Transcript Black & White Landscape

Part II
GPS SIGNALS AND BASIC OBSERVABLE
GPS ERROR SOURCES
REFERENCE SYSTEMS AND GPS TIME
SYSTEM
GS609
This file can be found on the course web page:
http://geodesy.eng.ohio-state.edu/course/gs609/
Where also GPS reference links are provided
Civil and Environmental Engineering and Geodetic Science
GPS Satellite System
•
•
•
•
•
24 satellites
altitude ~20,000 km
12-hour period
6 orbital planes
inclination 55o
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GPS Time System
Precise time measurement is behind the success of GPS
• GPS uses its own time system that is based on the atomic time
scale
• Basic units: second of the week (second since the beginning of
the week) and a week number
• The initial GPS epoch (week 0) is 0h UTC of January 6, 1980
• Universal Coordinated Time (UTC) is the time scale based on
atomic second that corresponds to Greenwich time, and is the basis
for most radio time signals and legal time systems
Civil and Environmental Engineering and Geodetic Science
Time Systems
There are three basic time systems that can be defined as follows:
- rotational time (sidereal and universal (solar) times based
on the diurnal rotation of the Earth that is not uniform)
- dynamical time, defined by the motion of the celestial
bodies in the Solar System; it is the independent variable in
the equations of motion
- atomic time, based on the electromagnetic oscillations
produced by the quantum transitions of an atom with the
basic unit being an atomic second, defined as the duration of
9192631770 cycles of radiation corresponding to the
transition between two hyperfine levels of the ground state of
cesium 133
Civil and Environmental Engineering and Geodetic Science
A basic unit of atomic time, based on the
electromagnetic oscillations produced by the quantum
transitions of an atom is an atomic second
atomic second is defined as the duration of 9192631770
cycles of radiation corresponding to the transition
between two hyperfine levels of the ground state of
cesium 133
Civil and Environmental Engineering and Geodetic Science
Time Systems
• Since TAI (atomic time) is independent of the Earth’s rotation, the concept of
Coordinated Universal Time (UTC), that is in some prescribed way connected to the
rotational time, was introduced in 1961, taking advantage of the stability,
predictability and almost immediate accessibility of TAI.
• UTC is based on the atomic second, thus its rate is uniform. Also, its epoch is
manipulated accordingly so that the difference between the time based on Earth
diurnal rotation and UTC is maintained on a level less than or equal to 0.7 s.
• For that purpose UTC is modified by introducing a leap second, when required,
e.g., on December 31 and/or June 30. As a result, UTC and TAI always differ by an
integer number of seconds that can change only every year or one-half year
Civil and Environmental Engineering and Geodetic Science
GPS Time System
• Since UTC is altered to keep it synchronized with the rotational
time (based on Earth rotation rate), the difference (in seconds)
between UTC and GPS time grows
• Consequently, what you see on most of GPS receiver displays is
the GPS time, which is close to UTC (Greenwich time), which is 5
hours ahead from our time zone
• One can usually set up the receiver to display local time if needed
Civil and Environmental Engineering and Geodetic Science
GPS Time System
• The Global Positioning System (GPS) experienced the first
rollover of its internal clock, termed the End of Week (EOW)
Rollover, on August 21, 1999
• The EOW rollover exists because the largest increment for
counting GPS system time is one week, and weeks are accumulated
in a 10-bit register
• GPS time started Jan. 6, 1980 with week "0000" and continued
until 23:59:47 Universal Time Coordinated (UTC), Aug. 21.
• After the rollover, the GPS clock reset itself to "0000." This was
the first EOW rollover since the GPS constellation was established.
Civil and Environmental Engineering and Geodetic Science
GPS Satellite System
• continuous signal transmit
• fundamental frequency 10.23 MHz
• almost circular orbit (e = 0.02)
• at least 4 satellites visible at all times
from any point on the Earth’s surface (5-7 most
of the time)
Civil and Environmental Engineering and Geodetic Science
GPS - Major Components
• Space Segment - responsible for satellite development,
manufacturing and launching
• Control Segment - continuous monitoring and
controlling the system, determining GPS time, prediction of
satellite ephemeris and the clock behavior, as well as
updating the navigation message for every satellite
• User Segment - numerous types of GPS receivers,
providing navigators, surveyors, geodesists and other users
with precise positioning and timing data
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Civil and Environmental Engineering and Geodetic Science
GPS Operational Modes
Precise Positioning Service (PPS) - only for authorized users,
provides 2D point positioning accuracy of about below 10 to 20 m (realtime), and 3-5m for static (abut 1 hour) observation
Standard Positioning Service (SPS) - available for numerous
civilian applications, provides 2D point positioning accuracy of about 40
m, and 3D accuracy of about ~70 m (much worse under SA);
However, the currently achievable accuracy, even with a hand-held
receiver, is
• Horizontal Accuracy (50%) - 4 meters
• Vertical Accuracy (50%) - 10 meters
• Horizontal Accuracy (95%) - 9 meters
• Vertical Accuracy (95%) - 22 meters
Civil and Environmental Engineering and Geodetic Science
Restricting the Accuracy of the Standard
Positioning Service
Department of Defense (DoD) has established a policy for
the implementation of Selective Availability (SA) and the
Anti-Spoofing (AS) for the GPS signal to limit the
number of unauthorized users and the level of accuracy
for nonmilitary applications. This results in the
degradation in the positioning performance and, in
general, complicates the solution strategy.
Under AS, the P-code gets encrypted by adding (modulo 2
sum) a W-code, which results in the Y-code, not known to
the civilian users.
Civil and Environmental Engineering and Geodetic Science
The fundamental frequency of GPS
signal
• 10.23 MHz
• two signals, L1 and L2, are coherently derived from the
basic frequency by multiplying it by 154 and 120,
respectively, yielding:
L1 = 1575.42 MHz (~ 19.05 cm)
L2 = 1227.60 MHz (~ 24.45 cm)
The adaptation of signals from two frequencies is a
fundamental issue in the reduction of the errors due to the
propagation media, mainly, ionospheric refraction and SA
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GPS Signals
• Two carrier frequencies (to remove ionospheric effects)
– L1: 1575.42 MHz (154  10.23 MHz)
wavelength - 19.05 cm
– L2: 1227.60 MHz (120  10.23 MHz)
wavelength - 24.45 cm
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New GPS Signal FOR Civilian Users
• Planned for Block IIF satellites (2005)
– L5: 1176.45 MHz (115  10.23 MHz)
wavelength – 25.5 cm
• Signal L2 will remain a civilian signal as well
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GPS Signals
• Carrier L1 and L2
• P-code (precise/protected code) on L1 and L2
(under AS policy encrypted with W-code leading
to Y-code, which is not directly accessible to
civilian users)
• C/A – code (clear acquisition) on L1
• The fourth type of signal transmitted by GPS
satellites is the broadcast message (navigation
message) on L1 and L2 (identical)
Civil and Environmental Engineering and Geodetic Science
GPS Signal Structure 1/2
• Code modulation (sequence of binary values: +1 or –1)
– L1: P1 & C/A code, navigation message
– L2: P2 code, navigation message
– P-code frequency - 10.23 MHz (i. e., 10.23 million binary digits
or chips per second)
– P-code repetition rate: 266.4 days, 7-day long portion of the
code are assigned to every satellite; codes are restarted every
week at midnight from Saturday to Sunday.
– P-code “wavelength” - 29.31 m
– C/A-code frequency - 1.023 MHz (i.e., 1.023 million binary
digits or chips per second; codes are repeated every
millisecond)
– C/A-code “wavelength” - 293.1 m
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How do we get the numbers right?
• Assuming 1.023 MHz frequency for C/A-code, and
repetition rate of 1 millisecond:
• 1,023,000 Hz * 10-3 sec = 1023 bits (or chips); this is the
length of the C/A code
• For 1023 chips in 1 millisecond we get separation between
two chips equal to (roughly) 1 microsecond
• 1 microsecond separation between the chips corresponds
to ~300 m chip length (for 300,000 km/sec speed of light)
• Check it out the same way for the P-code!!!
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GPS Signal Structure 2/2
– P-code spectrum has a bandwidth of 20 MHz, which
corresponds to a resolution of 1 nanosecond i.e. ~ 30 cm
for good signal-to-noise ratio
