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Global Positioning System
LUCID Summer Workshop July 29, 2004


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.

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.

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.

GPS: The Basics

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 ³man-made stars´ as reference points to calculate positions accurate to a matter of meters.

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.

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 p most accurate instruments could yield positions accurate only to within a few miles.

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).

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.

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.


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.

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.

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.

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.


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.

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

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.³ If you combine this information with the Boise information, you have two circles that intersect.

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«

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.

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.

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.

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:


Foghorn 1

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:
D D2

Foghorn 1

Foghorn 2

Possible Location of Mariner


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 D2

Foghorn 1

Foghorn 2

D3 Foghorn 3

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.

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 p 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

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.

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


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

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

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.

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.

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.

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.)

Aside: Introduction to Satellite Communications


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.

Satellite Orbits

A circular satellite orbit can be described as:
Satellite, m = mass r

R Earth

Circular satellite orbit

Using basic principles from physics, we can determine the orbit, i.e., find r, the radius of the circular orbit.

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.

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


Satellite Motion Description

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

Orbit Shapes

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

Apogee & Perigee

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

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.

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.

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.


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.

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.

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 39A, 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.

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.

Initial Boost (Cont¶d)

It takes a huge amount of energy to accelerate such a mass to 144 mph, and therefore a significant amount of fuel. Launching from the equator makes a real difference.

Putting Satellites into Orbit (Cont¶d)

Once the rocket reaches extremely thin air, at about 120 miles (193 km) up, the rocket's navigational system fires small rockets, just enough to turn the launch vehicle into a horizontal position. The satellite is then released. At that point, rockets are fired again to ensure some separation between the launch vehicle and the satellite itself.

Putting a Satellite in Orbit (Cont¶d)

A rocket must accelerate to at least 25,039 mph to completely escape Earth's gravity and fly off into space. Earth's escape velocity is much greater than what's required to place an Earth satellite in orbit. With satellites, the objective is not to escape Earth's gravity, but to balance it.

Orbit Velocity

Orbital velocity is the velocity needed to achieve balance between

gravity's pull on the satellite and the inertia of the satellite's motion -- the satellite's tendency to keep going.

Without gravity, the satellite's inertia would carry it off into space.

Orbit Velocity (Cont¶d)

Even with gravity, if the intended satellite goes too fast, it will eventually fly away. On the other hand, if the satellite goes too slowly, gravity will pull it back to Earth. At the correct orbital velocity, gravity exactly balances satellite's inertia. The orbital velocity of the satellite depends on its altitude above Earth. The nearer Earth, the faster the required orbital velocity.


In general, the higher the orbit, the longer the satellite can stay in orbit. At lower altitudes, a satellite runs into traces of Earth's atmosphere, which creates drag. Drag causes orbit to decay until the satellite falls back into the atmosphere and burns up. At higher altitudes, where the vacuum of space is nearly complete, there is almost no drag and a satellite can stay in orbit for centuries (take the moon as an example).

Different Roles for Satellites

Weather satellites help meteorologists predict the weather or see what's happening at the moment. The satellites generally contain cameras that can return photos of Earth's weather. Communications satellites allow telephone and data conversations to be relayed through the satellite. The most important feature of a communications satellite is the transponder -- a radio that receives a conversation at one frequency and then amplifies it and retransmits it back to Earth on another frequency.

Different Satellites (Cont¶d)

Broadcast satellites broadcast television signals from one point to another (similar to communications satellites). Scientific satellites perform a variety of scientific missions. The Hubble Space Telescope is the most famous scientific satellite, but there are many others looking at everything from sun spots to gamma rays. Navigational satellites help ships and planes navigate, e.g., GPS.

Different Satellites (Cont¶d)

Rescue satellites respond to radio distress signals. Earth observation satellites observe the planet for changes in everything from temperature to forestation to ice-sheet coverage. Military satellites are up there, but much of the actual application information remains secret.

Some Possible Military Applicaitons

Relaying encrypted communications Nuclear monitoring Observing enemy movements Early warning of missile launches Eavesdropping on terrestrial radio links Radar imaging Photography (using what are essentially large telescopes that take pictures of militarily interesting areas)

Similarities between Satellites

All satellites have a metal or composite frame and body, usually known as the bus. The bus holds everything together in space and provides enough strength to survive the launch. They have a source of power (usually solar cells) and batteries for storage.

Satellites Similarities

They have an onboard computer to control and monitor the different systems. They have a radio system and antenna. All satellites have an attitude control system. The ACS keeps the satellite pointed in the right direction.


Some satellites have (hundreds of) transponders for communication purposes. A transponder 1) receives transmissions from earth (uplink); 2) changes signal frequency; 3) amplifies the signal; and 4) transmits the signal to earth (downlink).

Satellite Subsystems

The main subsystems in a satellite are  communications;  power;  telemetry; tracking, and control (TTC);  propulsion;  attitude stabilization; and  antenna subsystems. Power subsystem consists of solar panels, batteries, dc-to-dc converters, and regulators. Solar panels convert sunlight into power to operate all satellite electronics and to charge batteries (used when sunlight is blocked).

Satellite Subsystems (Cont¶d)

The TTC subsystem contains a receiver that picks up commands from a ground station and translates them into control signals that initiate some action on board. The telemetry system monitors physical conditions within the satellites and converts them into electrical signals that are transmitted back to earth.

Ground Stations: The Other End

Satellites in space communicate (transmit/receive radio waves) with ground stations. Ground stations consist of subsystems:  transmit/receive;  Power;  Antenna;  TTC; and  ground control equipment (GCE).

