GEOG 425/525
GPS Concepts and
Techniques
John Benhart, Ph.D.
Indiana University of PA
Dept. of Geography & Regional Planning
What Are
Global Positioning Systems
(GPS)?
What is GPS Used For?
The Historical Context of the
Global Positioning System (GPS)
• The origins of surveying:
– Efforts to measure distance on the earth’s
surface
– Efforts to specify location on the earth’s
surface
– Efforts to determine property/land boundaries
• How?
How Eratosthenes Estimated
the Earth’s Size
Early Estimates of the
the Earth’s Size
1753 French Survey Establishes that the
Earth Bulges at the Equator
The Basics of Surveying
• Definition: The science of measuring and
mapping relative positions above, on, or below
the surface of the earth; or establishing such
positions from a technical plan or title description
• Types:
– Plane surveying: Does not take into account the
curvature of the earth
– Geodetic surveying: measurements covering larger
distances where the curvature of the earth must be
taken into account
Surveying: History
• Evidence of surveying has been recorded as
early as 5,000 years ago
• Ancient Egyptian surveyors called
harpedonapata (“rope stretcher”
– Ropes and knots were tied at pre-determined
intervals to measure distances
– The 3-4-5 triangle (later formalized by Pythgoras) was
discovered to derive a right angle easily by using a
rope knotted at 3,4, and 5 units
– Early Egyptian levels that were essentially plumb
lines were derived
Surveying: History
• Surveying inventions
– Lodestone used to identify magnetic north
– Thomas Diggs invents an instrument used to
measure angles called the theodolite in the
mid-1500s
– Jean Praetorius invents the plane table in
1610
– W.J. Young invents the transit based on the
theodolite, which “flips” to allow back sighting
in 1831
Theodolite
How a Theodolite Works
Plane Table and
Alidade
Surveyor’s Transit
Total Station
The Basics of Surveying
• Starting from a position with a known
location and elevation, known as a
“benchmark,” the distance and angles to
the unknown point are measured
– Using a leveled theodolite or total station
– Distance: previously chains, now lasers
– Horizontal angle: from compass on theodolite
– Vertical Angle: sighted in on a measuring or
leveling rod at the location in question
The Historical Context of the
Global Positioning System (GPS)
• 1978 – launch of first GPS satellite
• 1982 – macrometer prototype tested at MIT
• 1984 – geodetic network densification in
Montgomery, Co. PA
• 1989 – Launch of first Block II satellite; Wide Area
GPS concept tested
• 1990 – GEOID90 for NAD83 datum established
• 1993 – Real-time kinematic GPS implemented
• 1996 – First US GPS policy expressed in
presidential directive
• 1999 – US GPS modernization initiative
• 2000 – Selective availability (SA) deactivated
Overview of GPS - Logic
• A continuous coverage of satellites exists within view of
virtually every location on the earth’s surface (NAVSTAR)
• These satellites launch signals at recorded times on
specific frequencies that can be “received” by units on the
earth’s surface
• By calculating the amount of time it takes the signals from 4
satellites to reach a receiver on the earth surface, it is
possible to determine the distance between the receiver
and any satellite (pseudoranges)
• By using the intersection of the radii from 4 satellites, it is
possible to determine exactly where a GPS receiver is
located on the earth’s surface (trilateration)
** A huge amount of science and technology has to be applied
for any of these conditions above to exist…
Overview of GPS - Objectives
• The GPS was “conceived as a ranging system
from known positions in space to unknown
positions on land, at sea, in air and space.” (p.11)
• The original objectives of GPS were
“instantaneous determination of position and
velocity (i.e. navigation), and the precise
coordination of time (i.e. time transfer).”
• “The global NAVSTAR Global Positioning System
(GPS) is an all-weather space-based navigation
system under development by the DoD to satisfy
the requirements of the military forces to
accurately determine their position, velocity and
time in a common reference system, anywhere on
or near Earth on a continuous basis.”
Overview of GPS
• GPS can be conceptually be divided into 3
segments:
– Space Segment: the constellation of satellites
– Control Segment: tracking and monitoring of
the satellites
– User Segment: varying user applications and
receiver types
Overview of GPS
• Space Segment
– The NAVSTAR constellation: 24 evenly-spaced
satellites in 12-hour orbits inclined 55 degrees to the
equatorial plane…each is assigned a pseudorandom
noise code # (PRN code)
• Types: Block I, Block II, Block IIA, IIR, IIF, and Block III
– Continuous signal coverage of every location on the
earth’s surface
– Satellite signals: launched at extremely-precisely
recorded times (atomic clocks), and travel at the speed
of light (through earth atmosphere) to receivers on the
earth’s surface
• L1: 1575.42 MHz, L2: 1227.60 MHz
Overview of GPS
• Control Segment
– Master control station: located at the
Consolidated Space Operations Center at
Shriver Air Force Base, Colorado Springs, CO
• Collects monitoring data from global stations
• Calculates satellite orbits and clock parameters for
each satellite…passed to ground control stations
• Responsibility for satellite control
Overview of GPS
• Control Segment
– Monitoring Stations: Five located at Colorado Springs,
Hawaii, Ascension Island (South Atlantic), Diego Garcia
(Indian Ocean), Kwajalein (North Pacific)
• Precise atomic time standard
• Continuous calculation of satellite pseudoranges
• Official network for determining broadcast ephemerides
– Ground Control Stations
• Also located at Ascension, Diego Garcia, and Kwajalein
• Communication links to upload ephemeris, and clock
information to NAVSTAR satellites
GPS Monitoring Locations
Overview of GPS
• User Segment
– Military Users
• Original envisioned users; have access to precise
P-code satellite signals
– Civilian Users
• Range from recreational to GIS and survey grade
applications – all made possible by federal
infrastructure
– Receiver Types
• C/A code pseudorange; C/A code carrier phase; Pcode carrier phase; Y-code carrier phase
GPS Summary
• The system is predicated on:
– A constantly monitored constellation of
satellites
– Very accurate time measurement
– The ability to determine satellite location
– The use of unique radio signals on specified
wavelengths launched from satellites and
received by receivers on the earth’s surface
– The ability to translate pseudoranges into
recognized coordinates through trilateration
Reference Systems
• GPS satellites are orbiting earth and launching
signals with time stamps…we are usually trying
to determine locations on earth…to do this we
have to define suitable coordinate and time
systems
• 3 Types of reference systems that are relevant
in the context of GPS
– Earth-fixed reference: the international terrestrial
reference system
– Space-fixed reference: the international conventional
celestial reference system
– Geodetic reference system
The Earth and Its Axis of Rotation
• The Earth’s axis of rotation changes over time
• Why? 1) Mainly caused by the gravitational forces of
the moon and the sun…as well as other celestial
bodies 2) changes in the mass of earth-based
phenomena
– Precession – a slight change in the direction of the axis of
the rotating earth
– Nutation - a slight irregular motion in the axis of rotation of
an axially symetrical body (planet)
– Polar Motion - the movement of the earth’s axis across its
surface (~ 20 m westward since 1900)…due to motions in
the earth’s core and mantle, and redistribution of water
mass
• Who Cares? These factors cause the position of the
earth in its orbit (revolution) around the sun to
change over time (equinoxes and solstices)
• Precession
• Nutation
• Polar Motion
Precession: Cause
The gravitational pull of the sun on the closest part of the oblate spheroid is stronger…
Precession: Result
Nutation
Reference Systems and
Reference Frames
• Reference Systems: the complete
specification of a coordinate system, such
as the origin, coordinate axes, coordinate
units, etc.
