Global Positioning System Overview
Peter H. Dana
These materials were developed by Peter H. Dana, Department of
University of Texas at Austin, 1994. These materials may be
for study, research, and education in not-for-profit
If you link to or cite these materials, please credit the author,
H. Dana, The Geographer's Craft Project, Department of Geography,
of Colorado at Boulder. These materials may not be copied to
from another Web server without the author's express
Copyright © 1999-2015 Peter H. Dana. All commercial rights
If you have comments or suggestions, please contact the author or
Ken Foote at email@example.com.
This page is available in a framed
Selective Availability Turned Off
of May 2, 2000.
GPS is a Satellite Navigation System
GPS is funded by and controlled by the U. S. Department of
While there are many thousands of civil users of GPS world-wide,
was designed for and is operated by the U. S. military.
GPS provides specially coded satellite signals that can be
a GPS receiver, enabling the receiver to compute position,
Four GPS satellite signals are used to compute positions in
and the time offset in the receiver clock.
and Time from Four GPS Satellite Signals
The Space Segment of the system consists of the GPS satellites.
vehicles (SVs) send radio signals from space.
The nominal GPS Operational Constellation consists of 24
orbit the earth in 12 hours. There are often more than 24
as new ones are launched to replace older satellites. The
repeat almost the same ground track (as the earth turns beneath
each day. The orbit altitude is such that the satellites repeat
track and configuration over any point approximately each 24
hours (4 minutes
earlier each day). There are six orbital planes (with nominally
in each), equally spaced (60 degrees apart), and inclined at
degrees with respect to the equatorial plane. This constellation
the user with between five and eight SVs visible from any point
Satellites and Ground Tracks
Nominal Orbit Planes
The Control Segment consists of a system of tracking stations
Master Control and Monitor Network
The Master Control facility is located at Schriever Air Force
Falcon AFB) in Colorado. These monitor stations measure signals
SVs which are incorporated into orbital models for each
models compute precise orbital data (ephemeris) and SV clock
for each satellite. The Master Control station uploads ephemeris
data to the SVs. The SVs then send subsets of the orbital
to GPS receivers over radio signals.
The GPS User Segment consists of the GPS receivers and the user
GPS receivers convert SV signals into position, velocity, and
Four satellites are required to compute the four dimensions of
X, Y, Z
(position) and Time. GPS receivers are used for navigation,
time dissemination, and other research.
Navigation in three dimensions is the primary function of GPS.
receivers are made for aircraft, ships, ground vehicles, and
for hand carrying
Precise positioning is possible using GPS receivers at
providing corrections and relative positioning data for remote
Surveying, geodetic control, and plate tectonic studies are
Time and frequency dissemination, based on the precise clocks
the SVs and controlled by the monitor stations, is another use
Astronomical observatories, telecommunications facilities, and
standards can be set to precise time signals or controlled to
frequencies by special purpose GPS receivers.
Research projects have used GPS signals to measure atmospheric
GPS Positioning Services Specified In The
Precise Positioning Service (PPS)
Authorized users with cryptographic equipment and keys and
receivers use the Precise Positioning System. U. S. and Allied
certain U. S. Government agencies, and selected civil users
approved by the U. S. Government, can use the PPS.
PPS Predictable Accuracy
22 meter Horizontal accuracy
27.7 meter vertical accuracy
200 nanosecond time (UTC) accuracy
Standard Positioning Service (SPS)
Civil users worldwide use the SPS without charge or
receivers are capable of receiving and using the SPS signal. The
is intentionally degraded by the DOD by the use of Selective
SPS Predictable Accuracy
100 meter horizontal accuracy
156 meter vertical accuracy
340 nanoseconds time accuracy
These GPS accuracy figures are from the 1999 Federal
The figures are 95% accuracies, and express the value of two
of radial error from the actual antenna position to an ensemble
estimates made under specified satellite elevation angle (five
and PDOP (less than six) conditions.
