. The patternin the figures is due tothe variation of .The curves are brokenwhen the receiver lossthe lock (cycle-slip).
When a cycle-slip happens,the phase measurement L
changes by un unknowninteger number of cycles (N)
8/3/2019 Gpsdp Gage
43/219
43Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Combination of measurements:
Ionospheric combination
Ionosphere-Free combination
Wide-lane and Narrow-lane combinations
1. IONOSPHERIC COMBINATION
1. IONOSPHERIC COMBINATION
8/3/2019 Gpsdp Gage
44/219
44Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
TechnicalUniversityo
fCatalonia,
Barcelona,
Spain
+++++++=sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
staKKIonTropreldtdtcP 2222 )(
+++++++=sat
stasatsta
satsta
satsta
satsta
satsta
satsta KKIonTropreldtdtcP 1111 )(
1 1 1 1 1 1 1( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
2 2 2 2 2 2 2( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
Code measurements: C1,P1 ,P2
Phase measurements: L1,L2
;1satstaC
P2-P1
P2-P1
L1-L2
1-
2
phase Ambiguit ies
PI= P2-P1=Iono+ctt
LI= L1-L2= Iono+ctt+Ambig
PI= P2-P1=Iono+ctt
LI= L1-L2= Iono+ctt+Ambig
Ambiguity
1. IONOSPHERIC COMBINATION
1. IONOSPHERIC COMBINATION
8/3/2019 Gpsdp Gage
45/219
45Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
TechnicalUniversityo
fCatalonia,
Barcelona,
Spain
GPS observables
Pij= c t= c [trec(TR)-tems(T
S)]
Ambiguity
The pattern corresponds to
the ionospheric refraction(Ion), because the otherterms (K) are constant.
Notice that code
measurements are noisier.
The pattern corresponds to
the ionospheric refraction(Ion), because the otherterms (K) are constant.
Notice that codemeasurements are noisier.
PI= P2-P1=Iono+ctt
LI= L1-L2= Iono+ctt+Ambig
PI= P2-P1=Iono+ctt
LI= L1-L2= Iono+ctt+Ambig
1. IONOSPHERIC COMBINATION
1. IONOSPHERIC COMBINATION
8/3/2019 Gpsdp Gage
46/219
46Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
TechnicalUniversityo
fCatalonia,
Barcelona,
Spain
=][
][
),(rGPSreceiver
tterGPStransmir
e drtrNSTEC
r
r
r
2
40.3 Ion STEC
f=
The ionospheric delay (Ion) is proportionalto the electron density integrated along the
ray path (STEC).
The iono refract iondepends on:
Geographic location
Time of day Time with respect to
solar cycle (11y).
The iono refract iondepends on:
Geographic location
Time of day Time with respect to
solar cycle (11y).
1. IONOSPHERIC COMBINATION
1. IONOSPHERIC COMBINATION
8/3/2019 Gpsdp Gage
47/219
47Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
TechnicalUniversityo
fCatalonia,
Barcelona,
Spain
=][
][
),(rGPSreceiver
tterGPStransmir
e drtrNSTEC
r
r
r
2
40.3 Ion STEC
f=
The ionospheric delay (Ion) is proportionalto the electron density integrated along the
ray path (STEC).
The iono refraction depends on:
Geographic location
Time of day
Time wi th respect to solar
cycle (11y).
The iono refraction depends on:
Geographic location
Time of day
Time with respect to solar
cycle (11y).
Ambiguity
1. IONOSPHERIC COMBINATION
1. IONOSPHERIC COMBINATION
8/3/2019 Gpsdp Gage
48/219
48Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barcelona,
Spain
+++++++=sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
sta
sat
staKKIonTropreldtdtcP 2222 )(
+++++++=sat
stasatsta
satsta
satsta
satsta
satsta
satsta KKIonTropreldtdtcP 1111 )(
1 1 1 1 1 1 1( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
2 2 2 2 2 2 2( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
Code measurements: C1,P1 ,P2
Phase measurements: L1,L2
;1satstaC
PI= P2-P1=Iono+ctt
LI= L1-L2= Iono+ctt+Ambig
PI= P2-P1=Iono+cttLI= L1-L2= Iono+ctt+Ambig
AmbiguityNOTE:
Ionosphere delays code
Ionosphere advances phase
Ionospheric-Free Combination
2. IONOSPHERE-FREE COMBINATION (Pc,Lc)
8/3/2019 Gpsdp Gage
49/219
49Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
The ionospheric refraction depends on
the inverse of the squared frequencyand can be removed up to 99.9% combining f1and f2signals:
2
2
2
1
22
212
1
ff
PfPfPc
=
2
2
2
1
22
212
1
ff
LfLfLc
=
( ) sat sat sat sat sat sat sta sta sta sta sta csta c c c Lc c dt dt rel Trop k k Rc w = + + + + + + + +
+++++= stacsatstasatstasatstasatstasatsta KTropreldtdtcPc )(
The ionospheric refraction has been removed in Lcand Pc
c = 10.7 cmThe Rcambiguities are NOT integers!!
240.3 Ion STEC f=
1 2
1 2W W Rc N N
=
8/3/2019 Gpsdp Gage
50/219
50Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
Comments:
Two-frequency receivers are needed to apply the
ionosphere-free combination.
If a one-frequency receiver is used, a ionospheric
model must be applied to remove the ionosphericrefraction. The GPS navigation message provides theparameters of the Klobuchar model which accountsfor more than 60% of the ionospheric delay.
