Part 1: GPS Theory and Operation
• GPS Background
• GPS Signals and Ranging
• GPS Components
• GPS Accuracy
• World Geodetic Survey 84 (WGS 84)
• Receiver Autonomous Integrity Monitoring (RAIM)
• Fault Detection and Exclusion (FDE)
• Step Detector
• Barometric Altimeter Aiding (baro-aiding)
The Global Positioning System (GPS) is a satellite based
navigation system offering precision navigation capability. Originally
designed for military use, civilian access has been permitted to specific
parts of the GPS.
GPS offers a number of features making it attractive for use in
aircraft navigation. Civilian users can expect a position accuracy of 100
m or better in three dimensions. The GPS signal is available 24 hours
per day throughout the world and in all weather conditions. GPS offers
resistance to intentional (jamming) and unintentional interference. The
equipment necessary to receive and process GPS signals is affordable
and reliable and does not require atomic clocks or antenna arrays. For
the GPS user, the system is passive and requires a receiver only
without the requirement to transmit.
GPS Signals and Ranging
In its most basic terms, GPS determines the position of the user
by triangulation. By knowing the position of the satellite and the
distance from the satellite; combinations of satellites can be used to
determine the exact position of the receiver.
The fundamental means for GPS to determine distance is the use
of time. By using accurate time standards and by measuring changes
in time, distance is computed.
A simplified GPS system illustrates the concept of satellite ranging. A
satellite transmits a time signal, as shown. The receiver is stationary and has an
absolutely accurate clock, perfectly synchronized to GPS time. By measuring the
difference in time from when the signal left the satellite to when it is received by
the aircraft, the distance from the satellite to the user can be calculated. This is
the product of the time difference and the speed of light (300,000 km/sec).
With one satellite, and knowing the position of that satellite, the
location of the user would be anywhere along an arc. If three satellites
were used, the location of the user would be at the intersection of the
three arcs created by the satellites, as shown. Stated mathematically,
in order to solve for the three dimensional position (with three variables:
latitude, longitude and altitude), three equations (or satellites) are
Signal left the satellite at time = 100 sec
Satellite Reception Time Time Difference (sec) Distance (km)
1 100.0855 0.0855 25650
2 100.0900 0.0900 27000
3 100.0875 0.0875 26250
This example assumes a receiver clock in perfect synchronization
with the satellite and exhibiting the same accuracy. It is impractical and
prohibitively expensive for GPS receivers to use atomic clocks as those
used on the satellites to maintain an accurate time. As a result,
receiver clocks are not perfectly synchronized satellite time. For every
microsecond (one-millionth of second) difference between the satellite
clocks and the receiver clock, a 300 meter error is introduced. This
error is known as a clock bias.
The location of the receiver is somewhere in the area defined by the
clock bias for each satellite, as shown. Because of this bias, an extra satellite is
required to resolve this error. For example, with three satellites, only a two
dimensional position can be determined (clock bias, latitude and longitude). In
order to determine a position in three dimensions, a fourth satellite is required.
Stated mathematically, in order to solve for the three dimensional position (three
variables: latitude, longitude and altitude) and the time bias, four equations (or
satellites) are needed.
The electromagnetic radio waves or signals broadcast from the
GPS satellites form the means for a GPS receiver to perform the timing
and distance calculations. GPS receivers are passive devices meaning
that signals are received only with no requirement or means to transmit.
GPS ranging signals are broadcast on two frequencies: L1
(1575.42 MHz) and L2 (1227.6 MHz).
The L1 frequency is available for civilian use. The frequency has
1) The Clear Acquisition Code or C/A: this is the principal civilian
ranging signal and is always broadcast in a clear or unencrypted form.
The use of this signal is sometimes called the Standard Positioning
Service or SPS. This signal may be degraded intentionally but is
always available. The signal creates a short Pseudo Random Noise
(PRN) code broadcast a rate of 1.023 MHz. The satellite signal repeats
itself every millisecond. The C/A code is also used to acquire the P
2) Protected Code or P Code: this is also known as the Precise
Positioning Service. This signal has been encrypted and is not
available to civilian users.