For horizontal accuracy figures 95% is the equivalent of 2drms
root-mean-squared), or twice the radial error standard
deviation. For vertical
and time errors 95% is the value of two-standard deviations of
error or time error.
Receiver manufacturers may use other accuracy measures.
(RMS) error is the value of one standard deviation (68%) of the
one, two or three dimensions. Circular Error Probable (CEP) is
of the radius of a circle, centered at the actual position that
50% of the position estimates. Spherical Error Probable (SEP) is
equivalent of CEP, that is the radius of a sphere, centered at
position, that contains 50% of the three dimension position
As opposed to 2drms, drms, or RMS figures, CEP and SEP are not
by large blunder errors making them an overly optimistic
Some receiver specification sheets list horizontal accuracy in
RMS or CEP
and without Selective Availability, making those receivers
accurate than those specified by more responsible vendors using
GPS Satellite Signals
The SVs transmit two microwave carrier signals. The L1 frequency
MHz) carries the navigation message and the SPS code signals.
The L2 frequency
(1227.60 MHz) is used to measure the ionospheric delay by PPS
Three binary codes shift the L1 and/or L2 carrier phase.
The C/A Code (Coarse Acquisition) modulates the L1 carrier
phase. The C/A
code is a repeating 1 MHz Pseudo Random Noise (PRN) Code. This
code modulates the L1 carrier signal, "spreading" the spectrum
over a 1
MHz bandwidth. The C/A code repeats every 1023 bits (one
There is a different C/A code PRN for each SV. GPS satellites
identified by their PRN number, the unique identifier for each
code. The C/A code that modulates the L1 carrier is the basis
for the civil
The P-Code (Precise) modulates both the L1 and L2 carrier
phases. The P-Code
is a very long (seven days) 10 MHz PRN code. In the
mode of operation, the P-Code is encrypted into the Y-Code.
Y-Code requires a classified AS Module for each receiver
channel and is
for use only by authorized users with cryptographic keys. The
is the basis for the PPS.
The Navigation Message also modulates the L1-C/A code signal.
Message is a 50 Hz signal consisting of data bits that
describe the GPS
satellite orbits, clock corrections, and other system
The GPS Navigation Message consists of time-tagged data bits
time of transmission of each subframe at the time they are
by the SV. A data bit frame consists of 1500 bits divided into
subframes. A data frame is transmitted every thirty seconds.
subframes contain orbital and clock data. SV Clock corrections
in subframe one and precise SV orbital data sets (ephemeris data
for the transmitting SV are sent in subframes two and three.
four and five are used to transmit different pages of system
data. An entire
set of twenty-five frames (125 subframes) makes up the complete
Message that is sent over a 12.5 minute period.
Data frames (1500 bits) are sent every thirty seconds. Each
of five subframes.
Data bit subframes (300 bits transmitted over six seconds)
bits that allow for data checking and limited error correction.
Clock data parameters describe the SV clock and its relationship
Ephemeris data parameters describe SV orbits for short sections
satellite orbits. Normally, a receiver gathers new ephemeris
hour, but can use old data for up to four hours without much
ephemeris parameters are used with an algorithm that computes
the SV position
for any time within the period of the orbit described by the
Ephemeris and Clock Data Parameters
Ephemeris Parameter to SV Position Algorithm
Clock Parameter to SV Clock Correction Algorithm
Almanacs are approximate orbital data parameters for all SVs.
almanacs describe SV orbits over extended periods of time
(useful for months
in some cases) and a set for all SVs is sent by each SV over a
12.5 minutes (at least). Signal acquisition time on receiver
be significantly aided by the availability of current almanacs.
orbital data is used to preset the receiver with the approximate
and carrier Doppler frequency (the frequency shift caused by the
change in range to the moving SV) of each SV in the
Each complete SV data set includes an ionospheric model that is
the receiver to approximates the phase delay through the
any location and time.
