Global Positioning System

1. Global Positioning System LUCID Summer Workshop July 29, 2004

2. Background • In the past, humans had to go to pretty extreme measures to keep from getting lost. • They erected monumental landmarks, laboriously drafted detailed maps and learned to read the stars in the night sky.

3. Background (Cont’d) • Things are much, much easier today. • For less than $100, you can get a pocket-sized gadget that will tell you exactly where you are on Earth at any moment. As long as you have a GPS receiver and a clear view of the sky, you'll never be lost again.

4. Outline for Today • Today, we will review the basics of the GPS system: its key components, its history, etc. • To gain a full appreciation of the complexity of this system, we will also provide an introduction to satellite communications.

5. GPS: The Basics

6. What is it? • GPS: Global Positioning System is a worldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations. • A simplistic explanation: GPS uses these “man-made stars” as reference points to calculate positions accurate to a matter of meters.

7. What is it? (Cont’d) • Advanced forms of GPS make measurements to better than a centimeter. • Devised by the U.S. Department of Defense for fleet management, navigation, etc. • Although the U.S. military developed and implemented this satellite network as a military navigation system, it soon opened it up to everybody else.

8. A Little Bit of History • For centuries, only way to navigate was to look at position of sun and stars. • Modern clocks made it possible to find one's longitude. • Using this information and estimate of latitude  most accurate instruments could yield positions accurate only to within a few miles.

9. History (Cont’d) • Then, when the Soviet Union launched Sputnik on Oct. 4, 1957, it was immediately recognized that this "artificial star" could be used as a navigational tool. • Very next evening, researchers at Lincoln Labs at MIT were able to determine satellite's orbit precisely by observing specific properties of its transmitted radio wave (Doppler Shift).

10. More History • The proof that a satellite's orbit could be precisely determined from ground was first step in establishing that positions on ground could be determined by homing in on signals broadcast by satellites. • Then U.S. Navy experimented with a series of satellite navigation systems to meet navigational needs of submarines carrying nuclear missiles. • These submarines needed to remain hidden and submerged for months at a time.

11. More History (Cont’d) • By analyzing the radio signals transmitted by the satellites--in essence, measuring the Doppler shifts of the signals--a submarine could accurately determine its location in 10 or 15 minutes. • In 1973, Department of Defense was looking for a foolproof method of satellite navigation. • A brainstorming session at Pentagon over Labor Day weekend produced concept of GPS on basis of the department's experience with all its satellite predecessors.

12. More History (Cont’d) • The essential components of GPS were the 24 Navstar satellites built by Rockwell International, each the size of a large automobile and weighing some couple of thousand pounds. • Each satellite orbits the earth every 12 hours in a formation that ensures that every point on the planet will always be in radio contact with at least four satellites. • The first operational GPS satellite was launched in 1978, and the system reached full 24-satellite capability in 1993.

13. More Background • Each satellite is expected to last approximately 7.5 years and replacements are constantly being built and launched into orbit. • Each satellite transmits on three frequencies. • Civilian GPS uses the L1 frequency of 1575.42 MHz.

14. More Background (Cont’d) • Day-to-day running of GPS program and operation of system rests with the Department of Defense (DoD). • Management is performed by US Air Force with guidance from DoD Positioning/Navigation executive Committee. • This committee receives input from a similar committee within Department of Transportation (DoT) who act as civilian voice for GPS policy matters.

15. Background (Cont’d) • Each of these 3,000- to 4,000-pound solar-powered satellites circles the globe at about 12,000 miles (19,300 km), making two complete rotations every day. • The orbits are arranged so that at any time, anywhere on Earth, there are at least four satellites "visible" in the sky.

16. Triangulation • A GPS receiver's job is to locate four or more of these satellites, figure out the distance to each, and use this information to deduce its own location. • This operation is based on a simple mathematical principle called triangulation or trilateration. • Triangulation in three-dimensional space can be a little tricky, so we'll start with an explanation of simple two-dimensional trilateration.

17. An Example of 2D Triangulation • Imagine you are somewhere in the United States and you are TOTALLY lost -- for whatever reason, you have absolutely no clue where you are. • You find a friendly local and ask, "Where am I?" He says, "You are 625 miles from Boise, Idaho." • This is a nice, hard fact, but it is not particularly useful by itself. You could be anywhere on a circle around Boise that has a radius of 625 miles

18. Where in the U.S. am I? • To pinpoint your location better, you ask somebody else where you are. • She says, "You are 690 miles from Minneapolis, Minnesota.“ If you combine this information with the Boise information, you have two circles that intersect.