Both the C/A and P code use the same principle to measure the
time taken for the satellite signal to reach the receiver. The GPS signal
modulation consists of a repetitive binary signal that receivers use to
determine the time at which the code was sent from the satellite, as
shown. The waveform from the satellite is matched with an internally
generated waveform within the receiver. The time difference between
matching waveforms is used to compute the distance from a satellite.
The binary information found on the L2 frequency is
reserved for military use and is thus not available for civilian access.
Civilian users can access the L2 frequency and its carrier, however.
Both the L1 and L2 frequencies broadcast a satellite message as
part of their signal. This low frequency (50 bits per second) data
stream provides the receiver with a number of critical items required in
determining a position. This data stream is broadcast continually and is
repeated every 30 seconds. This data stream is broken down into five,
Subframes 1 through 5 each provide a synchronization, hand over word
and a C/A code time ambiguity removal. The remainder of the data is
formatted as follows:
Subframe 1: satellite clock corrections, age of data and various flags
Subframe 2 and 3: ephemeris (exact satellite orbit description)
Subframe 4: ionospheric model, UTC data, flags for each satellite
indicating whether anti-spoofing is on, almanac (approximate satellite
ephemeris allowing the receiver to select the best set of satellites or to
determine which satellites are in view) and health information for satellite
number 25 and greater
Subframe 5: almanac and health information for satellite number 1 to 24
The reception and decoding of the data stream is performed
automatically by a receiver without any intervention by the operator.
The information within this data is critical to GPS operation. The
almanac and ephemeris provides the description of the satellite orbit.
With this information, the receiver can determine the satellite’s position
at any time and combine this with the receiver distance from the
satellite, yielding a GPS position. The health information is critical to
prevent a receiver from using the ranging information from a satellite
that has been declared unfit for navigation purposes. The remainder of
the information found in the data stream – clock corrections,
ionospheric model, UTC data – are used to resolve potential sources of
GPS position errors. These will be discussed later.
The Global Positioning Systems consists of three major
components: satellites, control segment, and the user.
The GPS constellation is designed for a minimum of 24 satellites
(21 active satellites and three orbital spares) orbiting the earth. GPS
satellite orbit is designed to be circular however some eccentricity (non-
circular orbit) can be present. The satellites orbit the earth at an
altitude of 20,163 km above the earth’s surface or 26,562 km from the
center of the earth. The orbital velocity is 3.87 km/sec. The orbital
plane is inclined at 55 degrees with reference to the equator. The
satellites complete two orbits each sidereal day. To a viewer located
on the surface of the earth, the satellites are in constant motion (non-
geo-synchronous orbit) with satellites rising and setting.
Six orbital planes are in use, each spaced equally around the
earth, separated by 60 degrees (360 degrees/6 planes=60 degrees).
The planes are named A to F.
Each orbital plane hosts four satellites. These satellites are not
spaced evenly on each plane, however. Spacing between adjacent
satellites varies from 31.13 degrees to 119.98 degrees. Each plane
exhibits a different angular spacing for the satellites resident to it. A
computer model was used to determine the satellite spacing to
accommodate a single satellite failure and still maintain optimal satellite
geometry. Satellite geometry and its affect upon GPS accuracy are
The primary mission of GPS satellites is the transmission of
precisely timed GPS signals and the data stream required to decode
the signals to produce a position. The timing signals are referenced to
atomic clocks, either cesium or rubidium.
With the GPS satellites in constant motion, the number of
satellites in view and their relative location is dynamic. A 24-satellite
configuration provides adequate satellite coverage to perform three-
dimensional position fixing. Failures of satellites and/or the
requirement for more than four satellites (as discussed later) may result
in inadequate satellite coverage.
The following slide shows the motion of nine satellites. The
ground tracks show the movement of these satellites over a twelve
hour period and the position of the satellites at one moment in time.
The ground tracks show a number of features. Each satellite
follows a unique path over the ground. Also, every satellite operates
between 55 degrees North and 55 degrees south.