Satellite Dish

Ground stations feature large parabolic dish antennas with high gain and directivity for receiving the weak satellite signal.
Satellite signals

The larger the dish is the higher the received signal power.

Important Satellite Classifications

GEO (Geostationary Earth Orbit) satellites orbit about 36,000 km above Earth¶s surface. LEO (Low Earth Orbit) satellites are about 500-1500 km above earth¶s surface. MEO (Medium EO) satellites are about 6000-20,000 km above earth¶s surface. There are also HEO (Highly Elliptical Orbit) satellites.

Orbits of Different Satellites
LEO (Iridium) GEO (Inmarsat)


1000 km 10,000 km HEO 35,768 km


Not drawn to scale

GEO Satellites

The majority of communications satellites are GEOs. These support voice, data, and video services, most often providing fixed services to a particular region. For example, GEO satellites provide back-up voice capacity for majority of U.S. long distance telephone companies and carry bulk of nation-wide television broadcasts, which commonly are distributed via from a central point to affiliate stations throughout country.

GEO¶s (Cont¶d)

GEO systems are less complicated to maintain because fixed location requires relatively little tracking capability at ground. High orbital altitude allows GEOs to remain in orbit longer than systems operating closer to earth.

GEOs (Cont¶d)

These characteristics, along with their high bandwidth capacity, may provide a cost advantage over other system types. However, their more distant orbit also requires relatively large terrestrial antennae and highpowered equipment and are subject to delays.

Satellite Delay

An important artifact of satellite communications is delay. The radio signal has to travel a large distance to reach satellite from ground station (or to reach ground station from satellite).
Variation of Delay as a Function of Elevation Angle Delay

0 90 Elevation Angle, U, in degrees


Typical LEO satellite takes less than 2 hours to orbit the Earth, which means that a single satellite is "in view" of ground equipment for a only a few minutes. If transmission takes more than few minutes that any one satellite is in view, a LEO system must "hand off" between satellites to complete the transmission.

LEOs (Cont¶d)

Handoffs can be accomplished by relaying signals between satellite and various ground stations, or by communicating between satellites themselves using "inter-satellite links." LEO systems designed to have more than 1 satellite in view from any spot on earth at any given time.

LEOs (Cont¶d)

LEO systems must incorporate sophisticated tracking and switching equipment to maintain consistent service coverage. Advantages: very little delay, operate using smaller equipment (because signals travel shorter distance), etc. Disadvantages: highly complex and sophisticated control and switching systems, shorter life span (subject to greater gravitational pull and higher transmission rates lead to shorter battery life).


MEOs are ³in between´ a GEO and a LEO. Advantages/Disadvantages are also in between:  PRO: MEO systems will require far fewer satellites than LEOs, reducing overall system complexity and cost, while still requiring fewer technological fixes to eliminate signal delay than GEOs.  CON: MEO satellites, like LEOs, have a much shorter life expectancy than GEOs, requiring more frequent launches to maintain system over time.


Elliptical orbit causes satellite to move around earth faster when it is traveling close to earth and slower the farther away it gets. Satellite¶s beam covers more of earth from farther away. Orbits are designed to maximize amount of time each satellite spends in view of populated areas.

HEOs (Cont¶d)

Delay characteristics depend on where the satellite is in its orbit. Several of proposed global communications satellite systems actually are hybrids of the four varieties reviewed above.

Satellite Costs

Satellite launches don't always go well; there is a great deal at stake. The cost of satellites and launches to name one. For example, a recent hurricane-watch satellite mission cost $290 million. A missile-warning satellite cost $682 million.

Satellite Costs (Cont¶d)

A satellite launch can cost anywhere between $50 million and $400 million. Russian launches are generally the cheapest and the French launches are the most expensive. A shuttle mission pushes toward half a billion dollars (a shuttle mission could easily carry several satellites into orbit).

Major U.S. Satellite Firms

Hughes Ball Aerospace &Technologies Corp. Boeing Lockheed Martin

How can I see an Overhead Satellite?

This satellite tracking Web site ( shows how you can see a satellite overhead, thanks to the German Space Operations Center. You will then need your coordinates for longitude and latitude, available from the USGS Mapping Information Web site (

Locating an Overhead Satellite

Satellite-tracking software is available for predicting orbit passes. The above websites will help with this. Note the exact times for the satellites. Use binoculars on a clear night when there is not a bright moon. Ensure that your watch is set to exactly match a known time standard. A north-south orbit often indicates a spy satellite!

Space Junk: Another Type of Satellite

Space junk: objects large enough to track with radar that were inadvertently placed in orbit or have outlived their usefulness Approximately 23,000 items of space junk are floating above Earth. The actual number varies depending on which agency is counting. Payloads that go into the wrong orbit, satellites with run-down batteries, and leftover rocket boosters all contribute to the count.

Some Other Causes for Space Junk


Exploding rockets - This leaves behind the most debris in space. Jettisoned items - Parts of launch canisters, camera lens caps, etc. The slip of an astronaut's hand. Items initially placed into high orbits stay in space the longest.

Slip of the Astronaut¶s Hand

Suppose an astronaut doing repair in space drops a wrench -- it's gone forever. The wrench then goes into orbit, probably at a speed of something like 6 miles per second. If the wrench hits any vehicle carrying a human crew, the results could be disastrous. Larger objects like a space station make a larger target for space junk, and so are at greater risk.

Next Time

This concludes our introduction to satellite communications. Next time, we will study the GPS system in greater detail. In the second half, we will switch gears and look at the basics of the Internet. This will setup our discussion on WiFi, which starts next week.

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