Each SV sends the amount to which GPS Time is offset from
Time. This correction can be used by the receiver to set UTC to
Other system parameters and flags are sent that characterize
Position, and Time from GPS
The GPS receiver produces replicas of the C/A and/or P (Y)-Code.
code is a noise-like, but pre-determined, unique series of bits.
The receiver produces the C/A code sequence for a specific SV
form of a C/A code generator. Modern receivers usually store a
set of precomputed C/A code chips in memory, but a hardware,
implementation can also be used.
The C/A code generator produces a different 1023 chip sequence
phase tap setting. In a shift register implementation the code
shifted in time by slewing the clock that controls the shift
In a memory lookup scheme the required code chips are retrieved
Code Phase Assignments
The C/A code generator repeats the same 1023-chip PRN-code
millisecond. PRN codes are defined for 32 satellite
Code PRN Chips
The receiver slides a replica of the code in time until there is
with the SV code.
PRN Code Segment
If the receiver applies a different PRN code to an SV signal
there is no
When the receiver uses the same code as the SV and the codes
begin to line
up, some signal power is detected.
As the SV and receiver codes line up completely, the
signal is de-spread and full signal power is detected.
A GPS receiver uses the detected signal power in the correlated
to align the C/A code in the receiver with the code in the SV
a late version of the code is compared with an early version to
that the correlation peak is tracked.
GPS Receiver Block Diagram
A phase locked loop that can lock to either a positive or
(a bi-phase lock loop) is used to demodulate the 50 HZ
from the GPS carrier signal. The same loop can be used to
measure and track
the carrier frequency (Doppler shift) and by keeping track of
to the numerically controlled oscillator, carrier frequency
phase can be
tracked and measured.
Bit Demodulation and C/A Code Control
The receiver PRN code start position at the time of full
the time of arrival (TOA) of the SV PRN at receiver. This TOA is
of the range to SV offset by the amount to which the receiver
offset from GPS time. This TOA is called the pseudo-range.
The position of the receiver is where the pseudo-ranges from a
set of SVs
of Range Spheres
Position is determined from multiple pseudo-range measurements
at a single
measurement epoch. The pseudo range measurements are used
SV position estimates based on the precise orbital elements (the
data) sent by each SV. This orbital data allows the receiver to
the SV positions in three dimensions at the instant that they
Four satellites (normal navigation) can be used to determine
dimensions and time. Position dimensions are computed by the
Earth-Centered, Earth-Fixed X, Y, Z (ECEF XYZ) coordinates.
X, Y, and Z
Time is used to correct the offset in the receiver clock,
use of an inexpensive receiver clock.
SV Position in XYZ is computed from four SV pseudo-ranges and
correction and ephemeris data.
SV and Receiver XYZ
Receiver position is computed from the SV positions, the
(corrected for SV clock offsets, ionospheric delays, and
and a receiver position estimate (usually the last computed
Navigation Solution Example
Data Set Used in Pseudo-Range Navigation Solution Example
Three satellites could be used determine three position
a perfect receiver clock. In practice this is rarely possible
SVs are used to compute a two-dimensional, horizontal fix (in
and longitude) given an assumed height. This is often possible
at sea or
in altimeter equipped aircraft.
Five or more satellites can provide position, time and
SVs can provide extra position fix certainty and can allow
out-of-tolerance signals under certain circumstances.
Position in XYZ is converted within the receiver to geodetic
longitude and height above the ellipsoid.
XYZ to Geodetic Coordinate Conversion
to ECEF XYZ Coordinate Conversion
Latitude and longitude are usually provided in the geodetic
datum on which
GPS is based (WGS-84). Receivers can often be set to convert to
datums. Position offsets of hundreds of meters can result from
Overview, Department of Geography, University of Texas at
Velocity is computed from change in position over time, the SV
frequencies, or both.
Time is computed in SV Time, GPS Time, and UTC.
SV Time is the time maintained by each satellite. Each SV
atomic clocks (two cesium and two rubidium). SV clocks are
ground control stations and occasionally reset to maintain time
one-millisecond of GPS time. Clock correction data bits reflect
of each SV from GPS time.