• Reference Frames: consist of a set of
identifiable points along with their
coordinates, which serve as a realization
of the reference system
International (Conventional)
Celestial (Space) Reference
System
• The celestial reference system adopted by the
International Astronomical Union (IAU) for highprecision positional astronomy
• Characteristics: Origin at the solar system
barycenter (center of mass) and “space fixed”
axis directions
• Has been chosen by the IAU as the “most
appropriate coordinate system for expressing
reference data on the positions and motions of
celestial objects.”
International (Conventional)
Celestial (Space) Reference
System
• A set of specifications based on spacefixed axes defining the location of bodies
in space
• For example, the base plane of the system
is the extension of the earth’s equatorial
plane at J2000.0 (Jan. 1, 2000)
• Locations (of planets and stars) are
specified based on declination (northsouth) and right ascension (east)
Earth-Centered
Earth-fixed Reference
• The mass center of the earth is used as a
reference
• Conventional Terrestrial Reference System: X
axis is identical to the mean Prime (Greenwich)
Meridian; Z axis is identical to the earth’s mean
rotational axis (also called the Conventional
International Origin (CIO)); Y axis points to the
mean equatorial parallel
• See www.iers.org (the International Earth
Rotation and Reference Systems Service)
International Union of Geodesy and
Geophysics (1991) Resolution on the
Conventional Terrestrial Reference
System
The International Union of Geodesy and Geophysics,
Considering the need to define a Conventional Terrestrial Reference System (CTRS) which would be unambiguous at the
millimeter level at the Earth's surface and that this level of accuracy must take account of relativity and of Earth deformation, and
noting the resolutions on Reference Systems adopted by the XXIst General Assembly of the International Astronomical Union
(IAU) at Buenos Aires, 1991, endorses the Reference System as defined by IAU at the XXIst General Assembly at Buenos Aires,
1991 and recommends the following definitions of the CTRS:
1) CTRS to be defined from a geocentric non-rotating system by a spatial rotation leading to a quasiCartesian system,
2) the geocentric non-rotating system to be identical to the Geocentric Reference System (GRS) as
defined in the IAU resolutions,
3) the coordinate-time of the CTRS as well as the GRS to be the Geocentric Coordinate Time (TCG),
4) the origin of the system to be the geocenter of the Earth's masses including oceans and atmosphere,
and,
5) the system to have no global residual rotation with respect to horizontal motions at the earth's surface.
International (Conventional)
Terrestrial (Earth)
Reference System
The International Terrestrial
Reference Frame
• The Earth is constantly changing shape, because of
plate tectonics and regional subsidence and/or used
to represent the Earth when measuring its rotation
in space.
• To be understood in context, when the motion of the
Earth's crust is observed, it must be referenced. A
Terrestrial Reference frame provides a set of
coordinates of some points located on the Earth's
surface. It can be used to measure plate tectonics,
regional subsidence or loading and/or used to
represent the Earth when measuring its rotation in
space.
The International Terrestrial
Reference Frame
• This rotation is measured with respect to a frame tied
to the celestial reference frame. The International
Earth Rotation and Reference Systems Service
(IERS) was created in 1988 to establish and
maintain a Celestial Reference Frame, the ICRF, a
Terrestrial Reference Frame, the ITRF.
• The Earth Orientation Parameters (EOPs) connect
these two frames together. These frames provide a
common reference to compare observations and
results from different locations
• Reference locations are periodically evaluated for
position change to re-define the reference frame
• The ITRF is regularly updated by the IERS…the
latest frame is ITRF 2005
Earth-Centered
Earth-fixed Reference
• World Geodetic System of 1984 (WGS84)
– The reference system utilized in GPS
– Provides the basic reference frame and
geometric figure for the earth, based on the
USDMA (Defense Mapping Agency’s)
measurements and modeling of the earth
from a geometric, geodetic, and gravitational
standpoint, using techniques and technology
available in 1984
Earth-Centered
Earth-fixed Reference
• World Geodetic System of 1984
– WGS84: a = 6,378137 m, f = 1/298.2572236
– Geocentric coordinate system originally
realized from the coordinates of approx. 1500
reference stations derived from TRANSIT
observations
– Uniform specification of the earth’s size,
shape, geoid surface characteristics, and
reference station coordinates (unlike ITRF)
WGS84
Reference Systems
• Time – 3 major systems are used in GPS
– Sidereal time: a measure of the earth’s rotation…defined
as the hour angle of the vernal equinox (ie.
– Dynamical time: a uniformly-scaled time used to
describe the motion of bodies in a gravitational field
• Terrestrial dynamic time may be used to describe satellite
motion without taking into account the gravitational field of the
sun
– Atomic time: time systems kept and defined by atomic
clocks such as International Atomic Time (IAT)
• Uniformly-scaled time used in earth-centered coordinate
systems
• Because of the slowing of the earth’s rotation with respect to the
sun, “leap seconds” are used to create the Coordinated
Universal Time System (UTC)
• In most cases UTC and GPS time are synonymous….it is the
basis of GPS time calculations
Reference Systems –
Time Systems
• GPS Calendar references
– Julian Date (JD): defines the number of mean solar
days elapsed since January 1, 4713 BC
– Modified Julian Date (MJD): obtained by subtracting
2,400,000.5 days from JD
• Saves digits and has MJD start at midnight instead of noon
– GPS standard epoch (time, calendar): the atomic
time scale implemented by the atomic clocks in GPS
ground control stations and satellites
• GPS standard epoch was initiated on Jan. 6th, 1980
• Current GPS reference to January 1, 2000 (J2000.0)
Inertial Frame of Reference
• A reference frame in which…
– Newton’s first and second laws of motion are
valid: inertia; acceleration
• Newton’s laws are valid in an environment
that is nether rotating nor accelerating
relative to other bodies
• By contrast, bodies may be subject to
forces that result from the acceleration of
the reference frame itself….
Earth-Fixed (Non-Inertial)
Frame of Reference
• One in which a body violates Newton’s law
of Motion….that is, it is rotating or
accelerating
– An example of an non-inertial frame is an
earth-fixed coordinate reference, as the earth
is rotating and body (satellite) motion is
measured with respect to it
Inertial vs. Earth-fixed Reference
• The inertial frame of reference is
theoretical….
• Therefore, a satellite’s orbit, and it
relational location to the earth, must be
translated into an earth-fixed reference
• One that takes into account the movement
of the earth, including rotation, gravity
impacts, etc.
Johannes Kepler – 1571-1630
Scientist and Astronomer
Developed
important
theories (laws)
regarding
planetary orbits…
Terms Relating to Keplerian Motion
• Perigee: closest approach of a satellite
with respect to the earth’s center of mass
• Apogee: most distant position (in an orbit)
”“
• Nodes: intersections between the
equatorial and orbital planes
• Anomaly: instantaneous position of a
satellite within its orbit
What are we Saying?
• The orbits of satellites around the earth can be
described by an ellipse…that has the following
characteristics (parameters):
–
–
–
–
–
–
Right ascension of the ascending node
Inclination of the orbital plane
Argument of the perigree
Semimajor axis of the orbital ellipse
Numerical eccentricity of the ellipse
Epoch of the perigree passage
• Orbits do not occur in an inertial environment
Keplerian Motion and
Perturbed Motion
• Perturbed motion is “characterized by the
temporal variations of orbital parameters.”