– Thus the accuracy of single P-code range measurement is
assumed at ~30 cm level
– C/A-code spectrum has a bandwidth of 2 MHz, which
corresponds to a resolution of 10 nanosecond i.e. ~ 300 cm
for good signal-to-noise ratio
– Thus the accuracy of single C/A-code range measurement
is assumed at ~3 m level
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GPS Signal Structure
• The epochs of both codes are synchronized
• In civilian receivers, the short C/A code is
acquired first to allow access to the P-code
• Carrying two codes on L1 is achieved by
phase quadrature
• unmodulated L1 carrier is split off and
shifted in phase by 90º, then mixed with
C-code and then added to the
P-modulated signal – see Figure 7.8
below
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How are the signals generated
by the GPS satellite?
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APD(t)P(t)sin(1t)
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GPS Signals
Modulation
L1 carrier
1575.42 MHz
 19 cm
 293 m
C/A code
(SPS)
P code
(PPS)
19 cm
 29.3 m
L2 carrier
1227.60 MHz
 24 cm
24 cm
 29.3 m
P code
(PPS)
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
GPS Signal Summary Table
Component
Fundamental
frequency fo
L1 Carrier
L2 Carrier
P-code
C/A code
W-code
Navigation
message
Frequency
[MHz]
10.23
Ratio of
fundamental
frequency fo
1
Wavelength
[cm]
2932.6
1,575.42
1,227.60
10.23
1.023
0.5115
5010-6
154fo
120fo
1
fo/10
fo/20
fo/204,600
19.04
24.45
2932.6
29326
58651
N/A
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GPS Data
• Data File
• range (pseudorange) measurement derived from code
synchronization,
• measured phase of carrier frequency L1 and L2,
• and (optional) range rate (Doppler)
• Navigation Message (broadcast ephemeris) - provides
information about satellite orbits, time, clock errors and
ionospheric model to remove the ionospheric delay (error)
from the observations
• Provided in binary-receiver dependent format
• Usually converted to RINEX - Receiver Independent
Exchange format (ASCII file)
Civil and Environmental Engineering and Geodetic Science
GPS Navigation Message
SUBFRAME
NUMBER
1
TLM
HOW
CLOCK CORRECTION
2
TLM
HOW
EPHEMERIS
TLM
HOW
EPHEMERIS
TLM
HOW
IONOSPHERE, ETC.
TLM
HOW
ALMANAC
3
4
5
1500 BITS
30 SEC.
EACH FRAME: -10 30-BIT WORDS, 6 SEC .
TLM = Telemetry Word HOW = Handover Word (contains Z-count)
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 TLM, telemetry word – contains a synchronization pattern which
facilitates the access to the navigation data
 HOW, handover word allows direct access to the PRN code; first the
C/A code must be acquired, allowing access to HOW, and then the Pcode can be acquired, since C/A code ( allowing then access to
navigation message, i.e., the HOW) allows for time synchronization
• P-code can be accessed only after the C/A code-supported
receiver time synchronization with GPS time through the Z-count
• HOW contains so-called Z-count
 Z-count is defined as integer number of 1.5-second periods since the
beginning of the GPS week, and thus identifies the epoch of a data
record in GPS time
• If one knows the Z-count, one can acquire the P-code within the
next six seconds
Civil and Environmental Engineering and Geodetic Science
GPS Navigation Message (RINEX)
2
NAVIGATION DATA
DAT2RIN 1.00e
The Boss
RINEX VERSION / TYPE
29JUN98 17:59:25 GMT
PGM / RUN BY / DATE
COMMENT
.1118D-07 .0000D+00 -.5960D-07 .0000D+00
ION ALPHA
.9011D+05 .0000D+00 -.1966D+06 .0000D+00
ION BETA
-.142108547152D-13 -.372529029846D-08
12
61440
159
DELTA-UTC: A0,A1,T,W
LEAP SECONDS
END OF HEADER
3 97 10 10 18 0 0.0 .605774112046D-04 .352429196937D-11 .000000000000D+00
.760000000000D+02 .494687500000D+02 .448018661776D-08 .220198356145D+00
.264309346676D-05 .244920048863D-02 .842288136482D-05 .515366117668D+04
.496800000000D+06 .335276126862D-07 -.790250226717D+00 -.372529029846D-07
.951777921211D+00 .211531250000D+03 .259765541557D+01 -.819891294621D-08
.160720980388D-10 .100000000000D+01 .926000000000D+03 .000000000000D+00
.700000000000D+01 .000000000000D+00 .139698386192D-08 .588000000000D+03
.490320000000D+06
6 97 10 10 15 59 44.0 -.358093529940D-06 .000000000000D+00 .000000000000D+00
.220000000000D+02 .526250000000D+02 .438268255632D-08 -.281081720890D+00
…………………….
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Broadcast Ephemeris
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Orbital (Keplerian) Elements
• semimajor axis, a
Algorithm for computing satellite
coordinates from broadcast
ephemerides is given in GPS
Interface Control Document ICDGPS-200 (see also enclosed hand
out)
• eccentricity, e
• right ascension of the
ascending node, o
• argument of perigee, 
• inclination, io
• mean anomaly, Mo
ascending node
Civil and Environmental Engineering and Geodetic Science
GPS Observation File Header (RINEX)
2
OBSERVATION DATA
DAT2RIN 1.00e
The Boss
Mickey Mouse
CFM
5137
TRIMBLE 4000SSI
0
4000ST L1/L2 GEOD
RINEX VERSION / TYPE
29JUN98 17:59:19 GMT
PGM / RUN BY / DATE
OBSERVER / AGENCY
Nav 7.25 Sig 3. 7
REC # / TYPE / VERS
ANT # / TYPE
____0001
MARKER NAME
____0001
MARKER NUMBER
557180.9687 -4865886.9211 4072508.3413
0.0000
0.0000
1
1
0
4
L1
C1
APPROX POSITION XYZ
0.0000
ANTENNA: DELTA H/E/N
WAVELENGTH FACT L1/2
L2
P2
# / TYPES OF OBSERV
1
INTERVAL
1997
10
10
15
13
5.000000
TIME OF FIRST OBS
1997
10
10
16
38
8.000000
TIME OF LAST OBS
8
# OF SATELLITES
3 1598 1603 1504 1504
PRN / # OF OBS
6 4051 4051 4051 4051
PRN / # OF OBS
9 4208 4212 4150 4150
PRN / # OF OBS
……………………… (rest of the SV is given here)…………………………………
PRN / # OF OBS
END OF HEADER
Civil and Environmental Engineering and Geodetic Science
GPS Observation File (RINEX)
97 10 10 15 13 6.000 0 5 6 10 17 23 26
0.000215178
-331628.90610 21627234.69600 -258412.19950 21627239.86440
-330564.59210 23839375.76600 -264155.63150 23839382.29440
-344922.28510 20838559.61800 -268770.84150 20838564.48140
-344734.12710 22476960.02400 -268624.54850 22476965.59140
-338016.17810 20319996.64100 -263389.71350 20320000.46240
97 10 10 15 13 7.000 0 5 6 10 17 23 26
0.000215197
-329205.73500 21627695.91400 -256524.01640 21627700.98840
-327788.16700 23839904.12500 -261992.18640 23839909.89140
-346924.68000 20838178.43000 -270331.14940 20838183.24640
-346674.25800 22476590.73400 -270136.33740 22476596.25440
-337719.08000 20320053.10100 -263158.20940 20320056.88740
97 10 10 15 13 8.000 0 5 6 10 17 23 26
0.000215216
-326782.19000 21628157.18700 -254635.54040 21628162.34340
-325011.83600 23840432.60100 -259828.81640 23840438.14440
-348926.80400 20837797.46000 -271891.24440 20837802.31240
-348614.34600 22476221.42900 -271648.09340 22476226.99540
-337421.42500 20320109.74100 -262926.27040 20320113.51540
………………………………………………………………………………. continues
Civil and Environmental Engineering and Geodetic Science
RINEX 2 description:
http://www.ngs.noaa.gov/CORS/Rinex2.html
http://lox.ucsd.edu/GPSProcessing/Pythagoras/
rinex.html
Civil and Environmental Engineering and Geodetic Science
GPS Receiver
Multiple
channels
Antenna and
Preamplifier
Control and
Interface unit
Code
tracking loop
RF
Microprocessor
Carrier
tracking loop
Data
Storage
Power
Supply
Unit
Civil and Environmental Engineering and Geodetic Science
GPS Receiver: Major Components
- Antenna and preamplifier
- The GPS receiving antenna detects an electromagnetic signal
arriving from a satellite, and after a bandpass filtering, which
provides adequate filter selectivity to attenuate adjacent channel
interference, and initial preamplification, it transfers the signal to
the RF section for further processing by the receiver electronics.
- A typical GPS antenna is omnidirectional (azimuthal-plane), thus
having essentially non-directional pattern in azimuth and a
directional pattern in elevation angle.
- As the GPS signals are transmitted with right-hand circular
polarization, all GPS antennas must also be right-hand polarized.
- It is mandatory for a GPS antenna to maintain high sensitivity
(high gain) due to the relative weakness of the incoming signal
(gain is a measure of the ability to concentrate in a particular
direction the power accepted by the antenna)
- Preamplifier boosts the signal level before feeding it to the
receiver’s RF front-end section
Civil and Environmental Engineering and Geodetic Science
 The physical (geometric) center of the antenna usually does not coincide with the phase
center (the electrical center) of the antenna – a point, to which radio signal measurements
are referred.
 The phase centers for L1 and L2 generally do not coincide,
 To avoid problems: always align the leveled antennas in the same direction (local North),
which results in cancellation in both length and orientation of the offset between physical
and phase centers, when the same type of antenna is used at both ends of a short baseline.
For longer baselines, where local verticals can no longer be assumed parallel, as well as for