SV Time is set in the receiver from the GPS signals. Data bit
occur every six seconds and contain bits that resolve the Time
to within six seconds. The 50 Hz data bit stream is aligned with
code transitions so that the arrival time of a data bit edge (on
a 20 millisecond
interval) resolves the pseudo-range to the nearest millisecond.
range to the SV resolves the twenty millisecond ambiguity, and
code measurement represents time to fractional milliseconds.
and a navigation solution (or a known position for a timing
SV Time to be set to an accuracy limited by the position error
pseudo-range error for each SV.
SV Time is converted to GPS Time in the receiver.
Time to GPS Time Data Bits
GPS Time is a "paper clock" ensemble of the Master Control Clock
SV clocks. GPS Time is measured in weeks and seconds from
5, 1980 and is steered to within one microsecond of UTC. GPS
Time has no
leap seconds and is ahead of UTC by several seconds.
Week Number Rollover Comments
Time in Universal Coordinated Time (UTC) is computed from GPS
the UTC correction parameters sent as part of the navigation
At the transition between 23:59:59 UTC on December 31, 1998 and
UTC on January 1, 1999, UTC was retarded by one-second. GPS Time
ahead of UTC by 13 seconds.
from GPS Time
Carrier-phase tracking of GPS signals has resulted in a
revolution in land
surveying. A line of sight along the ground is no longer
precise positioning. Positions can be measured up to 30 km from
point without intermediate points. This use of GPS requires
carrier tracking receivers.
The L1 and/or L2 carrier signals are used in carrier phase
carrier cycles have a wavelength of 19 centimeters. If tracked
these carrier signals can provide ranging measurements with
of millimeters under special circumstances.
Tracking carrier phase signals provides no time of transmission
The carrier signals, while modulated with time tagged binary
no time-tags that distinguish one cycle from another. The
used in carrier phase tracking are differences in carrier phase
and fractions of cycles over time. At least two receivers track
signals at the same time. Ionospheric delay differences at the
must be small enough to insure that carrier phase cycles are
for. This usually requires that the two receivers be within
about 30 km
of each other.
Carrier phase is tracked at both receivers and the changes in
are recorded over time in both receivers.
All carrier-phase tracking is differential, requiring both a
and remote receiver tracking carrier phases at the same time.
Unless the reference and remote receivers use L1-L2 differences
the ionospheric delay, they must be close enough to insure
ionospheric delay difference is less than a carrier wavelength.
Using L1-L2 ionospheric measurements and long measurement
relative positions of fixed sites can be determined over
baselines of hundreds
Phase difference changes in the two receivers are reduced using
to differences in three position dimensions between the
and the remote receiver. High accuracy range difference
sub-centimeter accuracy are possible. Problems result from the
of tracking carrier signals in noise or while the receiver
Two receivers and one SV over time result in single differences.
Two receivers and two SVs over time provide double differences.
Post processed static carrier-phase surveying can provide 1-5 cm
positioning within 30 km of the reference receiver with
of 15 minutes for short baselines (10 km) and one hour for long
Rapid static or fast static surveying can provide 4-10 cm
1 kilometer baselines and 15 minutes of recording time.
Real-Time-Kinematic (RTK) surveying techniques can provide
in real time over 10 km baselines tracking five or more
real-time radio links between the reference and remote
GPS Error Sources
GPS errors are a combination of noise, bias, blunders.
Bias, and Blunders
Noise errors are the combined effect of PRN code noise (around
and noise within the receiver noise (around 1 meter).
Bias errors result from Selective Availability and other factors
Selective Availability (SA)
SA is the intentional degradation of the SPS signals by a
bias. SA is controlled by the DOD to limit accuracy for
non-U. S. military
and government users. The potential accuracy of the C/A code
30 meters is reduced to 100 meters (two standard
The SA bias on each satellite signal is different, and so
position solution is a function of the combined SA bias from
each SV used
in the navigation solution. Because SA is a changing bias
with low frequency
terms in excess of a few hours, position solutions or
individual SV pseudo-ranges
cannot be effectively averaged over periods shorter than a
few hours. Differential
corrections must be updated at a rate less than the
of SA (and other bias errors).