– Caused by: gravitational forces (sun, moon),
solar radiational pressure, eclipse periods,
etc.
• Perturbed motion also causes the
Keplerian orbit model specification to be
modified
Almanac
• A data file that contains the approximate
orbit information of all satellites, which is
transmitted by each satellite within its
Navigation Message. It is transmitted by a
GPS satellite to a GPS receiver, where it
facilitates rapid satellite signal acquisition
within GPS receivers.
Broadcast Ephemeris
• The "Broadcast Ephemeris (or
Ephemerides)" for a satellite are the
predictions of the current satellite position
and velocity determined by the Master
Control Station, uploaded by the Control
Segment to the GPS satellites, and
transmitted to the user receiver in the Data
Message.
Sources of Error
Typical amount of
Error (per Satellite)
Beyond quality of equipment/size of antennea, etc.
• Satellite Atomic Clock Errors
(corrected periodically)
1.5 m
• Satellite Orbit (Position) Errors
(corrected periodically)
2.5 m
• Earth’s ionosphere (charged particles)
5.0 m
• Earth’s troposphere (moisture)
0.5 m
• Receiver Noise (local conditions, radio interference) 0.3 m
• Multipath Errors (bounce off buildings, etc.)
• Local Weather (moisture in air, lightning)
• Poor Satellite Geometry (GDOP)
• Receiver Clock Errors (corrected by 4th + Satellites)
0.6+ m
GPS Masks: PDOP, Elevation,
SNR
Allow the user to control the quality of the data accepted at the time
of data collection (unacceptable readings are filtered out)
PDOP Mask: Allows the recording of positions only when there is
acceptable satellite geometry. Typically considers both quantity
and quality of satellites (e.g., 4 satellites with good precision, or
6 with reasonable precision, or 8 with average precision)
Elevation Mask: Sets minimum elevation above horizon for satellites to
be used. The lower on the horizon a satellite is the more
atmosphere the signal must pass through, thus the greater the
potential for signal diffraction (inaccurate estimations of
time/distance), as well as greater chance of multi-path errors.
Also, with Differential Correction, insures that all satellites used
are visible to base station as well as the field receiver.
SNR (Signal to Noise Ratio) Mask: (higher is better, stronger signal)
Filters out signals with excessive noise, using only those
satellites with low noise (more accurate). SNR ranges from 0-35;
10-15 is typical, less than 5 is generally considered unusable.
Differential Correction
• Can improve accuracy by up to 20 m. (50-90%)
• Requires local Base Station (w/in 100 miles)
• Requires “post-processing” (back in the lab)
OR can be done on-the-fly using Real-Time DGPS
• Need better data – longer recording period, better GDOP
• More Base Stations near coasts (navigation)
• No effect on multi-path and/or receiver errors
Differential Correction
Compare GPS data file from Rover file (handheld unit) with
a data file from a Base Station (at a known coordinate) for
the exact same time period. Relies on the fact that receivers
located relatively close together, will record similar errors
from the same constellation of satellites.
Uses the apparent “error” of the base station file to correct
the corresponding error of the Rover file.
Differential Correction 2
10m
GPS
Estimated Location
Receiver
(unknown Location)
Actual (Known)
Position
GPS Receiver
Estimated Location
Differentially Corrected
Estimated Position
10m
Base Station
(w/known coordinates)
GPS Data Collection Procedure
Using Trimble TerraSync
• Once you start the unit up and check
status (navigation screen)
• You will open a new data collection file
– .SSF file (default DDMMYYHH.SSF)
• A .DDF file is required data collection in an
.SSF file (data dictionary)
– A default is provided if one is not selected
• The .DDF file becomes the template for
the positional definition of features
THE GPS SIGNALS
Each Satellite transmits two carrier waves
L1 - frequency of 1575.42 MHz and a wavelength of approx 19cm
L2 - frequency of 1227.60 MHz and a wavelength of approx 24cm
The following satellite-specific signals, called the pseudo random noise (PRN)
codes are modulated on the carrier waves:
On L1: C/A (Coarse/Acquisition) code λ = approx 300m
- Accessible to civilian users
- Consists of a series of 1023 binary digits (called chips) that are
unique to each satellite.
- The chip pattern is repeated every millisecond
P (precise) code λ = approx. 30m
- Accessible only to military equipment
On L2: P code only
SVs transmit two microwave carrier (carry information) signals
L1 (1575.42 MHz): carries navigation message; SPS code
(SPS: standard positioning service)
L2 (1227.60 MHz): measures ionospheric delay
3 binary codes shift L1 and/or L2 carrier phases
C/A code (coarse acquisition) modulates L1 carrier phase
…repeating 1 MHz pseudo random noise (PRN) code
…pseudo-random because repeats every 1023 bits or
every millisecond…each SV has its own C/A code
…basis for civilian SPS
P-code (precise) modulates both L1 and L2
…long (7 days) pseudo random 10 MHz noise code
…basis for PPS (precise positioning service)
…AS (anti-spoofing) encrypts P-code into Y-code
(need classified module for receiver)
navigation message modulates L1-C/A; 50 Mhz signal
….describes satellite orbits, clock corrections, etc.
GPS receiver produces replicas of C/A and/or P (Y) code
receiver produces C/A code sequence for specific SV
C/A code generator repeats same 1023 chip
PRN code sequence every millisecond
PRN codes defined for
32 satellite ID numbers
modern receivers usually store complete set
of precomputed C/A code chips in memory
GPS Satellite Signals
• (Coarse Acquisition or C/A) Code Phase
– Based on each satellite’s unique pseudo Random Noise Code
(PRN)
– Each satellite’s PRN code is totally unique, and can be
replicated by GPS receivers
– The receiver “slides” its code later and later in time until it
matches up with the satellite’s code (code correlation)
– This is called “code phase lock”…however, even if this is
achieved, there can be significant error
• Because the PRN codes are not that complicated (large cycle width
~ microsecond ~ 300 m. of error)
• Even with highly accurate code phase lock, error can be 5-10
meters (with the signal traveling at 180,000 miles per second)
Code Signal Positioning
Subframe of message
Receiver Signal
Time Delay
Matching Subframe
Delayed Satellite Signal
The ‘mis-match’ between the code patterns is a measure of the
time the signal has taken to travel from satellite to receiver.