Comments:
Two-frequency receivers are needed to apply the
ionosphere-free combination.
If a one-frequency receiver is used, a ionospheric
model must be applied to remove the ionosphericrefraction. The GPS navigation message provides theparameters of the Klobuchar model which accountsfor more than 60% of the ionospheric delay.
Ionospheric-Free Combination
Narrow-lane (Pw) and Wide-lane Combination Lw
8/3/2019 Gpsdp Gage
51/219
51Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
The wide-lane combination Lw provides a signal with a large wave-length (=86.2cm~4*1). This makes it very useful for detectingcycle-slips through the Melbourne-Wbbena combination: Lw-Pw
21
2211ff
PfPfPw +
+
=21
2211ff
LfLfLw
=
The ambiguit ies Nw are INTEGERS!
w w w w w( ) sta sta
sat sat sat sat sat sat sat
sta sta sta sta sta Lw c dt dt rel Trop Ion k k N = + + + + + + + +
w w w( ) sta sta sat sat sat sat sat sat sat
sta sta sta sta sta Pw c dt dt rel Trop Ion K K = + + + + + + +The same sign
No wind-up
Detecting cycle-slips
8/3/2019 Gpsdp Gage
52/219
52Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
This cycle-slip
involves millionsof cycles it iseasy to detect!!
There is a cycle-
slip of only onecycle (~20cm)How to detect it?
Exercise 2:
8/3/2019 Gpsdp Gage
53/219
53Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
Exercise 2:
a) Using the file 95oct18casa___r0.rnx, generate the txt file
95oct18casa.a (with data ordered in columns).
b) Insert a cycle-slip of one wavelength (19cm) in L1measurement at t=5000 s (and no cycle-slip in L2).
c) Plot the measurements L1, L1-P1, LC-PC, Lw-Pw and LI anddiscuss which combination/s should be used to detect thecycle-slip.
Resolution:a)
b)
cat 95oct18casa___r0.rnx| rnx2txt > 95oct18casa.a
cat 95oct18casa.a | gawk {if ($4==18)
print $3,$5,$6,$7,$8} > s18.org
cat s18.org | gawk {if ($1>=5000) $2=$2+0.19;
printf %s %f %f %f %f \n, $1,$2,$3,$4,$5} > s18.cl
c) See next plots:
The geometry is the dominant term in the plot. The variationof in 1 sec may be hundreds of meters many times greater than
The geometry is the dominant term in the plot. The variationof in 1 sec may be hundreds of meters, many times greater than
8/3/2019 Gpsdp Gage
54/219
54Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
L1 (w ithout the cycle-slip)
L1 (w ith the cycle-slip)
1 1 1 1 1 1 1( ) sat sat sat sat sat sat sat sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
of in 1 sec may be hundreds of meters, many times greater thanthe cycle-slip (19 cm) the variation of shadows the cycle-slip!of in 1 sec may be hundreds of meters, many times greater thanthe cycle-slip (19 cm) the variation of shadows the cycle-slip!
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
1unit=
19cm
(L1cycles)
The geometry and clock offsets have been removed.
The trend is due to the Ionosphere The P1 code noise
The geometry and clock offsets have been removed.
The trend is due to the Ionosphere. The P1code noise
8/3/2019 Gpsdp Gage
55/219
55Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
L1-P1 (w ithout the cycle-slip)
L1-P1 (w ith the cycle-slip)
1 1 1 1 1 1 1( ) sat sat sat sat sat sat sat sta sta sta sta sta sta sta L c dt dt rel Trop Ion k k N w = + + + + + + + +
The trend is due to the Ionosphere. The P1code noiseshadows the cycle-slip, and without the reference (in blue), the
time where the cycle-slip happens could not be identified.
pshadows the cycle-slip, and without the reference (in blue), the
time where the cycle-slip happens could not be identified.
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
1 1 1 1( ) sat sat sat sat sat sat sat
sta sta sta sta sta sta sta P c dt dt rel Trop Ion K K = + + + + + + +
1 1 12 sat sat sat
sta sta sta L P Ion ctt ambig = + + +1unit=1
9cm
1unit=
19cm
(L1cycles)
The geometry, clock offsets and iono have been removed.
Th i t t tt l i Th P1 d i l
The geometry, clock offsets and iono have been removed.
There is a constant pattern plus noise The P1 code noise also
8/3/2019 Gpsdp Gage
56/219
56Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
LC-PC (w ithout the cycle-slip)
LC-PC (w ith the cycle-slip)
( ) sat sat sat sat sat sat sta sta sta sta sta sta c c Lc c dt dt rel Trop kc kc Rc w = + + + + + + + +
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
( ) sat sat sat sat sat sta sta sta sta sta sta Pc c dt dt rel Trop Kc = + + + + +
sat sat
sta sta Lc Pc ctt ambig = + +
There is a constant pattern plus noise. The P1code noise also
shadows the cycle-sl ip, and without the reference (in blue), thetime where the cycle-slip happens could not be identified.
There is a constant pattern plus noise. The P1code noise alsoshadows the cycle-slip, and without the reference (in blue), thetime where the cycle-slip happens could not be identified.
1unit=
10.7cm
(Lccycles)
The geometry, clock offsets and iono have been removed.
Th i t t tt l i Th P1 d i l
The geometry, clock offsets and iono have been removed.