mixed types of antennas, this effect would generally not cancelled out.
 In this case, a phase center location has to be a part of the data reduction process, as
the amount of the phase center offset is known and provided by the antenna
manufacturer.
 The location of the phase center can vary with variable azimuth and elevation of the
satellites and the intensity of the incoming signal. This effect should not, in general, exceed
1-2 cm, and for modern microstrip antennas it reaches only a few millimeters.
 Since GPS signal arrives at the phase center (L1 or L2), but most of the time the
coordinates of the ground mark are sought, the observations have to be mathematically
reduced to the ground mark location, using the antenna height.
Civil and Environmental Engineering and Geodetic Science
GPS Receiver: Major Components
- Radio Frequency (RF) section and tracking loops (heart of a GPS receiver )
- delay lock loop (code tracking)
- phase lock loop (carrier tracking)
- dedicated channel receivers
- switching (multiplexing ) receivers
- Basic components of the RF section
- precision quartz crystal oscillator used to generate a reference frequency,
- multipliers to obtain higher frequencies,
- filters to eliminate unwanted frequencies, and signal mixers.
The RF section receives the signal from the antenna, and translates the arriving
(Doppler-shifted) frequency to a lower one called beat or intermediate frequency (IF),
by mixing the incoming signal with a pure sinusoidal one generated by the local oscillator.
As a result, the modulation of IF remains the same, only the carrier frequency becomes the
difference between the original signal and the one generated locally and is more easily
managed by the rest of the receiver
Civil and Environmental Engineering and Geodetic Science
GPS Receiver: Major Components
- Major function of RF section
- Precorrelation sampling and filtering
- Signal splitting into multiple signal-processing channels: thus the processing
that follows is identical for each channel
- Doppler removal
- Generation of the reference PRN codes
- Satellite signal acquisition
- Code and carrier tracking from multiple satellites
- System data demodulation from the satellite signal
- Extracting of pseudorange measurement from PRN code
- Extracting of carrier frequency measurements from the satellite signal
- Extracting SNR information from the satellite signal
- Estimating the relationship to GPS system time
Civil and Environmental Engineering and Geodetic Science
Interaction between delay lock and
carrier tracking loops (no AS)
Delay
tracking
C/A-code
Acquisition
P-code
Acquisition
Code
Removal
Delay
Estimate
Signal
from RF
section
Coherent Navigation Data
Demodulation and Carrier
Recovery
Carrier
Phase
Estimate
Civil and Environmental Engineering and Geodetic Science
GPS Receiver: Major Components
- Microprocessor
- real-time operations, such as acquiring and tracking of the satellite signal,
decoding the broadcast message, timekeeping, range data processing for
navigation, multipath and interference mitigation, etc. are coordinated and
controlled by a microprocessor
- it can also perform data filtering to reduce the noise, position estimation, datum
conversion, interactive communication with the user via the control and display
unit, and managing the data flow through the receiver’s communication port
- Interface/control
- designed as keypad display unit, is used to input commands from the user and
display real-time diagnostic and/or navigation information, etc.
- Data storage
- internal microchips, removable memory cards or solid state (RAM) memory
- Power supply
- AC or DC (internal rechargeable NiCd batteries, or external batteries such as
Lithium Ion battery or Sealed Lead Acid batteries )
Civil and Environmental Engineering and Geodetic Science
Techniques to recover L2 signal under AS
• We already discussed how a GPS receiver measures the range (or
pseudorange) to the satellite by measuring the time delay between
the incoming signal and its replica generated by the receiver
• Signal synchronization provides the time measure
• The PRN code carried by the signal allows to achieve that (if its
known; currently, civilians know only C/A code)
• C/A code as less accurate allows for an approximate
synchronization
• But how do we get an access to the precise P-code under AS
policy, if the P-code is not known, and thus, the time
synchronization scheme will not work?
Civil and Environmental Engineering and Geodetic Science
Techniques to recover L2 signal under AS
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Reference Systems
and Frames
(related to GPS)
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Reference Systems and Frames
• A coordinate system is most commonly referred to as three mutually
perpendicular axes, scale and a specifically defined origin
• An access to the coordinate system is provided by coordinates of a set of
well defined reference points (forming a reference frame)
• Coordinate system and an ellipsoid create a datum; ellipsoid must be
defined by two parameters (a and f or a and e); ellipsoid must be oriented in
space (usually datum and reference system are used as synonyms)
• The most common way of representing a position is with a set of three
Cartesian coordinates.
• Modern systems, especially these derived from GPS observations are
Earth-centered, Earth-fixed (ECEF)
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Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
• National Imagery and Mapping Agency (NIMA), former Defense
Mapping Agency created WGS84 – World Geodetic Datum 84
• National Geodetic Survey (NGS) created NAD83 – North American
Datum 83
• International Earth Rotation Service (IERS) created ITRFxx, where xx
stands for the reference year at which the frame was (re)established or
(re)computed
• ITRF stands for International Terrestrial Reference Frame
• Currently, WGS84 and ITRF practically coincide
Civil and Environmental Engineering and Geodetic Science
What is ITRF ?
• The International Earth Rotation Service (IERS) has been established in
1988 jointly by the International Astronomical Union (IAU) and the
International Union of Geodesy and Geophysics (IUGG). The IERS mission is
to provide to the worldwide scientific and technical community reference
values for Earth orientation parameters and reference realizations of
internationally accepted celestial and terrestrial reference systems
• In the geodetic terminology, a reference frame is a set of points with their
coordinates (in the broad sense) which realize an ideal reference system
• The frames produced by IERS as realizations of ITRS are named
International Terrestrial Reference Frames (ITRF).
• Such frames are all (or a part of) the tracking stations and the related
monuments which constitute the IERS Network, together with coordinates and
their time variations.
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Civil and Environmental Engineering and Geodetic Science
Transformation between two
ITRFs
• Transformation between ITRF at epoch say 1997.0 and other frames is
defined in terms of 7-parameter transformation
• Ri represent rotations, D scale change and Ti stands for translation; i=1,2,3
• These parameters are provided by IERS with every new re-computation of
ITRF
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
TRANSFORMATION PARAMETERS AND THEIR RATES FROM ITRF94 TO
OTHER FRAMES
---------------------------------------------------------------------------------------------SOLUTION T1 T2 T3
D
R1
R2
R3 EPOCH Ref.
cm cm cm 10-8 .001" .001" .001"
.
.
.
RATES T1 T2 T3
.
.
.
.
D
R1
R2
R3
IERS Tech.
Note #, page
cm/y cm/y cm/y 10-8/y .001"/y .001"/y .001"/y
----------------------------------------------------------------------------------------------
ITRF93
0.6 -0.5 -1.5 0.04 -0.39 0.80 -0.96 88.0
RATES -0.29 0.04 0.08 0.00 -0.11 -0.19 0.05
18 82
ITRF92
0.8 0.2 -0.8 -0.08
0.0
0.0
0.0 88.0 18 80
ITRF91
2.0 1.6 -1.4 0.06
0.0
0.0
0.0 88.0 15 44
ITRF90
1.8 1.2 -3.0 0.09
0.0
0.0
0.0 88.0 12 32
ITRF89
2.3 3.6 -6.8 0.43
0.0
0.0
0.0 88.0
9 29
ITRF88
1.8 0.0 -9.2 0.74
0.1 0.0
0.0 88.0
6 34
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
• WGS 84 is an earth fixed global reference frame, including an earth
model.
• It is defined by a set of primary and secondary parameters
• The primary parameters define the shape of an earth ellipsoid, its angular
velocity, and the earth mass which is included in the ellipsoid reference
the secondary parameters define a detailed gravity model of the earth.
WGS 84 is used for
determining the orbits of
GPS navigation satellites
Civil and Environmental Engineering and Geodetic Science
WGS 84 Four Defining
Parameters
Parameter
Notation
Magnitude
Semi-major Axis
a
6378137.0 meters
Reciprocal of Flattening
1/f
298.257223563
Angular Velocity of the Earth