The snapshot of satellite positions show that a point on earth will
see a different set of satellites compared another point on the surface.
Also, as these satellites move in their orbits, the satellites in view at
each location changes with time.
The equatorial and polar regions enjoy the best satellite
coverage. Receivers located near the equator are able to view
satellites on both sides of the equator and at the limits of their orbits.
Receivers in the polar regions are able to view satellites towards the
equator but also satellites on the other side of the earth. Satellite
coverage and probability distribution for a 24 satellite constellation and
a 5 degree mask angle are provided. “Mask Angle” is a term describing
the angle from the horizon below which a receiver is unable to track
satellites. This value is determined by the capabilities of the antenna
and receiver as well as any local terrain.
4 5 6 7 8 9 10 11 12 13 4 5 6 7 8 9 10 11 12 13
Number of Satellites in View Number of Satellites in View
0 Degrees Latitude - Equator 35 Degrees Latitude
4 5 6 7 8 9 10 11 12 13 0
4 5 6 7 8 9 10 11 12 13
Number of Satellites in View Number of Satellites in View
40 Degrees Latitude 90 Degrees Latitude- Pole
Five monitoring stations are located throughout the world (Hawaii,
Colorado Springs, Ascension Island, Diego Garcia and Kwajalein
Island) provide continuous surveillance of the GPS constellation. Four
of these stations (all except Hawaii) have the ability to upload
information to the GPS satellites.
The objective of the GPS control segment is to:
• Maintain each of the satellites in its proper orbit through
infrequent, small commanded maneuvers,
• Make corrections and adjustments to the satellite clocks and
payload as needed,
• Track the GPS satellites and generate and upload navigation
data to each of the GPS satellites, and
• Command major relocations in the event of satellite failure to
minimize the impact.
The monitoring stations record a number of parameters including
satellite position, clock errors and GPS signal. This information is
transmitted to the Operational Control Center at Falcon Air Force Base,
Colorado Springs, Colorado. The data is processed to determine
ephemeris (orbit) errors, clock error, satellite health for each satellite,
etc. Navigation data packages are then prepared for uploading to the
satellites via the ground antenna stations for storage and use on the
satellites. Although uploads generally occur once per day, fresh
uploads can be provided up to three times daily. Uploaded data can be
used for up to 14 days – this feature provides the satellites with a
degree of autonomy should there be difficulties in uploading data for an
extended period of time.
The antenna receives the GPS signals and amplifies them for
further processing. A filtering eliminates signals or noise from adjacent
frequency bands. The signal is then sampled and fed to parallel sets of
delay locked loops where multiple satellites can be tracked
simultaneously. The pseudorange, carrier phases and navigation data
is then estimated. A signal generator replicating the signal produced by
the satellites is used to determine the time difference between when
the signal was transmitted by the satellite and received by the user.
Using the navigation data provided in the data message, the
pseudorange and phase information is then corrected for satellite clock
errors, earth rotation, ionospheric delay, tropospheric delay, relativistic
effects and equipment delays. This information is then processed with
other sensory data (if available) to produce a position and velocity
output. The coordinates are then converted by the appropriate
geodetic transformation to the local coordinate set.
World Geodetic Survey
A number of geodetic coordinate systems have been developed
and used to describe a position. A World Geodetic Survey (WGS) is a
“consistent set of parameters describing the size and shape of the
earth, the positions of a network of points with respect to the center of
mass of the earth, transformations from geodetic datums and the
potential of the earth”. The World Geodetic System of 1972 (WGS-72)
has been traditionally used by air navigation systems and Aviation
Information Publications (AIP’s) have used the North American Datum
of 1927 (NAD-27).
WGS-84 and NAD-83 are now in use in Canada and the United
States. The difference between these two is less than 100 feet within
the US, however the difference between these two datums and other
international datums can exceed more than two nautical miles. GPS
uses WGS-84 – a Cartesian earth-centered earth fixed (ECEF) –
If some countries do not publish AIP data in WGS-84 compatible
coordinates, navigation accuracy is limited. Enroute operations will not
be affected by this inaccuracy however approach operations and
23 accuracy is severely restricted.