There is a constant pattern plus noise The P1 code noise also
8/3/2019 Gpsdp Gage
57/219
57Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
LI-PI (w ithout the cycle-slip)
LI-PI (w ith the cycle-slip)
1 1 2 2sta sat sat sta I I I I LI Ion k k N N w = + + + + +
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
sat sat
sta I I sta I PI Ion K K = + + +
sat sat
sta sta LI PI ctt ambig = + +
There is a constant pattern plus noise. The P1code noise also
shadows the cycle-sl ip, and without the reference (in blue), thetime where the cycle-slip happens could not be identified.
There is a constant pattern plus noise. The P1code noise alsoshadows the cycle-slip, and without the reference (in blue), thetime where the cycle-slip happens could not be identified.
1unit=5.4cm
The geometry , clock offsets and iono have been removed.
There is a constant pattern plus noise The Pw code noise is
The geometry , clock offsets and iono have been removed.
There is a constant pattern plus noise. The Pw code noise is
8/3/2019 Gpsdp Gage
58/219
58Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
Lw-Pw (without the cycle-slip)
Lw-Pw (with the cycle-slip)
w w w w w( ) sta sta sat sat sat sat sat sat sat sta sta sta sta sta Lw c dt dt rel Trop Ion k k N = + + + + + + + +
There is a constant pattern plus noise. The Pw code noise isunder one cycle ofLw. Thence, the cycle-slip is clearly detected
p punder one cycle ofLw. Thence, the cycle-slip is clearly detected
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
w w w( ) sta sta sat sat sat sat sat sat sat
sta sta sta sta sta Pw c dt dt rel Trop Ion K K = + + + + + + +
sat sat
sta sta Lw Pw ctt ambig = + +1unit=8
6.2cm
1unit=8
6.2cm
(Lw
cycles)
The geometry and clock offsets have been removed.
The trend is due to the Iono The L1 code noise is few mm and
The geometry and clock offsets have been removed.
The trend is due to the Iono. The L1 code noise is few mm, and
8/3/2019 Gpsdp Gage
59/219
59Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
LI (w ithout the cycle-slip)
LI (w ith the cycle-slip)
A jump of=19 cm(one cycle in L1)has been introduced in L1at t=5000s
sat
sta I LI Ion ctt ambig + +
The trend is due to the Iono. The L1code noise is few mm, and
the variation of the ionosphere in 1 second is lower than 1=19 cmThence, the cycle-slip is detected.
The trend is due to the I ono. The L1code noise is few mm, andthe variation of the ionosphere in 1 second is lower than
1
=19 cmThence, the cycle-slip is detected.
mm
Iw
8/3/2019 Gpsdp Gage
60/219
60Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
LI-PI LC-PC
L1L1-P1
Ionospheric-Free Combination
The cycle-slips are detected by the Ionospheric combination(LI=L1-L2) and the Melbourne Wbbena (W=Lw-Pw)
8/3/2019 Gpsdp Gage
61/219
61Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
LI Lw -Pw
L1 L2
Two independent combinations, LI and Lw , allow to detecttw o independent cycle-slips (in L1 and L2 phase measur.).
Two independent combinations, LI and Lw , allow to detecttwo independent cycle-slips (in L1 and L2 phase measur.).
Notice that, from L1, L2 is not possible to detect short cycle-slipsNotice that, from L1, L2 is not possible to detect short cycle-slips
8/3/2019 Gpsdp Gage
62/219
62Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
Lesson 4
Satellite coordinates
8/3/2019 Gpsdp Gage
63/219
63Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityo
fCatalonia,
Barc
elona,
Spain
The GPS navigationmessage provides
8/3/2019 Gpsdp Gage
64/219
64Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityofCatalonia,
Barc
elona,
Spain
message provides
pseudo-Keplerianelements to computesatellite coordinates
(X, Y, Z, Vx, Vy, Vz) (a, e, i, , , V)
8/3/2019 Gpsdp Gage
65/219
65Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityofCatalonia,
Barcelona,
Spain
6 values are needed (x,y,z,vx,vy,vz) to provide theposition and velocity of a body. They can be map intothe six Kepler ian elements (a, e, i, , , V), which
provides the natural representation of the orbit!
V
erigee
xs
V
erigee
xs
(a, e, i, , , V)
8/3/2019 Gpsdp Gage
66/219
66Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityofCatalonia,
Barcelona,
Spain
a ae pe
focus
aa ae pe
focus
orbit
shape
orbit
orientation
position inthe orbit
a:semi major axis
e:eccentricity
i:inclination:argument of ascendingnode
:argument of perigeeV:true anomaly
Position in the orbit:
Fictitious body moving at
Satellite True anomaly (V)
8/3/2019 Gpsdp Gage
67/219
67Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
Tech
nicalUniversityofCatalonia,
Barcelona,
Spain
MVE
a ae
MVE
aa ae
Fictitious body moving at
velocity n=2/P=ctt. Mean anomaly (M)
0 3
2( ) ( ) ;
( ) ( ) sin ( )
1 ( )( ) 2arctan tan
1 2
M t n t T na
E t M t e E t
e E tV t
e
= = =
= +
+=
Perigee
0
2
, ,
T
nP
a e
=t V(t)
T0 : time of passage bysatellites perigee
Calculation of osculatrix orbital elements from posit ionand velocity (rv2ele_orb.f)
8/3/2019 Gpsdp Gage
68/219
68Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Calculation of position and velocity from orbital elements(ele_orb2rv.f, orb2xyz.f)
8/3/2019 Gpsdp Gage
69/219
69Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Where:
Due to the non-spherical nature of gravitational potential, the attractionof the sun and moon, the solar radiation pressure, etc., the truesatellite path deviates from the elliptic orbit.