GPS Observables – Code Phase
• The Pseudorange: The GPS receiver
measures the distance between the
satellite and antenna by measuring the
time the signal takes to propagate from the
satellite to the receiver…the pseudorange
is the time offset multiplied by the speed of
light
Code Pseudorange
• Based on travel time between when
signal is sent and when it is received
• Time data also includes errors in both
satellite and receiver clocks
– Δt = tr – ts = [tr(GPS)-δr] – [ts(GPS) – δs]
• Pseudorange given by R = c Δt = ρ + cΔδ
– Pseudo because of cΔδ (where Δδ = δs – δr)
factor
Code Phase Acquisition
• Code phase estimation
• PRN code characteristics
– Maximum autocorrelation at lag 0
– Minimum auto-correlation in all other cases
– Minimum cross-correlation in all cases
• Generate local PRN code
• Perform circular correlation to obtain code
phase
• Code phase is the circular shift of the local
code that gives maximum correlation
receiver slides replica of code in time until
finds correlation with SV signal
(codes are series of digital numbers)
if receiver applies different PRN code to SV signal
…no correlation
when receiver uses same code as SV and codes begin to align
…some signal power detected
when receiver and SV codes align completely
…full signal power detected
usually a late version of code is compared with early version
to insure that correlation peak is tracked
Acquisition
Incoming
code
Generated
code
Correlation
0
1
2
3
4
5
6
7
Code tracking
• Enhance the accuracy of code phase
obtained by acquisition
• Generate three local PRN codes 0.5 chips
apart
– Early
– Prompt
– Late
• Correlate the local codes with incoming
code
• Adjust code phase according to result of
correlation
Code tracking
Incoming code
Early
Prompt
Late
Correlation
1
0.5
0
-1
-0.5
0
0.5
1
Delay in chips
GPS Satellite Signals
• Carrier Phase
– The carrier signal has a much higher frequency than
the PRN code, and therefore if “matched” has a much
higher level of accuracy
– The carrier signal is ambiguous…that is it is much
less differentiated than the PRN code
– The code correlation is used to “narrow down” the
time frame of signal travel…then the carrier signal is
used to very accurately determine signal travel time
– Used for high end mapping grade and survey grade
GPS
Carrier Phase
• Based on the number of cycles
(wavelengths) between satellite and
receiver
• Phase data will include errors in both the
satellite and receiver as well as an initial
integer number, N

 c
   N
 
R    c  N
Combinations of
Code and Carrier Phase
• “Smoothing” of the code pseudorange
using carrier phase correlation
• Several different algorithms
Carrier Phase Acquisition
• Acquisition purpose
– Estimate coarse value of PRN code phase
– Estimate coarse value of carrier frequency
• Operates on 1ms blocks of data
– Corresponds to the length of a complete PRN
code
Acquisition
• Carrier frequency estimation
• Generate local carrier
• Adjust frequency until highest correlation
is obtained
Acquisition
Correlation
1
2
3
4
5
6
7
8
Acquisition
• Correct value for code phase and carrier
frequency provides a peak correlation
Carrier Tracking
• Enhance the accuracy of the carrier frequency
obtained by acquisition
• Generate local carrier signal
• Measure the phase error between incoming
carrier and local carrier signal
• Adjust frequency until phase and frequency
becomes stable
PRN code
Incoming
signal
Phase
discriminator
NCO carrier
generator
Loop
filter
GPS signal
Carrier
wave
1 data bit
Navigation
data
Carrier
and data
1ms
20ms
GPS signal
Carrier
and data
PRN code
Resulting
signal
GPS Navigation Message
• The GPS navigation message consists of timestamped data bits marking the time of
transmission of each data bit frame
– A data (bit) frame is transmitted every 30 seconds
and is comprised of 1500 bits, subdivided into 5 300bit subframes
• Subframe 1 – Clock correction (6 seconds)
• Subframes 2 and 3 – Ephemeris data for short segments of a
satellite’s orbit
• Subframe 4 – Ionospheric corrections (GPS-UTC time offset)
• Subframe 5 – Almanac information
– An entire navigation message (25 data frames made
up of 125 subframes) is sent over a 12.5 minute
period
GPS Navigation Message
Important tasks of a GPS receiver
• Prepare received signals for signal processing
• Find satellites visible to the receiver
• For each satellite
– Find coarse values for C/A code phase and carrier frequency
– Find fine values for C/A code phase and carrier frequency
– Keep track of the C/A code phase and carrier frequency as
they change over time
– Obtain navigation data bits
– Decode navigation data bits
– Calculate satellite position
– Calculate pseudorange
• Calculate position
Surveying with GPS
• Terminology
– Code range: less complex, unambiguous
signal…lower level of accuracy
– Carrier range: more complex, ambiguous
signal…higher level of accuracy
– Real-time processing: position results must be
available in the field immediately
– Post-processing: positional data are
processed later
Surveying with GPS
• Terminology continued
– Point positioning: a single receiver measures
pseudoranges
– Differential positioning: an improved point positioning
technique where corrections are applied to
pseudoranges
– Relative positioning: two receivers are used, and
simultaneously receive signals from the same
satellites
– In general…point = navigation; relative = surveying,
carrier phase; differential = code phase
Surveying with GPS
• Terminology continued
– Static point positioning: derivation of point
positions without correction; 10 m accuracy
– Static relative positioning (static surveying,
carrier): most accurate; surveying technique;
determination of the vector between two
stationary receivers; cms. accuracy
– Kinematic relative positioning: two receivers
perform observations simultaneously; one is
stationary and one is moving
Surveying with GPS –
Observation Techniques
• Point Positioning
– Standard Positioning Service is standard for
civilian users
– Precise Positioning Service for military
• Differential GPS: Two or more receivers
are used…one as a stationary “base”, and
the other as a mobile “rover”
– Position correction; and pseudorange
correction
Differential GPS
• Real-Time
– Wide Area Augmentation System (WAAS)
– Originated for commercial air flights
• Post-Processing
– National Oceanic and Atmospheric
Administration (NOAA) National Geodetic
Survey (NGS) Continuously Operating
Reference Station (CORS) network
Real-Time DGPS:
The WAAS Network
• Wide Area Augmentation System –
– Wide area ground reference stations (WRS) have been
linked to form a U.S. WAAS network.
• Signals from GPS satellites are received by these precisely
surveyed ground reference stations and any errors in the signals
are identified.
– Each station in the network relays the data to one of two
wide area master stations (WMS) where correction
information for specific geographical areas is computed.
– A correction message is prepared and uplinked to a
geostationary communications satellite (GEO) via a ground
uplink station (GUS).
– This message is broadcast on the same frequency as GPS
(L1, 1575.42 MHz) to GPS/WAAS receivers within the
broadcast coverage area
Wide Area Augmentation System
(WAAS)
Base Station Data:
Where Does it Come From?
• In many cases, base station data in the
United States is obtained from the
National Oceanic and Atmospheric
Administration (NOAA) National
Geodetic Survey (NGS)
•USNGS administers a program called
CORS – Continuously Operating
Reference Stations
•Data from a network of base stations
across the US is available…including
customized data sets
Surveying with GPS –
Relative Positioning
• “…the highest accuracies are achieved in
the relative positioning mode with
observed carrier phases.”
– Processing of baseline vectors
– Static relative positioning
– Kinematic relative positioning
– Pseudokinematic relative positioning
Surveying with GPS –
Planning a GPS Survey
• The Federal Geodetic Control
Subcommittee (FGCS) has classified GPS
surveys based on the levels of accuracy
necessary
– A & B – very high accuracy geodetic control
– 1st, 2nd , 3rd – surveying, engineering,
topographic mapping
• The higher the accuracy requirements, the more
planning required
Planning a GPS Survey
• GPS Survey Planning Parameters:
– Site characteristics (obstructions, cover, etc.)
– Satellite configurations (number, constellation
dispersion, data quality)
– Number and type of receivers
• Primitives
– Where, When, How Long, Quality
Planning a GPS Survey
• When – determination of the optimum
daily observation period(s)
– The period when the maximum number of
satellites can be observed simultaneously
– The period when the most advantageous
constellation of SV azimuth/elevation
combinations is “in view”
– Use of Plan modules available on receivers
and/or lab software
What have We Covered
• Context of the GPS
• Structure of the GPS
• Reference Systems
– Earth-fixed, Space-fixed, Geodetic
– Time systems
• Satellite orbits
– Specification and characteristics
– Keplerian motion; perturbed motion
• Characteristics of Trimble GeoXH and GeoXT GPS
receivers
• GPS Satellite Signals
– Code phase; pseudoranges
– Carrier phase; ambiguity
What have We Covered
• Combination of Code and Carrier phases
(smoothing)
• GPS Navigation message explanation
• Explanation of PathFinder Office and
TerraSync softwares
• Hands-on use of PathFinder Office and
TerraSync softwares
• Data Dictionary expanation/development
• Field Data Collection
• High Accuracy (survey-grade) GPS
What You Should Have Obtained
• Project experience
– Needs assessment
– Database design
– Data development
• Final Project documents (portfolio)
• References
• Other?
