Principles and Applications of Aviation Navigation Systems

1. 民航導航系統原理與應用 成大民航研究所 詹劭勳 老師 (c)Shau-Shiun Jan, IAA, NCKU

2. Course Information – Books • Avionics Navigation Systems, M. Kayton, W. R. Fried, John, ISBN: 0471547956 • Many reference books (Keywords: GPS, INS): • Global Positioning System (GPS): Signals, Measurements and Performance, P. Misra and P. Enge, Ganga-Jamuna, 2001 • Strapdown Inertial Navigation Systems, D. H. Titterton and J. L. Weston • The Global Positioning System and Inertial Navigation, Farrell and Barth, McGraw-Hill, 1999 • Integrated Aircraft Navigation, J. L. Farrell, Academic Press, 1976 • Global Positioning Systems, Inertial Navigation and Integration, Grewal, Weill and Andrews, Wiley Interscience, 2001 (c)Shau-Shiun Jan, IAA, NCKU

3. Outline • Part 1: Introduction • Part 2: Navigation Coordinate • Part 3: Radio Navigation Systems • Part 4: Global Positioning System • Part 5: Augmentation Systems (c)Shau-Shiun Jan, IAA, NCKU

4. Part 1: Introduction An Overview of Navigation and Guidance (c)Shau-Shiun Jan, IAA, NCKU

5. Navigation and Guidance • Navigation: The process of determining a vehicle’s / person’s / object’s position • Guidance: The process of directing a vehicle / person / object from one point to another along some desired path (c)Shau-Shiun Jan, IAA, NCKU

6. Example • Getting from AA building to Tainan Train Station • How would you tell someone how to get there? • How would you tell a robot to get there? • Both problems assume there is some agreed upon coordinate system. • Latitude, Longitude, Altitude (Geodetic) • North, East, Down with respect to some origin • Ad Hoc system (“starting from AA building you go 1 block…”) • Most of our work in this class is going to be with the Navigation problem (c)Shau-Shiun Jan, IAA, NCKU

7. Applications • Air Transportation • Marine, Space, and Ground Vehicles • Personal Navigation / Indoor Navigation • Surveying (c)Shau-Shiun Jan, IAA, NCKU

8. Steering commands Sensor #1 Navigation and/or Guidance Processor Sensor #2 : : Sensor #N Navigation state vector A Navigation or Guidance System • Steering commands: instructions on what to do to get the vehicle going to where it should be going • Turn right / left • Go up / down • Speed up / slow down (c)Shau-Shiun Jan, IAA, NCKU

9. Navigation State / State Vector • A set of parameters describing the position, velocity, altitude… of a vehicle • Navigation state vector: • Position = 3 coordinates of location, a 3x1 vector • Velocity = derivative of the position vector, a 3x1 vector • Attitude = a set of parameters which describe the vehicle’s orientation in space (c)Shau-Shiun Jan, IAA, NCKU

10. Position and Velocity • More often than not, we are interested in position and velocity vectors expressed in separate coordinates (more on this later…) (c)Shau-Shiun Jan, IAA, NCKU

11. Attitude • We will deal with two ways of describing the orientation of two coordinate frames • Euler angles: 3 angles describing relationship between 2-coordinate systems • Transformation matrix: maps vector in “A” coordinate frame to “B” (c)Shau-Shiun Jan, IAA, NCKU

12. Attitude (continued) • The first entry of the attitude “vector”, ψ, is called yaw or heading. (c)Shau-Shiun Jan, IAA, NCKU

13. Navigation and Guidance Systems • In this class we will look at ways to determining some or all of the components of the navigation state vector. • Some navigation systems provide all of the entries of the navigation state vector (inertial navigation systems) and some only provide a subset of the state vector. • Guidance systems give instructions on how to achieve the desired position. (c)Shau-Shiun Jan, IAA, NCKU

14. Navigation and Guidance Systems (c)Shau-Shiun Jan, IAA, NCKU

15. Categories of Navigation • Dead Reckoning • Positioning (position fixing) • Navigation systems are either one of the two or are hybrids. (c)Shau-Shiun Jan, IAA, NCKU

16. Dead Reckoning Systems • “Extrapolation” system: position is derived from a “series” of velocity, heading, acceleration or rotation measurements relative to an initial position. • To determine current position you must know history of past position • Heading and speed or velocity systems • Inertial navigation systems • System accuracy is a function of vehicle position trajectory (c)Shau-Shiun Jan, IAA, NCKU

17. Positioning / Position Fixing Systems • Determine position from a set of measurements. • Knowledge of past position history is not required • Mapping system – Pilotage (pp.504-505) • Celestial systems – Star Trackers • Radio systems – VOR, DME, ILS, LORAN… • Satellite systems – GPS, GLONASS, Galileo… • System accuracy is independent of vehicle position trajectory (c)Shau-Shiun Jan, IAA, NCKU