8/3/2019 Gpsdp Gage
70/219
70Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
p p
At any time an elliptical orbittangent to the true path can bedefined. This is the osculatrixorbit, whose Keplerian elements
vary with time t:
a(t),e(t),i(t),(t),(t),V(t)
Instantaneouselliptic tangent(osculatrix) orbit.
True path
Exercise 3: Orbital elements variation:
File 1995-10-18.eci contains the precise position and
8/3/2019 Gpsdp Gage
71/219
71Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
File 1995 10 18.eci contains the precise position and
velocities of GPS satellites every 5 minutes for October18th, 1995. [from JPL/ NASA server:ftp://sideshow.jpl.nasa.gov/pub/gipsy_products ]
a) Use program rv2ele_orb to compute theinstantaneous orbital elements for each epoch in thefile. That is:
b) Plot the orbital elements in function of time to show
their variation: a(t),e(t),i(t), (t),(t),V(t)
Solution:
a) cat 1995-10-18.eci| rv2ele_orb> orb.datb) See the following plots
(X, Y, Z, Vx, Vy, Vz) (a, e, i, , , V)
8/3/2019 Gpsdp Gage
72/219
72Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
8/3/2019 Gpsdp Gage
73/219
73Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversityofCatalonia,
Barcelona,
Spain
Ephemerids in navigation message:
8/3/2019 Gpsdp Gage
74/219
74Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversity
ofCatalonia,
Barcelona,
Spain
In order to calculate WGS84 satellite coordinates, you shouldapply de following algorithm [GPS/ SPS-SS, table 2-15] (see in thebook FORTRAN subroutine orbit.f, annex IV)
RINEX ephemeris fi le
RINEX ephemeris fi le
8/3/2019 Gpsdp Gage
75/219
75Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgrou
pofAstronomy
andGeomatics
TechnicalUniversity
ofCatalonia,
Bar
celona,
Spain
Computation of satellite coordinates from navigationmessage (orbit.f)
Computation of tk time since ephemerids reference epoch t (t and t
8/3/2019 Gpsdp Gage
76/219
76Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
TechnicalUniversity
ofCatalonia,
Bar
celona,
Spain
Computation oftk time since ephemerids reference epoch toe (tand toeare given in GPS seconds of week):
Computation of mean anomaly Mk for tk,
Iterative resolution of Keplers equation in order to compute eccentric
anomaly Ek :
Calculation of true anomaly vk :
Computat ion of latitude argument uk from perigee argument W , true
anomaly vk and corrections cucand cus:
k oet t t=
03
k kM n ta
= + +
sink k k E e E =
21 sinarctan
cos
k
k
k
e Ev
E e
=
( ) ( )cos 2 sin 2k k uc k us k u v c v c v = + + + + +
Computation of radial distance rk, taking into consideration
corrections crcand crs:
1 2cos cos 2 sin 2r a E c v c v = + + + +
8/3/2019 Gpsdp Gage
77/219
77Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomy
andGeomatics
TechnicalUniversity
ofCatalonia,
Bar
celona,
Spain
Calculation of orbital plane inclination ik from inclination ioat
reference epoch toeand corrections cicand cis :
Computation of ascending node longitude k(Greenw ich), fromlongitude 0 at start of GPS w eek, corrected from apparent variationof sidereal time at Greenw ich between start of week and and
reference time tk=t-t
oe, and also corrected from change of ascending
node longitude since reference epoch toe.
Calculation of coordinates in CTS system, applying three rotations
(around uk, ik, k) :
( ) ( ) ( )1 2cos cos 2 sin 2
k k rc k rs k r a E c v c v = + + + +
( ) ( )0 cos 2 sin 2k k ic k is k i i it c v c v = + + + + +
( )0k E k E oet t = +
3 1 3( ) ( ) ( ) 0
0
k
k k
k
k
kk
X
Y
Z
r
i u =
R R R
t (x,y,z)[CTS]Orbit.f
8/3/2019 Gpsdp Gage
78/219
78Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Bar
celona,
Spain
XGreenwich
y
z
[ ]
Nav. message
(ephemeris)
Conventional Terrestrial System(CTS):
Earth-Fixed System the reference system rotateswith Earth.
The program orbit.f provides the satellite coordinates in aEarth fixed system (CTS)
8/3/2019 Gpsdp Gage
79/219
79Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Bar
celona,
Spain
X GreenwichZ North Pole
Exercise 4: Orbits and clocks accuracy (S/ A=on)
The file eph.on contains satellite coordinates (x,y,z) and
8/3/2019 Gpsdp Gage
80/219
80Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Bar
celona,
Spain
The file eph.on contains satellite coordinates (x,y,z) andclocks, computed from the navigation message of GPSsatellites for March 23th, 1999. (with S/A=on)[the coordinates has been computed using the program orbit.f]
The file sp3.on contains precise coordinates and clocksof GPS satellites for March 23th, 1999
[Provided by the IGS server ftp://igscb.jpl.nasa.gov/igscb/product]
Plot the error of broadcast orbits and clocks and discussthe results.
