B737 GPSFMS

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B737 GPS/FMS

• Part 1 GPS Theory and Operation

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• Topics
• 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)

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GPS Background

• 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.

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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.

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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).
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• 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
  needed.

Signal left the satellite at time 100 sec
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• 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.

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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.
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• 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 two modulations
• 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 Code.
• 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.

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• 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.

Satellite Wave
Receiver Wave
Time Difference
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.
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• 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, six-second subframes

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
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• 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
  satellites 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.

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GPS Components

• The Global Positioning Systems consists of
  three major components satellites, control
  segment, and the user.
• Satellites
• 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 earths
  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.

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• Six orbital planes are in use, each spaced
  equally around the earth, separated by 60 degrees
  (360 degrees/6 planes60 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 discussed later.

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• 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.

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• 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.

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Control Segment

• 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.

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• 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.

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GPS User

• 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.

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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 (AIPs) 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) reference
  system.
• 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 accuracy is severely restricted.

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Error Sources

• 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
• Ionospheric
• The ionosphere is a region of ionized gases
  beginning at 75 to 100 km above the earths
  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.

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• 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
  earths 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
  signal.

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• Tropospheric
• The troposphere is the region of dry gases and
  water vapor extending from the earths surface to
  an altitude of approximately 50 km. The
  characteristics of the troposphere make it easier
  to model than the ionosphere.
• 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.

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• Multipath
• 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.
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• Selective Availability
• 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 1970s, 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.

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• Ranging Accuracy or GPS Error Budget

GPS receiver position accuracy is directly
related to the error sources described earlier.
These errors and their typical values are shown.
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• 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 is
  taken).
• 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 error sources.

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GPS Accuracy

• 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 Precision (DOP).
• Satellite position accuracy is defined as
  follows
• Position Accuracy (Ranging Accuracy) x
  (Dilution of Position)

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• 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 (mask angle).
• 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 position
  accuracy.
• 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 becomes 0.8944.
• 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.

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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
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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.
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• These pages from the CMA 900 MCDU illustrates
  the accuracy measurement capabilities of the
  Flight Management System.
• Different terminology is used. Figure of Merit
  (FOM) equates to ranging accuracy and HOR INT
  (Horizontal Integrity) is the position accuracy.
• 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.

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Receiver Autonomous Integrity Monitoring (RAIM)

• 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.

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• 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

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.
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• 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 Approach Point
• 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).

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Fault Detection and Exclusion (FDE)

• 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 navigation.
• 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.

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Step Detector

• 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.

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Barometric Altimeter Aiding (baro-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.

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• Note in the case of the Canadian Airlines B737
  installation, the local barometric altimeter
  setting is required to be inputted manually into
  the FMS.
• 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 Captains altimeter setting.

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