GPS is vulnerable to a variety of errors that serve to degrade its
accuracy. Adjustments are required to allow for imperfections of GPS
ranging. These are:
The ionosphere is a region of ionized gases beginning at 75 to
100 km above the earth’s surface and varies in thickness from 200 to
400km. The size and shape of the ionosphere experiences wide
fluctuations from day to day, between night and day (diurnal effect) and
with solar conditions.
The ionosphere path delay can have a significant effect upon GPS
timing. The extra time required for the GPS signal to pass through the
ionosphere can vary between 2 and 50 nanoseconds, creating a distance
error of between 0.67 m and 16 m, respectively. Further compounding the
path delay error is the obliquity factor - the angle at which the GPS signal
passes through the atmosphere. A GPS satellite passing overhead (90-
degree angle) experiences the least effect as the signal passes through the
smallest amount of ionosphere. With a lower elevation angle the obliquity
factor increases by a factor of 3 with a satellite on the horizon. An
ionospheric delay is therefore over 3 times the nominal value for satellites
with large elevation angles. What was a 16m error for a satellite located
above the receiver becomes a 48m error for the same satellite located just
above the earth’s surface.
The ionospheric delay can be mitigated by a number of techniques.
Receivers with access to both the L1 and L2 frequencies can compare the
time differences for the same timing signal to reach the receiver on the two
different frequencies. The ionospheric error can be calculated from this
time difference and adjusted for in determining the satellite range.
For users without access to the L2 frequency a mathematical model
is used to simulate the ionosphere. The necessary terms in the equation
vary with time and are uplinked to the satellite. These corrections are
transmitted to the user as part of the data modulation carried on the GPS
The troposphere is the region of dry gases and water vapor
extending from the earth’s surface to an altitude of approximately 50
km. The characteristics of the troposphere make it easier to model than
The time delay of a GPS signal passing through this region of the
atmosphere normally results in a position error of 2.6 m for a satellite at
the zenith (vertical) and can exceed 20 m for a satellite at elevation
angles less than 10 degrees. Modeling the effects of a dry atmosphere
are relatively simple and can eliminate 90% of the error. Dealing with a
wet atmosphere is more difficult and only 10% of the error can be
compensated for mathematically.
Multipath is the effect of the same satellite signal reaching the
GPS antenna more than once. The first signal to reach the antenna
takes a direct path from the satellite. The multipath signals are
reflected by either ground or water surfaces, as shown.
Aircraft are particularly vulnerable to this effect. Satellite signals
reflecting off the ground or sea present multipath errors. An antenna
design shield the multipath is not a viable option since satellites at
moderate or low elevation angles would also be shielded.
“Selective Availability (SA) is the intentional degradation of the
GPS signal with the objective to deny full position and velocity accuracy
to unauthorized users”. SA was not part of the original design of GPS.
During its initial testing in the 1970’s, accuracies were much better than
expected using C/A code (20-30 m position accuracies compared to the
expected greater than 100 m accuracy). The US Department of
Defense decided to intentionally degrade the accuracy to 500m (95%
probability) then modified it to 100 m (95%) to make it comparable to a
VOR used for non-precision approaches.
Two techniques are used to degrade GPS position using SA.
Manipulation of the satellite navigation orbit data degrades the
accuracy of the calculated satellite positions. The actual satellite
positions in space are unaffected but the parameters describing the
satellite orbits (ephemeris and almanac) are corrupted. This type of
error is slowly varying (periods measured in hours).
The second technique used to effect SA is clock dither. In this
case, the actual satellite clocks are manipulated to produce position
errors. This affects both C/A and P code (military) users. In addition,
this type of error is produces rapid changes and its period is in the
order of minutes.