Solution:See the following plots
s
ERROR in coordinates and clock S/ A=on
8/3/2019 Gpsdp Gage
81/219
81Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Bar
celona,
Spain
s
Exercise 5: Orbits and clocks accuracy (S/ A=off)
The file eph.on contains satellite coordinates (x,y,z) and
8/3/2019 Gpsdp Gage
82/219
82Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Bar
celona,
Spain
p ( ,y, )clocks, computed from the navigation message of GPSsatellites for May 15th, 2000 (with S/A=off)[the coordinates has been computed using the program orbit.f]
The file sp3.on contains precise coordinates and clocksof GPS satellites for May 15th, 2000
[Provided by the IGS server ftp://igscb.jpl.nasa.gov/igscb/product]
Plot the error of broadcast orbits and clocks and discussthe results.
Solution:See the following plots.
s
ERROR in coordinates S/ A=off
8/3/2019 Gpsdp Gage
83/219
83Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
s
Selective Availabil ity (S/ A): Intentional degradation of satellite
clocks and broadcast ephemeris. (from 25 March, 1990)
8/3/2019 Gpsdp Gage
84/219
84Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatics
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
GPS Before and After S/A was switched off
-200
-180-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5 6 7 8 9 10
Time of Day (Hours UTC)
Instantaneous
Error(meters)
Horizontal Error (meters)
Vertical Error (meters)
2 May 2000Colorado Springs, Colorado
ANALYSIS NOTES
- Data taken from Overlook PAN Monitor Station,equipped with Trimble SVeeSix Receiver
- Single Frequency Civil Receiver
- Four Satellite Position Solution at Surveyed Benchmark- Data presented is raw, no smoothing or editing
s
8/3/2019 Gpsdp Gage
85/219
85Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
Lesson 5
Model
s
Pseudorange modeling (code)
8/3/2019 Gpsdp Gage
86/219
86Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgroupofAstronomyandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
The pseudorange modeling is based in the GPS StandardPositioning Service Signal Specification (GPS/SPS-SS).
1 1 1 11 ( ) sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
C1
s
8/3/2019 Gpsdp Gage
87/219
87Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronomyandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
1 1 11 ( ) sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
s
Geometric range
8/3/2019 Gpsdp Gage
88/219
88Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronomyandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
Euclidean distance between satellite coordinates at emission timeand receiver coordinates at reception time.
( ) ( ) ( )2 2 2
sat sat sat sat
rec rec rec rec x x y y z z = + + =
sat
rec
Of course, receiver coordinates are not known (is the target of thisproblem). But ....
1 1 1 11 ( )
sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
s
( ) ( ) ( )2 2 2
sat sat sat sat
rec rec rec rec x x y y z z = + +
8/3/2019 Gpsdp Gage
89/219
89Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
Of course, receiver coordinates are not known (they arethe target of this problem). But, we can always assume that an
approximate position is known(it can be computedusing the Bancrofts method see next lesson--):
( )0 0 0, ,rec rec rec x y z
( ), ,rec rec rec x y z
Thence, as it will be shown in next lesson, the navigation problem willconsist on:
1.- To start from an approximate value for receiver position
(it can be computed with Bancrofts method)
2.- With the pseudorange measurements and the navigation
equations, compute the correction to have amore precise position of the receiver.
Thence, as it will be shown in next lesson, the navigation problem willconsist on:
1.- To start from an approximate value for receiver position
(it can be computed with Bancrofts method)
2.- With the pseudorange measurements and the navigation
equations, compute the correction to have amore precise position of the receiver.
( )0 0 0, ,rec rec rec x y z
( ), ,rec rec recdx dy dz
( ) ( ) ( )0 0 0, , , , , ,rec rec recrec rec rec rec rec rec x y z x y z dx dy dz = +
cs
Satellite coordinates at emission time (rec2ems.f)
Th GPS i l t l f
8/3/2019 Gpsdp Gage
90/219
90Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
The GPS signal travels fromsatellite coordinates atemission time (tems) toreceiver coordinates at
reception time (trec).
The satellite can moveseveral hundreds of meters
from tems
to trec.The receiver time-tags aregiven at reception time andin the receiver clock time.
An algorithm is needed to compute the satellitecoordinates at emission timein the GPS system time
from reception time in the receiver time tags.
An algorithm is needed to compute the satellitecoordinates at emission timein the GPS system timefrom reception time in the receiver time tags.
cs
C1C1
The satellite offset
l k dtS
b
The satellite offset
l k dtS
bT[ems]
8/3/2019 Gpsdp Gage
91/219
91Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
C1= ct= c [trec(TR)-tems
(TS
)]
C1C1
As it is known, the pseudorange measurements link the emissiontime (tems) in satellite clock (TS) with reception time (trec) in
receiver clock (TR) (receiver time tags).Thence, the emission time in the satellite clock is:
tems(TS)= trec(TR)-C1/c
Finally, since dtS= tS T is the time offset between satellite clock(tS)and GPS system time (T), thence:
T[ems]= tems(TS)-dtS= trec
(TR)-(C1/c+dtS)
clockdt can becomputed from thenavigation message
clockdt can becomputed from thenavigation message
Emissiontimeinthe
GPSsystemt
imeT
c
s
The algorithm provided by the GPS/SPS-SS (orbit.f) supplies satellite
coordinates in an Earth Fixed reference frame To compute the
Satellite coordinates computation at emission time
8/3/2019 Gpsdp Gage
92/219
92Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Barcelona,
Spain
coordinates in an Earth-Fixed reference frame. To compute thesatellite coordinates
At the emission time, the following algorithm can be applied:
1. From receiver time-tags, compute emission time in GPS systemtime:
2. Compute satellite coordinates at emission time T[ems]
3. Account for Earth rotation during traveling time from emission toreception t(CTS reference system at reception time is used tobuild the navigation equations).