18. Brief History of Navigation • Land Navigation – “pilotage” traveling by reference to land marks. • Marine Navigation • Greeks (300~350 B.C.) – Record of going far north as Norway, “Periodic Scylax” (Navigation manual). • Vikings (1000 A.D.) – had compass • Ferdinand Magellan (1519) – recorded use of charts (maps), devices for getting star fixes, compass, hour glass and log (for speed). • The important point to note is that these early navigators were using dead reckoning and position fixing (hybrid system) (c)Shau-Shiun Jan, IAA, NCKU

19. Determine Your Latitude Polaris h s γ RE Λ Equators Λ=Latitude (c)Shau-Shiun Jan, IAA, NCKU

20. How do you determine longitude? • Dead reckoning • Compass for heading, log for speed • Not very accurate, heading errors, speed errors → position errors • Errors grow with time (c)Shau-Shiun Jan, IAA, NCKU

21. The Longitude Problem • Longitude act of 1714 • £20,000 for 1/2o solution • £15,000 for 2/3o solution • £10,000 for 1o solution (about 111km resolution at equator!) • Board of longitude • Halley (“Halley Comet”) • Newton • Solution turned out to be a stable watch / clock (c)Shau-Shiun Jan, IAA, NCKU

22. 20th Century and Aviation • Position fixing (guidance) systems: • Pilotage • Fires (1920) – US mail routes • Radio beacons • Late 1940’s most of the systems we use today started entering services • By 1960’s VOR/DME and ILS become standard in commercial aviation • Dead reckoning • Inertial navigation (1940) • German v-2 Rocket • Nuclear submarine (US NAVY) • Oceanic commercial flight (c)Shau-Shiun Jan, IAA, NCKU

23. 20th Century and Aviation • Satellite based navigation systems • US NAVY Transit System (1964) • Global Positioning System • 1978 first satellite launched • 1995 declared operational • Other satellite navigation systems • GLONASS – Former Soviet Union • Galileo – being developed by the EU (c)Shau-Shiun Jan, IAA, NCKU

24. Performance Metrics and Trade-Off • Cost • Autonomy • Coverage • Capacity • Accuracy • Availability • Continuity • Integrity • Area of active research: 5,6,7,8 • Accuracy: we will visit it in detail later on. (c)Shau-Shiun Jan, IAA, NCKU

25. Part 2: Navigation Coordinate Frames, Transformations and Geometry of Earth. • Navigation coordinate frames • Geometry of earth (c)Shau-Shiun Jan, IAA, NCKU

26. Coordinate Frames • The position vector (the main output of any navigation system and our primary concern in this class) can be expressed in various coordinate frames. • Notation (c)Shau-Shiun Jan, IAA, NCKU

27. Why Multiple Coordinate Frames? • Depending on the application at hand some coordinates can be easier to use. • In some applications, multiple frames are used simultaneously because different parts of the problem are easier to manage. • For example, • GPS: normally position and velocity in “ECEF” • INS: normally position in geodetic and velocity in “NED” (c)Shau-Shiun Jan, IAA, NCKU

28. Cartesian ECEF ECI NED (locally tangent Frames) ENU (locally tangent Frames) Spherical/cylindrical Geodetic Azimuth-Elevation-Range Bearing-Range-Attitude Coordinate Frames Except for ECI, all are non-inertial frames, an inertial frames is a non-accelerating (translation and rotation) coordinate frames. (c)Shau-Shiun Jan, IAA, NCKU

29. ECEF and ECI • Earth Centered and Earth Fixed (ECEF) • Cartesian Frame with origin at the center of earth. • Fixed to and rotates with earth. • A non-inertial frame. • Earth Centered Inertial (ECI) • Cartesian frame with origin at earth’s center. • Z axis along earth’s rotation vector. • X-y plane in equatorial plane. (c)Shau-Shiun Jan, IAA, NCKU

30. Geodetic • Geodetic (Latitude, Longitude, Altitude) – Spherical • Latitude (Λ) = north – south of equator, range ± 90o • Longitude (λ) = east – west of prime meridian, range ± 180o • Altitude (h) = height above reference datum • “+” north latitude, east longitude, down (below) datum altitude (c)Shau-Shiun Jan, IAA, NCKU

31. NED and ENU • North-East-Down (NED) • Cartesian • No fixed location for the origin • Locally tangent to earth at origin • East-North-Up (ENU) • Cartesian • Similar to NED except for the direction of 1-2-3 axes. (c)Shau-Shiun Jan, IAA, NCKU