19. Where in the U.S. am I? (Cont’d) • If a third person tells you that you are 615 miles from Tucson, Arizona, you can eliminate one of the possibilities, because the third circle will only intersect with one of these points. You now know exactly where you are…

20. Where in the U.S. am I? (Cont’d) • You are in Denver, CO! • This same concept works in three-dimensional space, as well, but you're dealing with spheres instead of circles.

21. Another 2D Example • Consider the case of a mariner at sea (receiver) determining his/her position using a foghorn (transmitter). • Assume the ship keeps an accurate clock and mariner has approximate knowledge of ship’s location. Fog

22. Foghorn Example • Foghorn whistle is sounded precisely on the minute mark and ship clock is synchronized to foghorn clock. • Mariner notes elapsed time from minute mark until foghorn whistle is heard. • This propagation time multiplied by speed of sound is distance from foghorn to mariner’s ear.

23. Foghorn Example (Cont’d) • Based on measurement from one such foghorn, we know mariner’s distance (D) to foghorn. • With measurement from one foghorn, mariner can be located anywhere on the circle denoted below: D Foghorn 1

24. D2 Foghorn 2 Foghorn Example (Cont’d) • If mariner simultaneously measured time range from 2nd foghorn in same way. • Assuming, transmissions synchronized to a common time base and mariner knows the transmission times. Then: A D Foghorn 1 B Possible Location of Mariner

25. D2 Foghorn 2 Foghorn Example (Cont’d) • Since mariner has approximate knowledge of ship’s location, he/she can resolve the ambiguity between location A and B. • If not, then measurement from a third foghorn is needed. D Foghorn 1 B D3 Foghorn 3

26. How Foghorn Relates to GPS • The foghorn examples operates in 2D space. GPS performs similar location but in 3D. • The foghorn examples shows how time-of-arrival of signal (whistle) can be used to locate a ship in a fog. In this time-of-arrival of signal, we assumed we knew when the signal was transmitted. • We measured the arrival time of the signal to determine distance. Multiple distance measurements from other signals were used to locate the ship exactly.

27. Foghorn Example: Consider Effect of Errors • Foghorn/mariner discussion assumed ship’s clock was precisely synchronized to foghorn’s time base. • This may not be the case  errors in TOA measurements. • If we make a fourth measurement, we can remove this uncertainty. D2+e2 D+e1 Foghorn 1 Foghorn 2 D3+e3 Foghorn 3 Estimated Location Area of Ship

28. 3D Triangulation • Fundamentally, three-dimensional trilateration is not much different from two-dimensional trilateration, but it's a little trickier to visualize. • Imagine the radii from the examples in the last section going off in all directions. So instead of a series of circles, you get a series of spheres.

29. GPS Triangulation • If you know you are 10 miles from satellite A in the sky, you could be anywhere on the surface of a huge, imaginary sphere with a 10-mile radius. 10 miles Earth

30. GPS Triangulation (Cont’d) • If you also know you are 15 miles from satellite B, you can overlap the first sphere with another, larger sphere. The spheres intersect in a perfect circle. 15 miles 10 miles

31. GPS Triangulation (Cont’d) • The circle intersection implies that the GPS receiver lies somewhere in a partial ring on the earth. Perfect circle formed from locating two satellites Possible Locations of GPS Receiver

32. GPS Triangulation (Cont’d) • If you know the distance to a third satellite, you get a third sphere, which intersects with this circle at two points.

33. GPS Triangulation (Cont’d) • The Earth itself can act as a fourth sphere -- only one of the two possible points will actually be on the surface of the planet, so you can eliminate the one in space. • Receivers generally look to four or more satellites, however, to improve accuracy and provide precise altitude information.

34. GPS Receivers • In order to make this simple calculation, then, the GPS receiver has to know two things: • The location of at least three satellites above you • The distance between you and each of those satellites • The GPS receiver figures both of these things out by analyzing high-frequency, low-power radio signals from the GPS satellites.