T[ems]= trec(TR)-(C1/c+dtS)
T[ems] [orbit] (Xsat,Ysat,Zsat)CTS[emission]
(Xsat,Ysat,Zsat)CTS[reception] =R3(Et).(Xsat,Ysat,Zsat)CTS[emission]
See rec2ems.fSee rec2ems.f
c
s
Exercise 6: Using the GCAT program, compute satellitecoordinates at emission time and at reception time. Plot the moduleof the vector difference between both positions (use October 13th,
1998 data files)
8/3/2019 Gpsdp Gage
93/219
93Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
Tec
hnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
1998 data files).
tic
s
8/3/2019 Gpsdp Gage
94/219
94Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatic
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
tic
s
Satellite and receiver clock offsets
They are time offsets between satellite/receiver time and GPS
8/3/2019 Gpsdp Gage
95/219
95Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeomatc
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
-The receiver clock offset (dtrec) is estimated together with receivercoordinates.
- Satellite clock offset (dtsat) may be computed from navigation
message:
They are time-offsets between satellite/receiver time and GPSsystem time (provided by the ground control segment):
dtsat=a0+ a1(t-t0) + a2(t-t0)2
1 1 1 11 ( )
sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
tic
s
t0
0 1 2
dtsat=a0+a1(t-t0) +a2(t-t0)2
8/3/2019 Gpsdp Gage
96/219
96Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeoma
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
2 NAVIGATION DATA GPS RINEX VERSION / TYPE
srx/v1.8.1.4 BAI 95/10/19 03:18:35 PGM / RUN BY / DATE
CASA COMMENT
-2444431.2031 -4428688.6270 3875750.1442 COMMENTEND OF HEADER
14 95 10 18 00 51 44.0 1.129414886236D-05 1.136868377216D-13 0.000000000000D+00
1.730000000000D+02-5.175000000000D+01 4.375182243902D-09-5.836427291652D-01
-2.712011337280D-06 2.427505562082D-03 8.568167686462D-06 5.153718931198D+03
2.623040000000D+05 4.470348358154D-08 1.698435481558D+00 1.676380634308D-08
9.636381916043D-01 2.153437500000D+02 3.056960010495D+00-8.030691653399D-09-5.178787145843D-11 1.000000000000D+00 8.230000000000D+02 0.000000000000D+00
3.200000000000D+01 0.000000000000D+00 1.396983861923D-09 1.730000000000D+02
2.592180000000D+05 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00
2 NAVIGATION DATA GPS RINEX VERSION / TYPE
srx/v1.8.1.4 BAI 95/10/19 03:18:35 PGM / RUN BY / DATE
CASA COMMENT
-2444431.2031 -4428688.6270 3875750.1442 COMMENT
END OF HEADER
14 95 10 18 00 51 44.0 1.129414886236D-05 1.136868377216D-13 0.000000000000D+00
1.730000000000D+02-5.175000000000D+01 4.375182243902D-09-5.836427291652D-01
-2.712011337280D-06 2.427505562082D-03 8.568167686462D-06 5.153718931198D+03
2.623040000000D+05 4.470348358154D-08 1.698435481558D+00 1.676380634308D-08
9.636381916043D-01 2.153437500000D+02 3.056960010495D+00-8.030691653399D-09
-5.178787145843D-11 1.000000000000D+00 8.230000000000D+02 0.000000000000D+00
3.200000000000D+01 0.000000000000D+00 1.396983861923D-09 1.730000000000D+02
2.592180000000D+05 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00
PRN
t0YY MM DD H M S
a0 a1 a2
atic
s
n
8/3/2019 Gpsdp Gage
97/219
97Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeoma
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
atic
s
n
Relativistic correction (relij)
A constant component depending only on nom inal value of satellitesorbit major semi-ax is being corrected modifying satellites clock
8/3/2019 Gpsdp Gage
98/219
98Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeoma
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
p p g yorbit major semi-ax is, being corrected modifying satellite s clockoscillator frequency*:
A periodic component due to orbit eccentricity (to be corrected by user
receiver):
Being =3.986005 1014 (m3/ s2) universal gravity constant, c =299792458(m/s) l ight speed in vacuum, a is orbits major semi-ax is, eis its eccentricity,E is satellites eccentric anomaly, and rand vare satellites geocentricposition and speed in an inertial system.
*being f0 = 10.23 MHz, we have f=4.464 10-10 f0= 4.57 10-3 Hzso satellite should use f o=10.22999999543 M Hz.
2'
100 0
2
0
14.464 10
2
f f v U
f c c
= +
2 sin( ) 2 ( )a
rel e E metersc c
= =
r v
atic
s
n
8/3/2019 Gpsdp Gage
99/219
99Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeoma
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
atic
s
n
Ionospheric Delay
As a first approach, ionospheric delay
ji
I
8/3/2019 Gpsdp Gage
100/219
100Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeoma
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spain
For two-frequency receivers, it may be cancelled (99.9%) usingionosphere-free combination
For one-frequency receivers, it may be corrected (about 60%)
using Klobubhar model (defined in GPS/SPS-SS), whose
parameters are sent in navigation message. (See program klob.f)
1 1 1 11 ( )
sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
pp , p ydepends on frequency as given by:
Where Iis number of electrons per area unitin the direction of observation, or STEC(Slant Total Electron Content)
2
40.3ion I
f =
e I N ds=
2 2
1 2
2 2
1 2
1 2f L f LLC
f f
=
atic
s
n
Klobuchar model (klob.f)Vertica l delay
Sl d l
It was designed to minimize user
computational complexity.IPP
8/3/2019 Gpsdp Gage
101/219
101Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeom
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spai
Slant delayp p y
Minimum user computer storage
Minimum number of coefficientstransmitted on satellite-user link
At least 50% overall RMS ionosphericerror reduction worldwide.