Ranging Accuracy or GPS Error Budget
Ephemeris Data Satellite Clock Ionosphere Troposphere
GPS Measurement Error Sources Multipath Receiver Measurement Other
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
No S/A S/A
Receiver Measurement 0.5 0.5
Multipath 1.4 1.4
Troposphere 0.7 0.7
Ionosphere 4.0 4.0
Satellite Clock 2.1 20.0
Ephemeris Data 2.1 2.1
GPS receiver position accuracy is directly related to the error sources
described earlier. These errors and their typical values are shown.
With Selective Availability turned off the dominant error is
ionospheric delay followed satellite clock errors and ephemeris data.
The combination of all of the errors totals a UERE of 5.3 meters (the
effects are not added but are squared, added and then the square root
With S/A, the satellite clock error becomes dominant error source.
The combined UERE becomes 20.6 meters.
For aviation purposes, the assumed UERE is 33.3 meters for all
GPS position accuracy is the product of the ability of the GPS
system to accurately measure its pseudorange (User Equivalent Range
Error, UERE) and the effect of satellite geometry in degrading the
position accuracy (Dilution of Precision, DOP).
UERE represents the combined effects of ephemeris
uncertainties, propagation errors (ionosphere and troposphere), clock
and timing errors and receiver noise. This is typically expressed in a
measurement of length such as feet or meters.
DOP is an expression of how the satellite geometry contributes to
or degrades the position accuracy and is expressed as a scalar (non-
dimensional) number. A number of different terms are used to
pseudorange error including UERE and Figure of Merit (FOM)
Position accuracy represents the end state capability of a GPS
receiver. This is related to but not the same as ranging accuracy. The
quantity linking ranging accuracy to position accuracy is Dilution of
Satellite position accuracy is defined as follows:
31 Position Accuracy = (Ranging Accuracy) x (Dilution of Position)
Dilution of Precision (DOP)
The position of GPS satellites in relation to the receiver – satellite
geometry - forms the critical component of the DOP. The value of DOP
is also influenced by the number of satellites in view, the capability of
the receiver to simultaneously track satellites (number of channels) and
the minimum reception angle that an antenna can track a satellite
A two dimensional position requires three satellites for a position
solution. In this case, the optimum value of DOP is achieved with the
satellites spaced equally at 120 degrees apart, producing a Horizontal
Dilution of Precision (HDOP) of 1.1547. A different geometry of three
satellites will lead to an increase in HDOP and a resulting decrease in
With more than three satellites available for the two dimensional
solution, the value of HDOP can improve. In the ideal case with the
five satellites spaced equally at 72 degrees, the value of HDOP
The following illustrates the changes in HDOP and Vertical
Dilution of Precision (VDOP). Four satellites are used however their
position has shifted to reflect the movement of the satellites over time.
An infinite combination of satellites and their relative positions
exist. Moreover, with the satellites in constant motion, the DOP values
are also constantly changing.
In these examples, four satellites are provided. The example
on the left has four satellites at a 45 degree elevation and equally
spaced around the horizon yielding a Horizontal DOP (HDOP) of 2 and
a Vertical DOP (VDOP) of 162.2. Moving the same four satellites as
shown on the right changes the HDOP to 1.5 and the VDOP to 3
The position accuracy can now be determined as the product of the
UERE and the DOP. For example, with a UERE of 20 meters with a
HDOP of 3, the position accuracy is:
Position Accuracy = (Ranging Accuracy) x (Dilution of Position)
Position Accuracy = (20 meters) x (3)
Position Accuracy = 60 meters
For aviation purposes the assumed position error for enroute,
terminal and non-precision approaches is 100m or 0.054 nautical miles.
These pages from the
CMA 900 MCDU illustrates the
capabilities of the Flight
Different terminology is
used. Figure of Merit (FOM)
equates to ranging accuracy
and HOR INT (Horizontal
Integrity) is the position
The value of HOR INT is
also the the Actual Navigation
Performance (ANP) value
found on the following page.
These will be discussed
in more detail later.