7292115.0 x 10 -11 rad sec -1
Earth’s GravitationalConstant GM
3986004.418 x 10 8 m 3 /s 2
(Mass of Earth’s Atmosphere Included)
a and 1/f are the same as in the original definition of WGS 84
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
• The original WGS 84 reference frame established in 1987 was
realized through a set of Navy Navigation Satellite System (NNSS) or
TRANSIT (Doppler) station coordinates
• Significant improvements in the realization of the WGS 84 reference
frame have been achieved through the use of the NAVSTAR Global
Positioning System (GPS).
• Currently WGS 84 is realized by the coordinates assigned to the GPS
tracking stations used in the calculation of precise GPS orbits at NIMA
(former DMA).
• NIMA currently utilizes the five globally dispersed Air Force
operational GPS tracking stations augmented by seven tracking stations
operated by NIMA. The coordinates of these tracking stations have
been determined to an absolute accuracy of ±5 cm (1s).
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
Using GPS data from the Air Force and NIMA permanent GPS
tracking stations along with data from a number of selected core
stations from the International GPS Service for Geodynamics (IGS),
NIMA estimated refined coordinates for the permanent Air Force and
DMA stations. In this geodetic solution, a subset of selected IGS
station coordinates was held fixed to their IERS Terrestrial Reference
Frame (ITRF) coordinates.
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
 Within the past years, the coordinates for the NIMA GPS reference
stations have been refined two times, once in 1994, and again in 1996. The
two sets of self-consistent GPS-realized coordinates (Terrestrial Reference
Frames) derived to date have been designated:
• WGS 84 (G730 or 1994)
• WGS 84 (G873 OR 1997) , where the ’G’ indicates these
coordinates were obtained through GPS techniques and the number
following the ’G’ indicates the GPS week number when these
coordinates were implemented in the NIMA precise GPS ephemeris
estimation process..
 These reference frame enhancements are negligible (less than 30
centimeters) in the context of mapping, charting and enroute navigation.
Therefore, users should consider the WGS 84 reference frame unchanged
for applications involving mapping, charting and enroute navigation.
Civil and Environmental Engineering and Geodetic Science
Differences between WGS 84 (G873) Coordinates and WGS 84 (G730), compared at 1994.0
Station Location NIMA Station Number DEast (cm) DNorth (cm) DEllipsoid Height (cm)
Air Force Stations
Colorado Springs
85128
0.1
1.3
3.3
Ascension
85129
2.0
4.0
-1.1
Diego Garcia(<2 Mar 97)
85130
-3.3
-8.5
5.2
Kwajalein
85131
4.7
0.3
4.1
Hawaii
85132
0.6
2.6
2.7
Australia
85402
-6.2
-2.7
7.5
Argentina
85403
-1.0
4.1
6.7
England
85404
8.8
7.1
1.1
Bahrain
85405
-4.3
-4.8
-8.1
Ecuador
85406
-2.0
2.5
10.7
US Naval Observatory
85407
39.1
7.8
-3.7
China
85409
31.0
-8.1
-1.5
NIMA Stations
*Coordinates are at the antenna electrical center.
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
• The WGS 84 (G730) reference frame was shown to be in agreement,
after the adjustment of a best fitting 7-parameter transformation, with the
ITRF92 at a level approaching 10 cm.
• While similar comparisons of WGS 84 (G873) and ITRF94 reveal
systematic differences no larger than 2 cm (thus WGS 84 and ITRF94
(epoch 1997.0) practically coincide).
• In summary, the refinements which have been made to WGS 84 have
reduced the uncertainty in the coordinates of the reference frame, the
uncertainty of the gravitational model and the uncertainty of the geoid
undulations. They have not changed WGS 84. As a result, the refinements
are most important to the users requiring increased accuracies over
capabilities provided by the previous editions of WGS 84.
Civil and Environmental Engineering and Geodetic Science
World Geodetic System 1984 (WGS 84)
• The global geocentric reference frame and collection of
models known as the World Geodetic System 1984 (WGS 84)
has evolved significantly since its creation in the mid-1980s
primarily due to use of GPS.
• The WGS 84 continues to provide a single, common,
accessible 3-dimensional coordinate system for geospatial data
collected from a broad spectrum of sources.
• Some of this geospatial data exhibits a high degree of
’metric’ fidelity and requires a global reference frame which is
free of any significant distortions or biases. For this reason, a
series of improvements to WGS 84 were developed in the past
several years which served to refine the original version.
Civil and Environmental Engineering and Geodetic Science
Basic GPS Observables
• Pseudoranges
• precise/protected P1, P2 codes
- available only to the military users
• clear/acquisition C/A code
- available to the civilian users
• Carrier phases
• L1, L2 phases, used mainly in geodesy and surveying
• Range-rate (Doppler)
Civil and Environmental Engineering and Geodetic Science
Basic GPS Observables
• Pseudoranges - geometric range between the transmitter
and the receiver, distorted by the lack of synchronization
between satellite and receiver clocks, and the propagation
media
• recovered from the measured time difference between the
instant of transmission and the epoch of reception.
• P-code pseudoranges can be as good as 20 cm or less,
while the L1 C/A code range noise level reaches even a
meter or more
Civil and Environmental Engineering and Geodetic Science
Basic GPS observables
• Carrier phase - a difference between the phases of a
carrier signal received from a spacecraft and a reference
signal generated by the receiver’s internal oscillator
• contains the unknown integer ambiguity, N, i.e., the
number of phase cycles at the starting epoch that remains
constant as long as the tracking is continuous
• phase cycle slip or loss of lock introduces a new ambiguity
unknown.
• typical noise of phase measurements is generally of the
order of a few millimeters or less
Civil and Environmental Engineering and Geodetic Science
Basic GPS observables
• Instantaneous circular frequency f is a derivative of the phase with respect to
time
d
f 
dt
• By integrating frequency between two time epochs the signal’s phase results
t
   f dt
t0
• Assuming constant frequency, setting the initial phase (t0) to zero, and taking
into account the signal travel time tr corresponding to the satellite-receiver
distance , we get