It is assumed that the electroncontent is concentrated in a thinlayer at 350 Km in height.
The slant delay is computedfrom the vertical delay at theionospheric Pierce Point (IPP),
multiplying by the obliquity factor.
Obliquity factor
matic
s
in
IONOSPHERIC PIERCEPOINTS (IPP)
8/3/2019 Gpsdp Gage
102/219
102Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAGE
researchgro
upofAstronom
yandGeom
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spai
IPP
Vertica l Delay
Slant Delay
Ionospheric Layer
(350 Km in height)
IPPs trajectories
for a receiver inBarcelona , Spain
matic
s
in
30
Klobuchar model
Klobuchar
coefficients
8/3/2019 Gpsdp Gage
103/219
103Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgro
upofAstronom
yandGeom
TechnicalUniversity
ofCatalonia,
Ba
rcelona,
Spa
4 8 12 16 18 24
Amplitude
*Period
Local Time (hours)
5
10
15
20
25
TimeDelay(nsat1.6
GHz)
Dc=5ns
Where:
DC= 5ns= 14 (ctt. phase offset)
t = Local Time
3 3
0 0
:
;n
n
n n
n
n
Being
A P = =
= = = Geomagnetic Latitude
( )3
( )
( ) 1 16 0.53 /
SLANT VERT Ion Ion m
m
ele
elev elev
v
== +
2 ( )cos ( )
2 ( ); ( )
2
VERT
t DC A day
PIon t
DC if night P
+
= >
matic
s
ain
(time, rsta, rsat,0,1,2,3,0,1,2,3) [Klob] Iono
(time, rsta, rsat,0,1,2,3,0,1,2,3) [Klob] Iono
8/3/2019 Gpsdp Gage
104/219
104Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgro
upofAstronom
yandGeom
Te
chnicalUniversity
ofCatalonia,
Ba
rcelona,
Spa
2 NAVIGATION DATA RINEX VERSION / TYPE
CCRINEXN V1.5.2 UX CDDIS 24-MAR- 0 00:23 PGM / RUN BY / DATE
IGS BROADCAST EPHEMERIS FILE COMMENT
0.3167D-07 0.4051D-07 -0.2347D-06 0.1732D-06 ION ALPHA
-0.2842D+05 -0.2150D+05 -0.1096D+06 0.4301D+06 ION BETA
-0.121071934700D-07-0.488498130835D-13 319488 1002 DELTA-UTC: A0,A1,T,W
13 LEAP SECONDS
END OF HEADER
1 99 3 23 0 0 0.0 0.783577561379D-04 0.113686837722D-11 0.000000000000D+00
0.191000000000D+03-0.106250000000D+01 0.487163149444D-08-0.123716752769D+01
-0.540167093277D-07 0.476544268895D-02 0.713579356670D-05 0.515433833885D+04
0.172800000000D+06-0.260770320892D-07-0.850753478531D+00 0.763684511185D-07
0.957259887797D+00 0.241437500000D+03-0.167990552187D+01-0.823998608564D-08
0.174650132022D-09 0.100000000000D+01 0.100200000000D+04 0.000000000000D+00
0.320000000000D+02 0.000000000000D+00 0.465661287308D-09 0.191000000000D+03
0.172800000000D+06 0.000000000000D+00 0.000000000000D+00 0.000000000000D+00
elev,
matic
s
ain
8/3/2019 Gpsdp Gage
105/219
105Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgro
upofAstronom
yandGeom
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Spa
matic
s
ain
Tropospheric Delay
It does not depend on frequency and affects both the codeand carrier phases in the same w ay
It can be modeled (about 90% ) by:1001
8/3/2019 Gpsdp Gage
106/219
106Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgro
upofAstronom
yandGeom
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Spa
1 1 1 11 ( )
sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
ddry corresponds to the vertical delay of the dryatmosphere (basically oxygen and nitrogen in hydrostaticalequil ibrium) It can be modeled as an ideal gas.
dwet corresponds to the vertical delay of the wetcomponent (water vapor) difficult to model.
A simple model is:
2
1.001( )
0.002001 sin ( )m elev
elev=
+
[ ]
32.3exp( 0.116 10 )
0.1 ; :
dry
wet
d H meters
d m H heigh over the sea level
=
=
A more accurate model for ddry and dwet is provided for SBAS receivers in
RTCA-Do229C. This model depends on the latitude and the day-of-year,being interpolated over a table of several meteorological parameters.
More sophisticated models uses two different mappings (for wet and dry)
( ) ( )satrec dry wet Trop d d m elev= +
matic
s
ain
8/3/2019 Gpsdp Gage
107/219
107Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgro
upofAstronom
yandGeom
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Spa
matic
s
ain
Instrumental Delays
Some sources for these delays are antennas, cables, as well asseveral filters used in both satellites and receivers.