Receiver Autonomous Integrity
A unique aviation requirement of GPS avionics is RAIM. While
GPS provides the user with unparalleled levels of accuracy, one
significant deficiency of GPS is integrity, that is, the ability of the system
to provide a timely warning if the navigation solution is inaccurate or
erroneous. Navigation systems prior to GPS, particularly aviation
applications, provided a means to warn the aircraft that the signal was
outside certain limits. For example, a Category I ILS provides this
warning within six seconds.
The only means available for the GPS system itself to provide the
user with a warning of system unreliability is through the data message
forming part of the GPS signal. The “health” flag found in subframe 4
and 5 will alert the receiver to a failure of a GPS satellite.
The time lag from the beginning of the failure to when it is
incorporated in the health flag – up to eight hours - represents an
unacceptably long period of time for aviation.
To overcome this, RAIM was developed and is a mandatory
feature of all aviation-grade receivers. RAIM uses combinations of
satellites to determine the receiver position. Should a large
discrepancy between position solutions occur, a RAIM alert is created
rendering the GPS navigator unreliable.
Different phases of flight use different values of “integrity alarm
limits” prior to issuing a RAIM alert. These are as follows:
Phase of Flight Alarm Limit Time to Alarm
Enroute (oceanic, domestic, random and J/V routes) 2.0 n.m. 30 sec
Terminal 1.0 n.m. 10 sec
RNAV approach, non-precision 0.3 n.m. 10 sec
The ability of a receiver to perform RAIM computations is dependent
upon the number of satellites in view, their geometry and the mask angle
which is dependent upon the ability of the antenna to track satellites near the
horizon and any local terrain. Whereas GPS needs a minimum of four
satellites to produce a three-dimensional position, a minimum of five satellites
are required for RAIM. For this reason, RAIM may not be available in
circumstances of poor satellite coverage or poor satellite geometry.
Avionics certified under
Technical Standard Order (TSO)
C129 also provide the crew with
a number of other RAIM
capabilities. Upon transition
from terminal to approach
integrity satellite geometry is
automatically verified to ensure
RAIM availability at the Final
Approach Fix and Missed
A RAIM availability
prediction can be performed at
any time using any waypoint or
the destination and an ETA.
This provides a prediction for
ETA +/- 15 minutes in 5-minute
intervals. This also known as
Predictive RAIM (PRAIM).
Fault Detection and Exclusion
A RAIM integrity warning – the identification of one or more errant
satellites - will render the GPS system unusable for the intended phase
of flight and will require the aircraft to revert to another form of
Fault Detection and Exclusion (FDE) takes a RAIM alarm and
performs further analysis to identify the faulty satellite(s). The faulty
satellite(s) is (are) excluded from any navigation computations and the
GPS receiver is declared operational. This is particularly important for
uses of GPS as “primary means” and “sole means”. FDE occurs
automatically without any pilot input or annunciations. A minimum of
six satellites is required for FDE.
A GPS step-detector is another form of integrity check. In this
test, unreasonable pseudorange differences between consecutive
measurements are detected. This serves to monitor pseudorange step
failures and should a failure be detected that satellite will be removed
from the solution.
For example, if consecutive pseudorange measurements produce
a change of 10 meters per second and the change suddenly jumps to
50 meters per second, a ranging error is evident and the satellite gets
excluded from the position and velocity solution.
Barometric Altimeter Aiding
A barometric altimeter altitude can be introduced into the GPS
solution. This serves three important purposes: improved vertical
position accuracy, the elimination of one variable in the GPS solution
(altitude) and an improved level of RAIM and FDE availability as the
baro input serves to act like a satellite in the position computation.
The input of the barometric altitude is performed automatically in
aviation grade GPS receivers. Normally the pressure altitude is
provided with a requirement for the input of the local barometric
altimeter setting for terminal and approach operations. This is normally
performed in two ways: the crew is alerted by the GPS receiver to input
this altimeter setting or the barometric setting is automatically derived
by the altimeter setting of one of the altimeters.
Note: in the case of the
Canadian Airlines B737
installation, the local
setting is required to be
inputted manually into the
This feature is found on
Progress page 4/4, shown.
An upcoming modification
(Fall 1999) will
automatically provide the
local barometric setting by
using the Captain’s