35. GPS Receivers (Cont’d) • Better units have multiple receivers, so they can pick up signals from several satellites simultaneously. • Radio waves travel at the speed of light (about 186,000 miles per second, 300,000 km per second in a vacuum). • The receiver can figure out how far the signal has traveled by timing how long it took the signal to arrive. (Similar to foghorn example.)

36. Aside: Introduction to Satellite Communications

37. Satellites • The basic component of a communications satellite is a receiver-transmitter combination called a transponder. • A satellite stays in orbit because the gravitational pull of the earth is balanced by the centripetal force of the revolving satellite. • Satellite orbits about the earth are either circular or elliptical.

38. Satellite Orbits • A circular satellite orbit can be described as: • Using basic principles from physics, we can determine the orbit, i.e., find r, the radius of the circular orbit. Satellite, m = mass r R Circular satellite orbit Earth

39. Satellite Orbits (Cont’d) • Satellites orbit the earth from heights of 100 to 22,300 mi and travel at speeds of 6800 to 17,500 mi/h. • A satellite that orbits directly over the equator 22,300 mi from earth is said to be in a geostationary orbit. • Geostationary (GEO) satellite: revolves in synchronism with the earth’s rotation, so it appears to be stationary when seen from points on the earth.

40. 3D Orbit • Satellite orbits are not just determined by radius. There is also an inclination of the orbit relative to the equatorial plane (plane formed by the earth’s equator). Orbit of Satellite Inclination Equatorial Plane Earth Orbital Plane

41. Satellite Motion Description • To describe this 3D motion of a satellite, three typical measurements are used: roll, pitch, and yaw.

42. Orbit Shapes • Only some of the satellites have circular orbits. • Others have elliptical orbits. These orbits have further classifiers: • Apogee • Perigee

43. Apogee & Perigee • Perigee: point on orbit when satellite is closest to earth. • Apogee: point on orbit when satellite is farthest from earth.

44. Stabilizing Satellite Orbits • A satellite is stabilized in orbit by spinning it on its axis or building in spinning flywheels for each major axis (roll, pitch, yaw). • Attitude adjustments on a satellite are made by firing small jet thrusters to change the satellite’s position or speed. • Satellites are launched into orbit by rockets that give them vertical as well as forward motion.

45. Putting Satellites into Orbit • All satellites today get into orbit by riding on a rocket or by riding in the cargo bay of the Space Shuttle. • Several countries and businesses have rocket launch capabilities, and satellites as large as several tons make it safely into orbit on a regular basis. • For most satellite launches, the scheduled launch rocket is aimed straight up at first. This gets the rocket through the thickest part of the atmosphere most quickly and best minimizes fuel consumption.

46. Putting Satellites in Orbit (Cont’d) • After a rocket launches straight up, the rocket control mechanism uses the inertial guidance system to calculate necessary adjustments to the rocket's nozzles to tilt the rocket to the course described in the flight plan. • In most cases, the flight plan calls for the rocket to head east because Earth rotates to the east, giving the launch vehicle a free boost. N S

47. Initial Boost offered by Earth • The strength of this boost given by earth’s rotation depends on the rotational velocity of Earth at the launch location. • The boost is greatest at the equator, where the distance around Earth is greatest and so rotation is fastest.

48. Initial Boost (Cont’d) • How big is the boost from an equatorial launch? • To make a rough estimate, we can determine Earth's circumference by multiplying its diameter by pi (3.1416). • The diameter of Earth is approximately 7,926 miles. Multiplying by pi yields a circumference of something like 24,900 miles. • To travel around that circumference in 24 hours, a point on Earth's surface has to move at 1,038 mph.

49. Initial Boost (Cont’d) • A launch from Cape Canaveral, Florida, doesn't get as big a boost from Earth's rotational speed. • The Kennedy Space Center's Launch Complex 39-A, one of its launch facilities, is located at 28 degrees 36 minutes 29.7014 seconds north latitude. • The Earth's rotational speed there is about 894 mph. • The difference in Earth's surface speed between the equator and Kennedy Space Center is about 144 mph.

50. Initial Boost (Cont’d) • Considering that rockets can go thousands of miles per hour, what does a difference of only 144 mph mean? • Rockets, together with their fuel and their payloads, are very heavy. • For example, February 11, 2000 lift-off of the Space Shuttle Endeavor with the Shuttle Radar Topography Mission required launching a total weight of 4,520,415 pounds.