They are composed by a delay corresponding to satellite and
8/3/2019 Gpsdp Gage
108/219
108Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeom
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Sp
1 1 1 11 ( ) sat sat sat sat sat sat sat
rec rec rec rec rec rec recC c dt dt rel Trop Ion K K = + + + + + + +
TGD
They are composed by a delay corresponding to satellite andother to receiver, depending on frequency:
R1recmay be assumed as zero (including it in receiver clock offset). TGDsat is transmitted in satellites navigation message (Total Group Delay)
According to ICD GPS-2000, control segment monitors satellite timing, so
TGD cancels out when using free-ionosphere combination. That is why wehave that particular equation for L2
2
1
2
2
1 1
2 2
sat sat
rec rec
sat sat
rec rec
K R TGD
f K R TGD
f
=
=
matics
pain
8/3/2019 Gpsdp Gage
109/219
109Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Sp
omatics
pain
Measurement noise (thermal noise)
Main noiseWavelengthGPS signal
Antispoofing (A/ S):The code P is encrypted to Y.
Antispoofing (A/ S):The code P is encrypted to Y. Only the code C at
8/3/2019 Gpsdp Gage
110/219
110Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Sp
characteristics(1% of ) [*](chip-rate)GPS signal
2 mm
2 mm
30 cm
30 cm
3 m
24.45 cmL2
Precise
but ambiguous
19.05 cmL1Phase measurements
30 mP2 (Y2): encrypted
30 mP1 (Y1): encryptedUnambiguous
but noisier
300 mC1
Code measurements
[*] codes may be smoothed w ith the phases in order to reduce noise
(i.e., C1 smoothed with L1 50 cm noise)
Only the code C at
frequency L1 is available.
Only the code C at
frequency L1 is available.
1 1 1 1
1 ( ) sat sat sat sat sat sat sat
rec rec rec rec rec rec rec
C c dt dt rel Trop Ion K K = + + + + + + +
omatics
pain
Multipath
One or more reflected signals reach the antenna in additionto the direct signal. Reflective objects can be earth surface
(ground and w ater), build ings, trees, hills, etc.
It ff t b th d d i h t d it
8/3/2019 Gpsdp Gage
111/219
111Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Ba
rcelona,
Sp
It affects both code and carrier phase measurements, and itis more important at low elevation angles.
Code: up to 1 .5 chip-length up to 450m for C1 [theoretically]Typically: less than 2-3 cm.
Phase: up to / 4 up to 5 cm for L1 and L2 [theoretically]Typically: less than 1 cm
Butterfly shape
omatics
pain
Exercise 7:
Plot code and phase ionospheric combination for satellite PRN 15 offile 97jan09coco___r0.rnx and discuss the results.
8/3/2019 Gpsdp Gage
112/219
112Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Barcelona,
Sp
Note: A/S=onButterfly shape:High multipath for low elevationrays (when satellite rises and sets)
omatics
pain
Exercise 8:
Files gage2710.98.a, 2720.98.b and gage2730.98.a contain 1-secondmeasurements collected by a static receiver in three consecutive days.
Plot the combination P1-L1 and identify the multipath (note: shift theplots 3m56s= 236 sec each day)
8/3/2019 Gpsdp Gage
113/219
113Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Barcelona,
S
1 1 1
2 [ ] sat sat sat
sta sta sta
L P Ion ctt ambig Multipath noise = + + + +
The trend is due tothe ionosphere
For a static receiver:Each sidereal day is
(24h
-3m
56s
), thegeometry repeats the mult ipath repeats
For a static receiver:Each sidereal day is
(24h-3m56s), thegeometry repeats the mult ipath repeats
omatics
Spain
Exercise 9: Computat ion of modeled pseudorange
Using data of files 13oct98.rnx and 13oct98.eph,t b h d th d l d d f
8/3/2019 Gpsdp Gage
114/219
114Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.
JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGeo
Te
chnicalUniversityofCatalonia,
Barcelona,
S
compute by hand the modeled pseudorange forsatellite PRN 14 at t=38230 sec (10h37m10s).
Follow these steps:
1 0, 1 1[mod] sat sat sat sat sat sat sat
rec rec rec rec rec PR cdt rel Trop Ion K = + + + +
omatics
Spain
1. Select orbital elements closer to 38230
2. Compute satellite clock offset
3. Compute satellite-receiver aprox. geometric range
8/3/2019 Gpsdp Gage
115/219
115Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGe
Te
chnicalUniversit
yofCatalonia,
Barcelona,
S
1 0, 1 1[mod]
at sat sat sat sat sat sat
rec rec rec rec rec PR cdt rel Trop Ion K = + + + +
3.1 Compute emission time from receiver (reception) time-tagsand code pseudorange.
3.2 Compute satellite coordinates at emission time3.3 Compute approximate geometric range.
4. Compute satellite Instrumental delay (TGD):
5. Compute relativistic correction6. Compute tropospheric delay
7. Compute ionospheric delay
8. Compute modeled pseudorange from previous values:
eomatics
Spain
1. Selection of orbital elements: From file 13oct98.eph,select the last transmitted navigation message blockbefore instant
t=38230 s (10h37m10s).
8/3/2019 Gpsdp Gage
116/219
116Hernndez-Pajares M., Juan M., Sanz J, Salazar D., Ramos P.JEAGAL, 2004-2005
gAG
E
researchgroupofAstronom
yandGe
Te
chnicalUniversit
yofC
Top Related