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
X,Y,Z
(Lat, Lon, h) based on the definition of WGS84
ellipsoid
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).
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.
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.
Differences between WGS 84 (G873) Coordinates and WGS 84 (G730), compared at 1994.0
Station Location NIMA Station Number  East (cm)  North (cm)  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.
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.
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.
Other commonly used spatial reference systems
• North American Datum 1983 (NAD83)
• State Plane Coordinate System (SPCS) based on NAD83
• Universal Transverse Mercator (UTM)
North American Datum (NAD)
NAD27 established in 1927
 defined by ellipsoid that best fit the North American
continent, fixed at Meades Ranch in Kansas
over the years errors and distortions reaching several
meters were revealed
In 1970’s and 1980’s NGS carried out massive readjustment
of the horizontal datum, and redefined the ellipsoid
The results is NAD83 (1986)
 based on earth-centered ellipsoid that best fits the globe
and is more compatible with GPS surveying
 in 1990’s state-based networks readjustment and
densification, accuracy improvement with GPS (HARN and
CORS networks)
NAD 83 Defining Parameters
Parameter
Notation
Semi-major Axis
Reciprocal of Flattening
a
1/f
Magnitude
6378137.0 meters
298.2572221
Datum point – none
Longitude origin – Greenwich meridian
Azimuth orientation – from north
Best fitting – worldwide
X,Y,Z
(Lat, Lon, h) based on the definition of GRS80
ellipsoid
State Plane Coordinate System
 Based on Lambert and Transverse Mercator projections
 Developed in 1930’s and redefined in 1980’s and 90’s
 NAD ellipsoid was projected to the conical (Lambert)
and cylindrical (Transverse Mercator) flat surfaces
Allowed the entire USA to be mapped on a set of flat
surfaces with no more than one foot distortion in every
10,000 feet (maximum scale distortion 1 in 10,000)
 Coordinates used are called easting and northing;
derived from NAD latitude, longitude and ellipsoidal
parameters
Lambert projection
Lambert projection
Transverse Mercator Projection
State Plane Coordinate System
 The scale of the Lambert projection varies from north
to south, thus, it is used in areas mostly extended in the
east-west direction
 Conversely, the Transverse Mercator projection varies
in scale in the east-west direction, making it most suitable
for areas extending north and south
 Both projections retain the shape of the mapped surface
 Each state is usually covered by more than one zone,
which have their own origins – thus, passing the zone
boundary would cause the coordinate jump!
Universal Transverse Mercator, UTM
 Developed by the Department of Defense for military
purpose
 It is a global coordinate system
 Has 60 north-south zones numbered from west to east
beginning at the 180th meridian
 The coordinate origin for each zone is at its central
meridian and the equator
Universal Transverse Mercator
• UTM zone numbers designate 6-degree longitudinal
strips extending from 80 degrees south latitude to 84
degrees north latitude
• UTM zone characters designate 8-degree zones
extending north and south from the equator
• There are special UTM zones between 0 degrees and 36
degrees longitude above 72 degrees latitude, and a
special zone 32 between 56 degrees and 64 degrees north
latitude
UTM Zones
• Each zone has a central meridia. Zone 14, for example,
has a central meridial of 99 degrees west longitude. The
zone extends from 96 to 102 degrees west longitude
• Easting are measured from the central meridian, with a
500 km false easting to insure positive coordinates
• Northing are measured from the equator, with a 10,000
km false northing for positions south of the equator
Ohio State Plane (Lambert projection, two zones)
and UTM Coordinate Zone
Universal Transverse Mercator, UTM
Vertical Datum Definition 1/2
 Horizontal control networks provide positional information (latitude
and longitude) with reference to a mathematical surface called sphere or
spheroid (ellipsoid)
 By contrast, vertical control networks provide elevation with
reference to a surface of constant gravitational potential, called geoid
(approximately mean see level)
• this type of elevation information is called orthometric height
(height above the geoid or mean sea level) determined by spirit
leveling (including gravity measurements and reduction formulas).
 Height information referenced to the ellipsoidal surface is called
ellipsoidal height. This kind of height information is provided by GPS
Height Systems Used in the USA
 Orthometric
 Normal (orthometric normal)
 Dynamic
 Ellipsoidal
Variety of height systems (datums) used requires
careful definition of differences and transformation
among the systems
Vertical Datum Definition 2/2
 Vertical datum is defined by the surface of reference – geoid or
ellipsoid
 An access to the vertical datum is provided by a vertical control
network (similar to the network of reference points furnishing the access
to the horizontal datums)
 Vertical control network is defined as an interconnected system of
bench marks
 Why do we need vertical control network?
• to reduce amount of leveling required for surveying job
• to provide backup for destroyed bench marks
• to assist in monitoring local changes
• to provide a common framework
The height reference that is mostly used in
surveying job is orthometric
 Orthometric height is also commonly
provided on topographic maps
Thus, even though ellipsoidal heights are
much simpler to determine (eg. GPS) we still
need to determine orthometric heights
 - angle between the normal to the ellipsoid and the vertical direction (normal
to the geoid), so-called deflection of the vertical
H – orthometric height
h – ellipsoidal height
h=H+N
N – geoid undulation (computed from geoid model provided by NGS)
Normal to the
ellipsoid

P
H
h
N
Normal to the geoid
(plumb line or vertical)
terrain
geoid
ellipsoid
Orthometric vs Ellipsoidal Height
(Orthometric height)
(computed from a
geoid model)
So, how do we determine orthometric height?
 By spirit leveling
 And gravity observations along the leveling path, or
 Recently -- GPS combined with geoid models (easy!!!) but
not as accurate as spirit leveling + gravity observations
H = h-N
But why do we need gravity observations with spirit leveling?
Because the sum of the measured height differences along the
leveling path between points A and B is not equal to the difference
in orthometric height between points A and B
Why?
Level Surfaces and Plumb Lines 1/2
Equipotential surfaces are not parallel to each other
Level Surfaces and Plumb Lines 2/2
 The level surfaces are, so to speak, horizontal everywhere, they share
the geodetic importance of the plumb line, because they are normal to it
Plumb lines (line of forces, vertical lines) are curved
 Orthometric heights are measured along the curved plumb lines
Equipotential surfaces are rather complicated mathematically and they
are not parallel to each other
 Consequently:
 Orthometric heights are not constant on the equipotential
surface !
 Thus, points on the same level surface would have different
orthometric height !
Spirit leveling
Height differences between the consecutive locations of backward and forward rods
correspond to the local separation between the level surfaces through the bottom of the
rods, measured along the plumb line direction
Orthometric Height vs. Spirit Leveling
C4
dh4
dh3
C3
C2
dh2
dh1
C1
dhi  H
C1, C2, C3, C4 – geopotential numbers corresponding to level (equipotential)
surfaces
dh1, dh2, dh3, dh4 – height difference between the level surfaces (determined
by spirit leveling, path-dependent); their sum is not equal to H !