  f t  ttr   f  t 


c
Civil and Environmental Engineering and Geodetic Science
Basic GPS observables
s(t) phase of received carrier with frequency fs
R(t) phase of reconstructed carrier with frequency fR
 (t )  f t  f
s
s
s

c
  0s,c
 R (t )  f R t   R 0,c
where
 Ro,c and 0s,c are clock errors
 0s,c   f s dt s and  R 0,c   f R dt R
 Rs (t )   s (t )   R (t )   f s

c
 f s dt s  f R dt R ( f s  f R )t
Civil and Environmental Engineering and Geodetic Science
assuming thefrequencydifferenceat t heorder of 1.510-3 Hz
(assuming df / f  1012 is theoscillat orinstability, and f  1.5GHz)
is negligible theequation can be simplified:
 Rs (t )   f

 f (dt s  dt R )
c
since only thefractionalpart of phaseis measuredat t he
init ialepoch t0 , theinit ialintegernumber N of cycles
between satelliteand thereceiveris unknown
Introducing theinit ialfractionalbeat phase 0 and denot ing
f
c

where  is a wavelength :
 Rs (t )  
1


c

(dt s  dt R )  N  ( 0s   0 R )
     c(dt s  dt R )  N   ( 0s   0 R ) which is phase range in [m]
Civil and Environmental Engineering and Geodetic Science
And for pseudorange we have:
Prs  (t r  t s )  c  (t r o  dtr  tto  dts )  c 
(t r o  tto )  c  (dtr  dts )  c   rs  (dtr  dts )  c
where t r o and tto are the true (ideal clock)receiveand transmit times
and t r and t s are themeasured receiveand trasmit imes
t
nd dtr and dts are receiverand satelliteclock corrections
Taking into account all error sources (and also simplifying
some terms), we arrive at the final observation equations for
pseudorange and phase-range observable, of the following
form
Civil and Environmental Engineering and Geodetic Science
Basic GPS Observables
k
I
Pi ,k1   ik  i  Ti k  c( dti  dt k )  bi , 2  Mik,1  eik,1
f
2
1
k
I
Pi ,k2   ik  i  Ti k  c( dti  dt k )  bi , 3  Mik, 2  eik, 2
f
2
2
Iik
  