Other Bias Error sources;
SV clock errors uncorrected by Control Segment can result in
Ephemeris data errors: 1 meter
Tropospheric delays: 1 meter. The troposphere is the lower
level to from 8 to 13 km) of the atmosphere that experiences
in temperature, pressure, and humidity associated with
Complex models of tropospheric delay require estimates or
of these parameters.
Unmodeled ionosphere delays: 10 meters. The ionosphere is
the layer of
the atmosphere from 50 to 500 km that consists of ionized
air. The transmitted
model can only remove about half of the possible 70 ns of
a ten meter un-modeled residual.
Multipath: 0.5 meters. Multipath is caused by reflected
signals from surfaces
near the receiver that can either interfere with or be
mistaken for the
signal that follows the straight line path from the
is difficult to detect and sometime hard to avoid.
Blunders can result in errors of hundred of kilometers.
Control segment mistakes due to computer or human error can
from one meter to hundreds of kilometers.
User mistakes, including incorrect geodetic datum selection,
errors from 1 to hundreds of meters.
Receiver errors from software or hardware failures can cause
of any size.
Noise and bias errors combine, resulting in typical ranging
errors of around
fifteen meters for each satellite used in the position solution.
Geometric Dilution of Precision (GDOP) and
GPS ranging errors are magnified by the range vector
the receiver and the SVs. The volume of the shape described by
from the receiver to the SVs used in a position fix is
Poor GDOP, a large value representing a small unit
when angles from receiver to the set of SVs used are
Good GDOP, a small value representing a large
when angles from receiver to SVs are different.
GDOP is computed from the geometric relationships between the
position and the positions of the satellites the receiver is
navigation. For planning purposes GDOP is often computed from
and an estimated position. Estimated GDOP does not take into
that block the line-of-sight from the position to the
GDOP may not be realizable in the field.
GDOP terms are usually computed using parameters from the
Navigation Solution Example
In general, ranging errors from the SV signals are multiplied
by the appropriate
GDOP term to estimate the resulting position or time error.
terms can be computed from the navigation covariance matrix.
ECEF XYZ DOP
terms can be rotated into a North-East Down (NED) system to
horizontal and vertical DOP terms.
PDOP = Position Dilution of Precision (3-D), sometimes the
HDOP = Horizontal Dilution of Precision (Latitude,
VDOP = Vertical Dilution of Precision (Height).
TDOP = Time Dilution of Precision (Time).
While each of these GDOP terms can be individually computed,
they are formed
from covariances and so are not independent of each other. A
(time dilution of precision), for example, will cause receiver
which will eventually result in increased position errors.
Differential GPS (DGPS)
The idea behind all differential positioning is to correct bias
at one location with measured bias errors at a known position. A
receiver, or base station, computes corrections for each
Because individual pseudo-ranges must be corrected prior to the
of a navigation solution, DGPS implementations require software
reference receiver that can track all SVs in view and form
corrections for each SV. These corrections are passed to the
rover, receiver which must be capable of applying these
corrections to each SV used in the navigation solution. Applying
position correction from the reference receiver to the remote
has limited effect at useful ranges because both receivers would
be using the same set of SVs in their navigation solutions and
GDOP terms (not possible at different locations) to be
by bias errors.
Differential Code GPS
Differential corrections may be used in real-time or later,
Real-time corrections can be transmitted by radio link. The
U. S. Coast
Guard maintains a network of differential monitors and
transmits DGPS corrections
over radiobeacons covering much of the U. S. coastline. DGPS
are often transmitted in a standard format specified by the
Commission Marine (RTCM).
Corrections can be recorded for post processing. Many public
agencies record DGPS corrections for distribution by
Private DGPS services use leased FM sub-carrier broadcasts,
or private radio-beacons for real-time applications.