Because equipotential surfaces are not parallel to each other
Geopotential Numbers 1/3
 The difference in height, dh, measured during each set up of leveling can be
converted to a difference in potential by multiplying dh by the mean value
of gravity, gm, for the set up (along dh).
geopotential difference = gm*dh
 Geopotential number C, or potential difference between the geoid level
W0 and the geopotential surface WP through point P on the Earth surface (see
Figure 2-8), is defined as
P
 gdh  C  W
0
 WP
0
Where g is the gravity value along the leveling path. This formula is used to
compute C when g is measured, and is independent on the path of integration!
Geopotential Numbers 2/3
Since the computation of C is not path-dependent, the geopotential number
can be also expressed as
C = gm*H,
where H is the height above the geoid (mean sea level) and gm represents the
mean value of gravity along H (along the plumb line at point P on Figure 2-8;
see “orthometric height vs. spirit leveling)
 the last relationship justifies the units for C being kgal*meter; it is not used
to determine C!
 Finally:
 Geopotential number is constant for the geopotential (level) surface
 Consequently, geopotential numbers can be used to define height
and are considered a natural measure for height
REMEMBER: Orthometric heights are not constant on the equipotential
surface !
 Observed difference in height depends on leveling route
 Points on the same level surface have different orthometric heights
Local normal (plumb line direction) to
equipotential (level) surfaces
dhup
P1
dhdown
P2
S3
H1
Reference surface (geoid)
H2
S2
S1
Orthometric height measured
along the plumb line
direction
H = H1-H2  dhup + dhdown  0
No direct geometrical
relation between the
results of leveling and
orthometric heights
What then, if not orthometric height, is directly obtained
by leveling?
 If gravity is also measured, then geopotential numbers, C
(defined by the integral formula shown earlier), result from
leveling
 Thus, leveling combined with gravity measurements
furnishes potential difference, that is, physical quantities
 Consequently, orthometric height are considered as
quantities derived from potential differences
 Thus, leveling without gravity measurements introduces
error (for short lines might be neglected) to orthometric height
Geopotential Numbers 3/3
Let’s summarize:
The sum of leveled height differences between two pints, A and B, on the
Earth surface will not equal to the difference in the orthometric heights HA
and HB
The difference in height, dh, measured during each set up of leveling
depends on the route taken, as level (equipotential) surfaces are not parallel
to each other
 Consequently, based on the leveling and gravity measurements
 the geopotential numbers are initially estimated (using the integral
formula introduced earlier), based on the leveling and gravity
measurements along the leveling path
 geopotential numbers can then be converted to heights (orthometric,
normal or dynamic – see definitions below) if gravity value along the
plumb line through surface point P is known
Height = C/gravity
Height Systems 1/5
 In order to convert the results of leveling to orthometric heights we need
gravity inside the earth (along the plumb line)
 since we cannot measure it directly, as the reference surface lies within
the Earth, beneath the point, we use special formulas to compute the mean
value of gravity, along the plumb line, based on the surface gravity
measured at point P
reduction formulas used to compute the mean gravity, gm, based on
gravity measured at point P on the Earth surface lead to:
 Orthometric height, (H = C/gm) or
 The reduction formula used to compute mean gravity, based on normal
gravity at point P on the Earth surface leads to:
 Normal (also called normal orthometric) height, (H* = C/ m )
Where  is so-called normal gravity (model) corresponding to the gravity
field of an ellipsoid of reference (Earth best fitting ellipsoid), and subscript
“m” stands for “mean”
Height Systems 2/5
 We can also define dynamic heights
 use normal gravity, 45, defined on the ellipsoid at 45 degree
latitude, (HD = C/ 45)
Note: term “normal gravity” always refers to the gravity defined for
the reference ellipsoid, while “gravity” relates to geoid or Earth itself
Height Systems 3/5
Sometimes, instead of formulas provided above (involving C), it is
convenient to use correction terms and apply them to the sum of
leveled height differences:
 Consequently, the measured elevation difference has to be
corrected using so-called orthometric correction to obtain
orthometric height (height above the geoid)
Max orthometric correction is about 15 cm per 1 km of
measured height difference
 Or, the measured elevation difference has to be corrected using
so-called dynamic correction to obtain dynamic height (no
geometric meaning and factual reference surface; defined
mathematically)
 Or, normal correction is used to derive normal heights
 All corrections need gravity information along the leveling path
(equivalent to computation of C based on gravity observations!)
Height Systems 4/5
 Dynamic heights are constant for the level surface, and have no
geometric meaning
 Orthometric height
differs for points on the same level surface because the level
surfaces are not parallel. This gives rise to the well-known paradoxes
of “water flowing uphill”
 measured along the curved plumb line with respect to geoid level
 Normal height of point P on earth surface is a geometric height above
the reference ellipsoid of the point Q on the plumb line of P such as normal
gravity potential and Q is the same as actual gravity potential at P.
 measured along the normal plumb line (“normal” refers to the line
of force direction in the gravity field of the reference ellipsoid
(model))
 All above types of heights are derived from geopotential numbers
Height Systems 5/5
A disadvantage of orthometric and normal heights is that
neither indicates the direction of flow of water. Only dynamic
heights possess this property.
That is, two points with identical dynamic heights are on the
same equipotential surface of the actual gravity field, and water
will not flow from one to the other point.
Two points with identical orthometric heights lie on different
equipotential surfaces and water will flow from one point to
the other, even though they have the same orthometric height
The last statement holds for normal heights, although due to
the smoothness of the normal gravity field, the effect is not as
severe
Vertical Datums: NGVD 29 and NAVD 88
 NGVD 29 – National Geodetic Vertical Datum of 1929
• defined by heights of 26 tidal stations in US and Canada
• uses normal orthometric height (based on normal gravity formula)
 NAVD 88 – North American Vertical Datum of 1988
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• 585,000 permanent bench marks
• uses Helmert orthometric height (based on Helmert gravity formula)
• removed systematic errors and blunders present in the earlier datum
• orthometric height compatible with GPS-derived height using geoid
model
• improved set of heights on single vertical datum for North America
Vertical Datums: NGVD 29 and NAVD 88
 Difference between NGVD 29 and NAVD 88
• ranges between – 40 cm to 150 cm
• in Alaska between 94 and 240 cm
• in most stable areas the difference stays around 1 cm
• accuracy of datum conversion is 1-2 cm, may exceed 2.5 cm
• transformation procedures and software provided by NGS
(www.ngs.noaa.gov)
International Great Lake Datum (IGLD)
1985
 IGLD 85
• replaced earlier IGLD 1955
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• uses dynamic height (based on normal gravity at 45 degrees latitude)
• virtually identical to NAVD 88 but published in dynamic heights!
Vertical Datums
 Use of proper vertical datum (reference surface) is very
important
 Never mix vertical datums as ellipsoid – geoid separation can
reach 100 m!