 Ti k   1 N ik,1  c(dti  dt k )   1  0k   i   mik,1   ik,1
f
k
i ,1
k
i
2
0
1
Iik
  
 Ti k   2 N ik, 2  c(dti  dt k )  bi ,1   2  0k   i   mik, 2   ik, 2
f
k
i ,2
k
i
2
2

k
i ,0
0

 
2
 
2
 sqrt X  X i  Y  Yi  Z  Z i
k
k
k

2
The primary unknowns are Xi, Yi, Zi – coordinates of the user (receiver)
1,2 stand for frequency on L1 and L2, respectively
i –denotes the receiver, while k denotes the satellite
Civil and Environmental Engineering and Geodetic Science
Basic GPS Observables (cont.)
Pi ,k1 , Pi ,k2  pseudoranges measured between station i and satellite k on L1 and L2
ik,1 , ik,2 phase ranges measured between station i and satellite k on L1 and L2
 0k , i initial fractional phases at the transmitter and the receiver, respectively
0
Nik,1 , Nik,2  ambiguities associated with L1 and L2 , respectively
1  19 cm and 2  24 cm are wavelengths of L1 and L2 phases
 ik - geometric distance between the satellite k and receiver i,
Iik Iik
, - ionospheric refraction on L1 and L2, respectively
f f
2
1
2
2
Ti k - the tropospheric refraction term
Civil and Environmental Engineering and Geodetic Science
Basic GPS Observables (cont.)
dti - the i-th receiver clock error
dtk - the k-th transmitter (satellite) clock error
f1, f2 - carrier frequencies
c - the vacuum speed of light
eik,1 , eik,2 ,  ik,1 ,  ik,2 - measurement noise for pseudoranges and phases on L1 and L2
Mik,1 , Mik,2 , mik,1 , mik,2  multipath on phases and ranges
bi,1, bi,2 , bi,3 - interchannel bias terms for receiver i that represent the
possible time non-synchronization of the four measurements
bi ,1 - interchannel bias between ik,1 and ik,2
bi ,2 , bi ,3  biases between ik,1 and Pi ,k1 , ik,1 and Pi ,k2
Civil and Environmental Engineering and Geodetic Science
• The above equations are non-linear and require linearization
(Taylor series expansion) in order to be solved for the unknown
receiver positions and (possibly) for other nuisance unknowns, such
as receiver clock correction
• Since we normally have more observations than the unknowns,
we have a redundancy in the observation system, which must
consequently be solved by the Least Squares Adjustment technique
• Secondary (nuisance) parameters, or unknowns in the above
equations are satellite and clock errors, troposperic and ionospheric
errors, multipath, interchannel biases and integer ambiguities.
These are usually removed by differential GPS processing or by a
proper empirical model (for example troposphere), and processing
of a dual frequency signal (ionosphere).
Civil and Environmental Engineering and Geodetic Science
Basic GPS observables
(simplified form)
R1 = cdt +I/f12 + T + eR1
R2 = cdt I/f22 + T + eR2
11 =  I/f12 + T + 1N1 1
22 =  I/f22 + T + 2N2 2
N1 ,N2 - integer ambiguities
I / f2 - ionospheric effect
T - tropospheric effect
eR1, eR2, 1,2 white noise
R  pseudorange
 phase
  geometric range
 wavelength
Civil and Environmental Engineering and Geodetic Science
Doppler Effect on GPS observable
• The Doppler equation for electromagnetic wave, where fr and fs are received
and transmitted frequencies
v
1  cos
fr
c

fs
 v2 
1  2 
 c 
dr
 v cos thus :
dt

v2
v4
 r 
f r  f s 1  1  2  4   neglectinghigherorder term s
 c  2c 8c

r 
 r 
f r  f s 1  
 c
Civil and Environmental Engineering and Geodetic Science
Doppler Effect on GPS observable
• In case of moving emitter or moving receiver the receiver frequency is
Doppler shifted
• The difference between the receiver and emitted frequencies is proportional
to the radial velocity of the emitter with respect to the receiver (neglecting the
relativistic effect)
dr
v 
 r
dt
1
Df  f r  f s   vr  f s
c
• For GPS satellites orbiting with the mean velocity of 3.9 km/s, assuming
stationary receiver, neglecting Earth rotation, the maximum radial velocity 0.9
km/s is at horizon, and is zero at the epoch of closest approach
• For 1.5 GHz frequency the Doppler shift is 4.5·103 Hz (4.5 cycles phase
change after 1 millisecond, or change in the range by 90 cm)
Civil and Environmental Engineering and Geodetic Science
Integrated Doppler Observable
• The frequency difference between the received signal and the locally
generated replica fg can be used to recover pseudorange difference
through so-called integrated Doppler count:
N jk 
Tk
f
g
 f r dT
Tj
where T j and Tk are t imemarksfor count ingint erval
rij
rik
for T j  t j  and Tk  t k 
c
c
and assuming thenumber of cycles transmitted
is equal to thenumber of cycles received
t j and t k are timesof sending thesignal from thesatellite
thatcorrespondto thereceivetimesT j and Tk
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
Integrated Doppler Observable
tk
Tk
 f dt   f dT substituting it in theequationabove we get :
s
tj
r
Tj
N jk   f g  f s t k  t j  
fg
c
r
ik
 rij 
with unknownsbeing
stationcoordinates X, Y, Z
and frequencydifference f g  f s
Civil and Environmental Engineering and Geodetic Science
Instantaneous Doppler
• Observed Doppler shift scaled to range rate; time derivative
of the phase or pseudorange observation equation
 j   j  cDt j

i
i
i
Dti j is a derivativeof thecombined
clock error(dti  dt j ), i  receiver,
ij  v cos
j  satellite
Instantaneous radial velocity between the satellite j and the
receiver i, and v is satellite tangential velocity, see a slide
“Doppler effect on GPS observable” (corresponds to r in the
notation used in figure 6.3)
Civil and Environmental Engineering and Geodetic Science
Instantaneous Doppler
• Used primarily to support velocity estimation
• Can be used for point positioning
 j   j  cDt j

i
i
i
Dti j is a derivativeof thecombined
clock error(dti  dt j ), i  receiver,
j  satellite
 (t ) j   i
j

 i   (t ) 

