B737 GPS/FMS

1. B737 GPS/FMS Part 1: GPS Theory and Operation

2. 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)

3. 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.

4. 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.

5. 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).

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. 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

12. 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.

13. 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 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.

14. 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 discussed later.

15. 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.

17. 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.

19. 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.

20. 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.

21. 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.

22. 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) – 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.

23. 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 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.

24. 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 signal.

25. Tropospheric • 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 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.

26. 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.

27. 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 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.

28. 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.

29. 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.

30. 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)

31. 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.

32. 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

33. 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.

34. 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.

35. 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.

36. 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.

37. 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).

38. 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.

39. 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.

40. 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.

41. 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 Captain’s altimeter setting.