 Geoid undulation, N, is provided by models (high accuracy,
few centimeters in the most recent model) developed by the
National Geodetic Survey (NGS) and published on their web
page
www.ngs.noaa.gov
So, in order to derive the height above the see level (H) with
GPS observations – determine the ellipsoidal height (h) with
GPS and apply the geoid undulation (N) according to the
formula H = h - N
Space-fixed Reference
• The Conventional Celestial Reference System
– Based on a kinematical definition, making the axis
directions defining the coordinate system fixed with
respect to distant matter of the universe
– A celestial reference frame defined by the precise
coordinates of extragalactic objects (mostly quasars)
– Based on IAU recommendations, the coordinate
origin is to be at the barycenter of the solar system,
and the axes should be fixed with respect to the
quasars
– Principal coordinate plane to be as close as possible
to the mean earth equator at J2000.0
Satellite Orbits
• Implementation of GPS depends heavily
on being able to quantify satellite orbits
• Keplerian Motion – a satellite is supposed
to move in a central force field
– Equation of satellite motion is described by
Newton’s second law of motion: where f is the
attracting force; m is the mass of the satellite
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
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
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
GPS Signals
• Carrier L1 and L2
• Codes superimposed on carrier
• P-code (precise/protected code, under AS it’s
replaced by a Y-code) on L1 and L2
• C/A – code (clear/coarse acquisition) on L1
• The fourth type of signal transmitted by GPS satellites
is the broadcast message (navigation message) on L1
and L2 (identical)
GPS Signal Structure
• 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
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!!!
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
APD(t)P(t)sin(1t)
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
GPS Message
• Data File - carrier phase, pseudorange, and 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)
GPS Navigation Message
SUBFRAME
NUMBER
1
T LM
HOW
CLOCK CORRECT ION
2
T LM
HOW
EPHEMERIS
T LM
HOW
EPHEMERIS
T LM
HOW
IONOSPHERE, ET C.
T LM
HOW
ALMANAC
3
4
5
1500 BITS
30 SEC.
EACH FRAME: -10 30-BIT WORDS, 6 SEC.
TLM = Telemetry Word
HOW = Handover Word (contains Zcount)
 TLM, telemetry word – contains a synchronization pattern which
facilitates the access to the navigation data
 HOW, handover word allows direct access to the P code; but first the
C/A code must be acquired to allow for time synchronization; this
allows an access to HOW from the navigation message, and then the Pcode can be acquired
• 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
But we don’t know the actual P-code (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 (correlation) provides the signal
travel time measure
• The PRN code (P-code) carried by the signal allows to
achieve that (if its known; currently, civilians know only C/A
code)
• But how do we get an access to the precise code under AS
policy, if the Y-code (replacing the P-code) is not known, and
thus, the time synchronization scheme will not work?
Techniques to recover L2 signal under AS
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
…………………….
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
0.0000
APPROX POSITION XYZ
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
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
RINEX 2 description:
http://www.ngs.noaa.gov/CORS/Rinex2.html
http://lox.ucsd.edu/GPSProcessing/Pythagoras/
rinex.html
GPS Observables
Data
•
•
•
•
•
Code Pseudorange
Carrier Phase Pseudorange
Doppler
Combinations of data
Biases and Noise terms
Doppler
• Doppler shift depends on radial velocity
– More useful for determining velocities than for
determining positions
• To get positions, need to integrate Doppler
shifts (phase differences)
d d
D

 c
dt
dt
Data Combinations
• Theoretically, data can be obtained from
– Code ranges – RL1, RL2
– Carrier phases – ΦL1, ΦL2
– Doppler shifts – DL1, DL2
• Combinations of these data could be used
as well
Data Combinations
• In general, linear combinations of phase
will look like
– φ = n 1 φ1 + n 2 φ2
– Where n1 and n2 can be any integer
• Noise level increases for combined data
– Assuming noise levels are equal for both, the
increase is by a factor of √2
Data Combinations
• If n1 = n2 = 1, then
– ΦL1+L2 = ΦL1 + ΦL2
• Denoted narrow-lane
• λL1+L2 = 10.7cm
• If n1 = 1 and n2 = -1, then
– ΦL1-L2 = ΦL1 – ΦL2
• Denoted wide-lane
• λL1-L2 = 86.2cm
• Used for integer ambiguity resolution
Data Combinations
• If n1 = 1 and n2 = –fL2/fL1, then
– ΦL3 = ΦL1 – fL2/fL1 ΦL2
– Called L3 (sometimes denoted ionospherefree)
• Used to reduce ionospheric effects
What to do with Errors?
• There are essentially 4 options:
– Ignore them
• Works if the errors are small (negligible)
– Model them
• Need good models
• Not all effects can be modeled
– Solve for them
• Increases complexity of solution
– Make them go away
GPS Ephemeris Errors
• 3 types of ephemerides
– Almanac – very crude (~100m), used only for
planning purposes
– Broadcast – reasonably accurate (~1m), used
for real-time work
– Precise – very accurate (~10cm), used for
high precision work
• Available after the fact
Selective Availability (SA)
• Way to degrade the navigation accuracy of
the code pseudorange
• Comprised of two parts:
– Dithering the satellite clock (δ-process)
– Manipulating the ephemerides (ε-process)
Selective Availability
• Dithering the satellite clock
– Changing the fundamental frequency
– Changes over the course of minutes
– Can be eliminated by differencing between
receivers
• Manipulating the ephemerides
– Truncating the navigational information
– Changes over the course of hours
Clock Errors
• Both satellites and receivers will have clock
errors
– There’s no such thing as a perfect clock
• Any error in a clock will propagate directly into
a positioning error
– Remember distance = velocity*time
• Satellite clock errors can be reduced by
applying the corrections contained in the
broadcast
Ionospheric Delay
• Caused by the electrically charged upper
atmosphere, which is a dispersive
medium
– Ionosphere extends from 40 to 1100 km
– Effects carrier phase and code ranges
differently
– Effect on the phase and group velocity
• nph = 1 + c2/f2 …
• ngr = 1 – c2/f2
– Note that this will effect frequencies
differently
• Higher frequency is affected less
Ionospheric Delay
• Measured range given by s = ∫n ds
– n is the refractive index
– ds is the path that the signal takes
• The path delay is given by
– Δphiono = –(40.3/f2) ∫Ne ds0 = –40.3/f2 TEC
– Δgriono = (40.3/f2) ∫Ne ds0 = 40.3/f2 TEC
• Where TEC = ∫Ne ds0 is the total electron content
Ionospheric Delay
• Still need to know TEC
• Can either
– Measure using observations
– Estimate using models
• Note that with data on 2 frequencies,
estimates of the unknowns can be made
Tropospheric Delay
• Caused by the neutral atmosphere, which is a
nondispersive medium (as far as GPS is
concerned)
– Troposphere extends up to 40 km
– Effects carrier phase and code ranges the same
• Typically separate the effect into
– Dry component
– Wet component
• ΔTrop = 10-6∫NdTrop ds + 10-6∫NwTrop ds
– Where N is the refractivity
– ds is the path length
Tropospheric Delay
• Dry component contributes 90% of the
error
– Easily modeled
• Wet component contributes 10% of the
error
– Difficult to model because you need to know
the amount of water vapor along the entire
path
Tropospheric Delay
• There are many models which estimate
the wet component of the tropospheric
delay
– Hopfield Model
– Modified Hopfield Model
– Saastamoinen Model
– Lanyi Model
– NMF (Niell)