(
t
)
 (t ) j   i
j
 (t ) j and i
j
i
Are instantaneous position vector of the satellite, and the
unknown receiver position vector; correspond to rs and rp
in the notation used in Figure 6.3
• dot denotes time derivative
Civil and Environmental Engineering and Geodetic Science
Civil and Environmental Engineering and Geodetic Science
D A, Bi 
RBi  RAi
c
Civil and Environmental Engineering and Geodetic Science
GPS Errors
• Bias errors - can be removed from the direct
observables, or at least significantly reduced, by using
empirical models (eg., tropospheric models), or by
differencing direct observables
- satellite orbital errors (imperfect orbit modeling),
- station position errors
- propagation media errors and receiver errors
• White noise
Civil and Environmental Engineering and Geodetic Science
GPS Errors
Bias errors
•
•
•
•
•
Satellite and receiver clock errors
Satellite orbit errors
Atmospheric effects (ionosphere, troposphere)
Multipath: signal reflected from surfaces near the receiver
Selective Availability (SA)
- epsilon process: falsifying the navigation broadcast data
- delta process: dithering or systematic destabilizing of the
satellite clock frequency
• Anti-spoofing (AS): limits the number of unauthorized users
and the level of accuracy for nonmilitary applications
• Antenna phase center
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Timing errors: receiver and satellite, including SA
• satellite clock (as a difference between the precise and
broadcast clocks ): 0.1-0.2 microseconds which
corresponds to 30-60 m error in range
• first-order clock errors are removed by differencing
technique
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Orbital errors and Selective Availability (SA)
• nominal error for the broadcast ephemeris: 1-5 m on
average
• precise (post-mission) orbits are good up to 5-10 cm
and better; available with 24-hour delay
• Selective Availability: not observed on the orbit
• first-order orbital errors are removed by differencing
technique
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Propagation media
• ionosphere (50-1000km)
• the presence of free electrons in the geomagnetic field causes a
nonlinear dispersion of electromagnetic waves traveling through the
ionized medium
• group delay (code range is measured too long) and phase advance
(phase range is measured too short) , frequency dependent; can
reach ~150 m near the horizon;
c2
  group refractiveindex (group of waves, such as code GP S signal)
2
f
c
n ph  1  22   phase refractiveindex
f
ngr  1 
constantc2  40.3N e [ Hz 2 ] thus ngr  n ph since electrondensity N e is always positive
Civil and Environmental Engineering and Geodetic Science
Propagation media cont.
• the propagation delay depends on the total electron content (TEC)
along the signal’s path and on the frequency of the signal itself as
well as on the geographic location and time (ionosphere is most
active at noon, quiet at night; 11-year Sun spot cycle)
• integration of the refractive index renders the measured range, and
the ionospheric terms for range and phase are as follows:
measured distances   n ds
D
iono
gr
40.3
40.3
iono
 2 TEC and D ph   2 TEC where totalelectroncontentT EC
f
f
T EC   N e ds0 [1016 electronsper m 2 ] where s0 is thegeometricrange at zenith
• differencing technique and ion-free combination of observations on
both frequencies eliminate first-order terms, secondary effects can be
neglected for the short baselines
• differential effect on the long baselines: 1-3 cm
Civil and Environmental Engineering and Geodetic Science
11-year Sun Spot Cycle
Civil and Environmental Engineering and Geodetic Science
Estimated Ionospheric Group Delay
for GPS Signal
First Order:
1/f 2
Second Order:
1/f 3
Third
1/f 4
Order:
Calibrated 1/f 3
Term Based on
a Thin Layer
Ionospheric
Model
L1
L2
Residual
Range Error
16.2 m
26.7 m
0.0
~ 1.6 cm
~ 3.3 cm
~ -1.1 cm
~ 0.86 mm
~ 2.4 mm
~ -0.66 mm
~ 1-2 mm
The phase advance can be obtained from the above table by multiplying each
number by -1, -0.5 and -1/3 for the 1/f 2, 1/f 3 and 1/f 4 term, respectively
Civil and Environmental Engineering and Geodetic Science
Ionospheric Effect Removal by
Using Dual Frequency Receivers
• ionosphere-free phase measurement
1, 2   11   2 2
f 12
1  2
f 1  f 22
2
   T   1 1 N1   2  2 N 2   1 1   2 2
f
2   2 2 2
f1  f 2
• similarly, ionosphere-free pseudorange can be obtained
f12
R1, 2  R1  2 R2
f2
• The conditions applied are that sum of ionospheric effects on both
frequencies multiplied by constants to be determined must be zero;
second condition is for example that sum of the constants is 1, or
one constant is set to 1 (verify!).
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Troposphere (up to 50 km) - frequency-independent, same for all
frequencies below 15 GHz (troposphere is not dispersive for frequencies
below 15 GHz )
• group and phase delay are the same
• elimination by dual frequency is not possible
• affects relative and point positioning
• empirical models (functions of temperature, pressure and relative
humidity) are used to eliminate major part of the effect
• differential effect is usually estimated (neglected for the short baselines
with similar atmospheric effects)
• total effect in the zenith direction reaches 2.5, and increases with the
cosecant of the elevation angle up to 20-28 m at 5deg elevation
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The tropospheric propagation effect is usually represented as a function of
temperature, pressure and relative humidity
• Obtained by integration of the refractivity Ntrop
Dtrop   10 6 N trop ds
where integration is performed along the geometric path
• It is separated into two components: dry (0-40 km) and wet (0-11km)
Dtro p  Dd  D w
N 0trop  c1
p
e
e
 c2  c3 2
T
T
T
• Represents an example of refractivity model at the surface of the earth; c1, c2, c3
are constants, T is temperature in Kelvin (K), e is partial pressure of water vapor
[mb], p is atmospheric pressure [mb]
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The dry component, which is proportional to the density of the gas molecules
in the atmosphere and changes with their distribution, represents about 90%
of the total tropospheric refraction
• It can be modeled with an accuracy of about 2% that corresponds to 4
cm in the zenith direction using surface measurement of pressure and
temperature
• The wet refractivity is due to the polar nature of the water molecules and the
electron cloud displacement
• Since the water vapor is less uniform both spatially and temporally, it
cannot be modeled easily or predicted from the surface measurements
• As a phenomenon highly dependent on the turbulences in the lower
atmosphere, the wet component is modeled less accurately than the dry
• The influence of the wet tropospheric zenith delay is about 5-30 cm that
can be modeled with an accuracy of 2-5 cm
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• The tropospheric refraction as a function of the satellite’s zenith distance
is usually expressed as a product of a zenith delay and a mapping function
• A generic mapping function represents the relation between zenith effects
at the observation site and at the spacecraft’s elevation
• Several mapping functions have been developed (e.g., by Saastamoinen,
Goad and Goodman, Chao, Lanyi), which are equivalent as long as the
cutoff angle for the observations is at least 20o
• The tropospheric range correction can be written as follows:
D trop  f d  zD0d  f w  zD0w
where
fd(z), fw(z) - mapping functions for dry and wet components, respectively,
- vertical dry and wet components, respectively
D0d , D0w
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• Tropospheric refraction accommodates only the systematic part of the
effect, and some small un-modeled effects remain
• Moreover, errors are introduced into the tropospheric correction via
inappropriate meteorological data (if applied) as well as via errors in the
zenith mapping function
• These errors are propagated into station coordinates in the point
positioning and into base components in the relative positioning
• For example, the relative tropospheric refraction errors affects mainly a
baseline’s vertical component (error in the relative tropospheric delay at
the level of 10 cm implies errors of a few millimeters in the horizontal
components, and more than 20 cm in the vertical direction)
Civil and Environmental Engineering and Geodetic Science
Tropospheric Effects (cont.)