32. Azimuth-Elevation-Range • Azimuth-Elevation-Range • Spherical • No fixed origin • Azimuth is angle between a line connecting the origin and the point of interest (in the tangent plane) and a line from origin to north pole • Elevation is the angle between the local tangent plane and a line connecting the origin to a point of interest • Range is the slant or line-of-sight distance (c)Shau-Shiun Jan, IAA, NCKU

33. Azimuth-Elevation-Range • Two types of azimuth or heading angles • True: measured with respect to the geographic (true) north pole (ψT) • Magnetic: measured with respect to the magnetic north pole (ψM) (c)Shau-Shiun Jan, IAA, NCKU

34. Earth Magnetic Field • 1st order approximation is that of a simple dipole • Poles move with time. • In 1996 magnetic north pole was located at (79oN,105oW) • In 2003 it is located at (82oN,112oW) • Also, can “wander” by as much as 80km per day (c)Shau-Shiun Jan, IAA, NCKU

35. Earth Magnetic Field • Magnetic poles are used in navigation because ψM is easier to measure than ψT • Bx and By are measured by devices called magnetometers (Ch.9) • Anomalies such as local iron deposits lead to erroneous ψM reading • Iron range deposits of N.E. Minnesota can lead to errors as large as 50o (c)Shau-Shiun Jan, IAA, NCKU

36. Shape / Geometry of Earth • Topographical / physical surface • Geoid • Reference ellipsoid (c)Shau-Shiun Jan, IAA, NCKU

37. Shape / Geometry of Earth (continued) • Topographical surface – shape assumed by earth’s crust. Complicated and difficult to model mathematically. • Geoid – an equipotential surface of earth’s gravity field which best fits (least squares sense) global mean sea level (MSL) • Reference ellipsoid – mathematical fit to the geoid that is an ellipsoid of revolution and minimizes the mean-square deviation of local gravity (i.e., local norm to geoid) and ellipsoid norm, WGS-84 (c)Shau-Shiun Jan, IAA, NCKU

38. Latitude (c)Shau-Shiun Jan, IAA, NCKU

39. WGS–84 • Four defining parameters • Other parameters are derived from the four • Equatorial radius = 6378.137km • Flattening = 1/298.257223563 • Rotation rate of earth in inertial space = 15.041067 degree/hour • Earth’s gravitational constant (GM) = 3.986004x108m3/s2 (c)Shau-Shiun Jan, IAA, NCKU

40. Part3:Radio Navigation Systems I: Fundamentals • I: Fundamentals • II: Survey of Current Systems (c)Shau-Shiun Jan, IAA, NCKU

41. Radio Navigation Systems • These are systems that use Radio Frequency (RF) signals to generate information required for navigation. • C = speed of electromagnetic waves in free space (“ speed of light ”) • “ Radio waves ” correspond to electromagnetic waves with frequency between 10 KHz and 300 GHz (c)Shau-Shiun Jan, IAA, NCKU

42. Frequency (c)Shau-Shiun Jan, IAA, NCKU

43. GPS signals are L band Signals • MLS uses C band signals Expand Frequency (c)Shau-Shiun Jan, IAA, NCKU

44. Radio Signal Propagation (1/3) • Ground Waves • Waves below the HF range (i.e., < 3 MHz) • Unpredictable path characteristics • Required large antenna • Atmospheric noise (c)Shau-Shiun Jan, IAA, NCKU

45. Radio Signal Propagation (2/3) • Line of Sight Waves: • Signals > 30 MHz • 100 MHz – 3 GHz – predictable • Above 3 GHz – absorption • Above 10 GHz – discrete absorption (c)Shau-Shiun Jan, IAA, NCKU

46. Radio Signal Propagation (3/3) • Sky Waves • HF and below (i.e., < 30 MHz) • Multipath • Fading • Skip distance: depends of frequency and ionosphere conditions (c)Shau-Shiun Jan, IAA, NCKU

47. Modulation Techniques • Modulation – how you place information of the RF signal • Amplitude modulation (AM) – change the amplitude of sinusoid to relay information • Frequency modulation (FM) – change in frequency of transmitted signal to relay information • Phase modulation (PM) – change phase of transmitted signal to relay information • The signal can be transmitted as a pulse or a continuous wave. Either one can be modulated by the above methods. (c)Shau-Shiun Jan, IAA, NCKU

48. How do you distinguish one beacon from another? • Frequency division multiple access (FDMA) – each transmitter/beacon uses a different frequency • Time division multiple access (TDMA) – each transmitter/beacon transmits at a specified time • Code division multiple access (CDMA) –each transmitter/beacon uses an identifier code to distinguish itself from the other transmitters or beacons (c)Shau-Shiun Jan, IAA, NCKU

49. Important Conclusions • Low frequency systems – ground wave transmission – long range systems, Loran. • High frequency systems – line of sight systems (c)Shau-Shiun Jan, IAA, NCKU

50. (c)Shau-Shiun Jan, IAA, NCKU