To remove Selective Availability (and other bias errors),
corrections should be computed at the reference station and
the remote receiver at an update rate that is less than the
time of SA. Suggested DGPS update rates are usually less
than twenty seconds.
DGPS removes common-mode errors, those errors common to both
and remote receivers (not multipath or receiver noise). Errors
often common when receivers are close together (less than 100
position accuracies of 1-10 meters are possible with DGPS
based on C/A
code SPS signals.
Reduced by Differential Corrections
All carrier-phase tracking is differential, requiring both a
and remote receiver tracking carrier phases at the same time.
In order to correctly estimate the number of carrier
wavelengths at the
reference and remote receivers, they must be close enough to
the ionospheric delay difference is less than a carrier
usually means that carrier-phase GPS measurements must be
taken with a
remote and reference station within about 30 kilometers of
Special software is required to process carrier-phase
Newer techniques such as Real-Time-Kinematic (RTK) processing
centimeter relative positioning with a moving remote receiver.
Common Mode Time
When time information is transferred from one site to another,
techniques can result in time transfers of around 10 ns over
as long as 2000 km.
GPS Techniques and
Receiver costs vary depending on capabilities. Small civil SPS
can be purchased for under $200, some can accept differential
Receivers that can store files for post-procesing with base
cost more ($2000-5000). Receivers that can act as DGPS reference
(computing and providing correction data) and carrier phase
(and two are often required) can cost many thousands of dollars
to $40,000). Military PPS receivers may cost more or be
difficult to obtain.
Other costs include the cost of multiple receivers when needed,
software, and the cost of specially trained personnel.
Project tasks can often be categorized by required accuracies
determine equipment cost.
Low-cost, single-receiver SPS projects (100 meter accuracy)
Medium-cost, differential SPS code Positioning (1-10 meter
High-cost, single-receiver PPS projects (20 meter accuracy)
High-cost, differential carrier phase surveys (1 mm to 1 cm
Applications, Costs, and Signals
1999 Federal Radionavigation Plan, February 2000. Washington,
Department of Transportation and Department of Defense.
Available on line
Coast Guard Navigation Center
Global Positioning System Standard Positioning Service
Edition, June2, 1995. Available on line from United
States Coast Guard Navigation Center
NAVSTAR GPS User Equipment Introduction. 1996. Available on line
States Coast Guard Navigation Center
GPS Joint Program Office. 1997. ICD-GPS-200: GPS Interface
ARINC Research.Available on line from United
States Coast Guard Navigation Center
Hoffmann-Wellenhof, B. H. Lichtenegger, and J. Collins. 1994. GPS:
and Practice. 3rd ed.New York: Springer-Verlag.
Institute of Navigation. 1980, 1884, 1986, 1993. Global
System monographs. Washington, DC: The Institute of
Kaplan, Elliott D. ed. 1996. Understanding GPS: Principles
Boston: Artech House Publishers.
Leick, Alfred. 1995. GPS Satellite Surveying. 2nd. ed.
John Wiley & Sons.
National Imagery and Mapping Agency. 1997. Department of Defense
Geodetic System 1984: Its Definition and Relationship with Local
Systems. NIMA TR8350.2 Third Edition. 4 July 1997. Bethesda, MD:
Imagery and Mapping Agency. Available on line from
National Imagery and Mapping Agency
Parkinson, Bradford W. and James J. Spilker. eds. 1996. Global
System: Theory and Practice. Volumes I and II. Washington,
Institute of Aeronautics and Astronautics, Inc.
Wells, David, ed. 1989. Guide to GPS positioning.
Canada: Canadian GPS Associates.
(These and other references are available from Navtech Seminars
Supply, 6121 Lincolnia Rd. Suite 400, Arlington, VA 22312-2707
USA - (800)
628-0885 or (703) 256-8900). Fax: (703) 256-8988
Seminars and GPS Supply