• If the zenith delay error is 1 cm, the effect on the horizontal coordinates
will be less than 1 mm but the effect on the vertical component will be
significant, about 2.2 cm
• The effect of the tropospheric refraction error increases with the latitude
of the observing station and reaches its maximum for the polar sites. It is a
natural consequence of a diluted observability at high latitudes where
satellites are visible only at low elevation angles
• The scale of a baseline derived from observations that are not corrected
for the effect of the tropospheric delay is distorted; the baseline is
measured too long.
Civil and Environmental Engineering and Geodetic Science
The average a posteriori standard deviation in the local
East, North and Vertical directions as a function of the
number of tropospheric scaling factors estimated per day
for the station in Matera for GPS week 784
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
• Multipath - result of an interaction of the upcoming signal
with the objects in antenna surrounding; causes multiple
reflection and diffraction; as a result signal arrives via direct
and indirect paths
• magnitude tends to be random and unpredictable, can reach
1-5 cm for phases and 10-20 m for code pseudoranges
• can be largely reduced by careful antenna location
(avoiding reflective objects) and proper antenna design, e.g.,
proper signal polarization, choke-ring or ground-plane
antennas
Civil and Environmental Engineering and Geodetic Science
Multipath
• As opposed to interference, which disrupts the signal and can virtually
provide no or useless data, multipath would allow for data collection, but the
results would be wrong!
• Existing multipath rejection technology (in-receiver) usually applies to the
C/A code-based observable, and can increase the mapping accuracy by 50%
(differential code positioning with a multipath rejection technology can be
good to 30-35 cm in horizontal and 40-50 cm in vertical directions).
• Signal processing techniques, however, can reject the multipath signal only
if the multipath distance (difference between the direct and the indirect
paths) is more that 10 m.
• In a typical geodetic/surveying application, however, the antenna is about 2
m above the ground, thus the multipath distance reaches at most 4 m;
consequently, the signal processing techniques cannot fully mitigate the
effects of reflected signals.
Civil and Environmental Engineering and Geodetic Science
Multipath
• However, properly designed choke ring antennas can almost entirely
eliminate this problem for the signals reflected from the ground and the
surface waves
• The multipath from the objects above the antenna still remains an
unresolved problem
• The performance of the choke ring antennas is usually better for L2 than for
L1, the reason being that the choke ring can be optimized only for one
frequency. If the choke ring is design for L1, it has no effect for L2, while a
choke ring designed for L3 has some benefits for L1.
• Naturally, the optimal solution would be to have choke rings optimized
separately for L1 and L2, which is the expected direction of progress for the
geodetic antennas.
Civil and Environmental Engineering and Geodetic Science
Multipath mitigation
Receiver and Observable Type
GPS CardTM
GPS CardTM with choke ring antenna
P-XII C/A- code
P-XII C/A-code with choke ring antenna
P-XII P-code
P-XII P-code with choke ring antenna
Measuring
Noise
10 cm
100 cm
10 cm
Noise Plus
Multipath
70 cm
30 cm
300 cm
200 cm
70 cm
30 cm
Civil and Environmental Engineering and Geodetic Science
GPS Major Error Sources
Interference and jamming (intentional interference)
• Radio interference can, at minimum, reduce the GPS signal’s apparent
strength (that is reduce the signal to noise ratio by adding more noise) and
consequently – the accuracy, or, at worse, even block the signal entirely
• Medium-level interference would cause frequent losses of lock or cycle
slips, and might render virtually useless data.
• It is, therefore, important to make sure that the receiver has an
interference protection mechanism, which would detect and eliminate (or
suppress) the interfering signal.
Civil and Environmental Engineering and Geodetic Science
Main Sources of Errors and Their
Contributions to the Single Range
Observation Equation
Source
Satellite
- Orbit
- Clock
Signal propagation
- Ionosphere (2 frequencies)
- Ionosphere (model)
- Troposphere (model)
- Multipath Effects
- Relativistic Propagation
Receiver
- Observation Noise
- Hardware Delays
- Antenna Phase Center
P-code
SA off
SA on
C/A-code
SA off
SA on
5m
1m
10 - 40 m
10 - 50 m
5m
1m
10 - 40 m
10 - 50 m
cm - dm
dm
1m
~ 2 cm
cm - dm
dm
1m
~ 2 cm
cm - dm
2 - 100 m
dm
5m
~ 2 cm
cm - dm
2 - 100 m
dm
5m
~ 2 cm
0.1 - 1 m
dm - m
mm - cm
0.1 - 1 m
dm - m
mm - cm
1 - 10 m
m
mm - cm
1 - 10 m
m
mm - cm
Civil and Environmental Engineering and Geodetic Science
Earth Rotation Correction
• If the observation equation is expressed in the terrestrial reference
frame, ITRF, then the Earth rotation correction must be applied to the
satellite coordinates.
• During the signal propagation from the transmitter to the terrestrial
antenna, the ITRF frame rotates with the Earth with respect to the
satellite (at the equator it rotates by ~ 32 m).
• As a consequence, the position of the transmitter’s antenna at the
time of signal transmission has changed in the ITRF frame.
• Thus, the spacecraft’s coordinates at the transmission time must be
rotated forward about the third axis of the ITRF frame by the amount
equal to the propagation time dt (~0.07 s) multiplied by the Earth’s
rotational velocity, e. The angle of rotation is expressed as follows:
   e dt
X ECEF rotated  R3 ( ) X ECEF original
Civil and Environmental Engineering and Geodetic Science
Relativistic Effects
 Moving clock seems to run slower than the one at rest
 consequently for the satellite, the orbital period T would be measured shorter
 furthermore, nominal emitted frequency f=2/T would appear to be higher
 Four Primary Effects on GPS
• Gravitational field causes relativistic perturbation of the satellite orbit
• Gravitational field causes space-time curvature of the signal, thus propagation correction has
to be applied to the phase observable
• The motion of the satellite and the fact the the satellite and observer are located in different
parts of gravitational field (special and general relativity) result in relativistic frequency
difference between the two
• Relativistic effect on GPS receiver clock (due to the fact that the receiver is placed in the
gravitational field and rotates with the Earth) is corrected by the receiver software; it amounts to
1ns = 30 cm after 3 hours
Civil and Environmental Engineering and Geodetic Science
Relativistic Effects
• The combined effect of a direct relativistic effect on the orbital motion of the
satellite (relativistic perturbation) and the phase observable amounts to 0.001 ppm
in positioning
• Earth gravitation and the fact that the satellite moves, affect the satellite clock’s
frequency at the order of 1010
• The dynamic and propagation effects strongly depend on the geometry
between station, satellite and geocenter
• The maximum effect in the range units (ct) for the single phase
measurement is 19 mm.
• This effect is significantly reduced (to 0.001 ppm) for the relative positioning.
Civil and Environmental Engineering and Geodetic Science
Relativistic Effects (cont.)
• The phase measurement relativistic propagation correction reads as
follows (max 19 mm)
t  2GM / c  lnr  R   / r  R  
3
r, R - geocentric distances to the satellite and station, respectively,
 - range distance between satellite and the receiver,
c - speed of light in a vacuum,
GM - gravitational constant multiplied by the mass of the Earth.
Civil and Environmental Engineering and Geodetic Science
Relativistic Effects (cont.)
• The constant drift which is a part of the total correction due to relativistic time
difference between the receiver and the satellite is compensated for before
launch time by reducing the frequency of the satellite clock by 0.00455 Hz from
its nominal value of 10.23 MHz.
• However, the periodic term has to be modeled
• for GPS altitude, it has the maximum amplitude of ~30 ns in time or 10 m
in distance
• the periodic part can be canceled by performing between-stations
differencing, but for point positioning is still harmful if not properly
accommodated.
Civil and Environmental Engineering and Geodetic Science