– Many, many more
Special Relativistic
Considerations
• Time dilation
– Moving clock runs slow
• Lorentz contraction
– Moving object seems contracted
• Second order Doppler effect
– Frequency is modified like time
• Mass relation
General Relativistic
Considerations
• Perturbations in the satellite orbit
• Curvature of the path of the signal
– Longer than expected in Euclidian space
• Effects on the satellite clock
– Clocks run fast further out of the potential
well
• Effects on the receiver clock (Sagnac
effect)
Phase Center Errors
• Phase center is the ‘point’ from which the GPS
location is measured
• Difficult to measure precisely
• Changes with different factors:
– Elevation
– Azimuth
– Frequency
• Either model the error or reduce the effect of the
error by always orienting antenna the same
direction
Receiver Noise
• All electronic devices will have a certain
amount of noise
• Because of the characteristics of the noise
modeling is not an option
• The best that can be done is average the
data to reduce the effects of the noise
Multipath Errors
• GPS assumes that the signal travels
directly from the satellite to the receiver
• Multipath results from signal reflecting off
of surface before entering the receiver
– Adds additional (erroneous) path length to the
signal
• Difficult to remove; best to avoid
Multipath Illustration
From
http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap6/6212.htm
Geometric Factors
• The strength of figure of the satellites is
taken into consideration by the dilution of
precision (DOP) factor
– Depends on number of satellites
– Depends on location of satellites
Geometric Factors
From http://www.romdas.com/surveys/sur-gps.htm
Geometric Factors
• Different kinds of DOPs
– HDOP (horizontal)
– VDOP (vertical)
– PDOP (position) (3-D component)
– TDOP (time)
– GDOP (geometric) (PDOP and TDOP)
User Equivalent Range Error
(UERE)
• Crude estimate of the expected error
• Consists of contributions from
– Measurement noise
– Satellite biases
– Wave propagation errors
• Transmitted through the Navigation
message
• Combined with DOP information
GPS signals
• Navigation data
• Pseudo-random noise sequences
• Carrier wave
Navigation data
•
•
•
•
•
•
Satellite orbit information (ephemerides)
Satellite clock information
Satellite health and accuracy
Satellite orbit information (almanac)
Bit-rate of 50bps
Repeated every 12.5 minutes
Pseudo-random noise sequences
•
•
•
•
•
•
•
Spreading sequences (C/A)
Length of 1023 chips
Chipping rate of 1.023Mcps
1 sequence lasts 1ms
32 sequences to GPS satellites
Satellite identification
Separate signals from different satellites
Carrier wave
• Signal transmission
• Two frequencies: L1=1575.42MHz
L2=1227.60MHz
• C/A code on L1
• Bipolar phase-shift keying (BPSK)
modulation
Receiver overview
• Prepare received signals for signal
processing
RF
front-end
A/D
converter
Acquisition
Receiver
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
channel
Position
calculation
Receiver overview
• Find satellites visible to the receiver
– Find coarse values for C/A code phase and
carrier frequency
RF
A/D
Acquisition
Receiver
Position
Receiver
front-end
for eachconverter
satellite
channel
calculation
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
channel
Receiver overview
• Find fine value for C/A code phase
• Find fine value for carrier frequency
• Keep track of the C/A code phase and
Bit synDecode
Code
Carrier
Calculate
Calculate
carrier
chronization
nav. data
tracking
Tracking
satellite
pseudoposition
range
frequency as they change over time
Receiver channel
Receiver overview
• Obtain navigation data bits
Code
tracking
Receiver channel
Carrier
Tracking
Bit synchronization
Decode
nav. data
Calculate
satellite
position
Calculate
pseudorange
Receiver overview
• Decode navigation data bits
Code
tracking
Receiver channel
Carrier
Tracking
Bit synchronization
Decode
nav. data
Calculate
satellite
position
Calculate
pseudorange
Receiver overview
• Calculate satellite position
Code
tracking
Receiver channel
Carrier
Tracking
Bit synchronization
Decode
nav. data
Calculate
satellite
position
Calculate
pseudorange
Receiver overview
• Calculate pseudorange
Code
tracking
Receiver channel
Carrier
Tracking
Bit synchronization
Decode
nav. data
Calculate
satellite
position
Calculate
pseudorange
Receiver overview
• Calculate position
RF
front-end
A/D
converter
Acquisition
Receiver
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
Receiver
channel
channel
Position
calculation
Implemented parts


Prepare received signals for signal
 processing
 Acquisition
 Code tracking
 Carrier tracking
 Bit synchronization
 Decode navigation messages
 Calculate satellite positions
Signal conditioning
• Purpose of signal conditioning
– Remove possible disturbing signals by
filtering
– Amplify signal to an acceptable amplitude
Intermediate
Antenna
– Down-sample signal to an intermediate
frequency
signal
signal
Mixer
frequency Amplifier
Filter
Filter
Local
oscillator
receiver PRN code start position at time of full correlation
is time of arrival of the SV PRN at receiver
the time of arrival is a measure of range to SV
offset by amount to which receiver clock is offset from GPS time
…the time of arrival is pseudo-range
position of receiver is where pseudo-ranges from set of SVs intersect
• position determined from multiple pseudo-range measurements
from a single measurement epoch (i.e. time)
• psuedo-range measurements used together with SV position
estimates based on precise orbital elements
(ephemeris data) sent by each SV
GPS navigation data
from
navigation message
each SV sends amount to which GPS time is offset from
UTC (universal time) time…
correction used by receiver to set UTC to within 100 nanoseconds
THE GPS MEASUREMENT PRINCIPLE
 Based on the basic physical relationship:
distance = velocity * time
 Observations (pseudo-ranges) from 4 satellites provide 3 dimensional
position (3 positional and 1 time unknown)
 Coordinate system realized by the satellite orbits (ephemerides) and
by the coordinates and physical locations of the control and tracking
stations
Trilateration
A
The Geocentric Cartesian Coordinate System
Z
Satellite P
Greenwich
Meridian
N
ZP
A
Y
XP
Equator
S
YP
X
AP = √(XP-XA)2 + (YP-YA)2 + (ZP-ZA)2
Geometric Dilution of Precision
- Measures the effect of geometry on the precision of the observations
- Multiply GDOP by the Std Error to get actual uncertainty
- Also HDOP, VDOP
Position Dilution of Precision (PDOP)
- This is positional part of GDOP
Post-processing vs Real Time Correction
Real Time Kinematic (RTK)
Differential corrections are broadcast via radio
Base station over known point
Base station over free point
“Site Calibration/Local Transformation”
THIRD PARTY DIFFERENTIAL CORRECTION SERVICE
 Service
available commercially (e.g. Omnistar)
 Sub-meter accuracies possible when used in combination with L1
 User needs only one receiver
GPS satellites
Geostationary
Communication
Satellite
Differential Base
Station
Rover
Footprint of Communication
Satellite coverage
See http://www.omnistar.com/
Eccentric Points
Geostationary
Communication
Satellite
Useful when Canopy prevents direct occupation of point
or when Communication Satellite is blocked
GPS TECHNOLOGY CLASSIFICATION
APPROXIMATE ACCURACY
100 m
mapping
grade
geodetic
grade
navigation/
recreational
grade
20 m
10 m
5m
1m
0.5 m
dm
cm
mm
A
B
RELATIVE
POSITIONING
C
D
E
POINT (ABSOLUTE)
POSITIONING
A: Geodetic (carrier phase with resolved ambiguities), real-time/post-processed
B: Carrier smoothed C/A Code Phase, post-processed
C: Real-time (RTCM SC104), post-processed C/A Code
D: Real time P-Code (Precise Positioning Service [PPS])
E: Real time C/A-Code (Standard Positioning Service [SPS])
Selective Availability switched off – see http://geography.about.com/library/weekly/aa050400a.htm