eges-504 02/21/2006 p-1 engineering division colorado school of mines gk-12 gk-12 gps

Engineering Division

Colorado School of MinesGK-12

GK-12GPS



Outline for the segment

• Brief discussion of historical and interesting information of GPS

• Discuss uses of GPS and the math involved

• GPS Scavenger Hunt• Comments and questions from

scavenger hunt • Potential uses in a math or science

classroom



What does GPS stand for?

Global Positioning System



General Information

• GPS is free, provided you have a receiver• GPS was originally for military applications, but in

the 1980s, the system was made available for civilian use

• The first GPS satellite was launched in 1978• A full constellation of 24 satellites was achieved

in 1994• There are currently 30 satellites in use• Since GPS satellites are in orbit, they utilize solar

power, giving them a virtually endless supply of power for twenty-four hours at a time (sunlight and moonlight).



Random Facts

• A GPS satellite weighs approximately 2,000 pounds and is about 17 feet across with the solar panels extended.

• The cost of maintaining the system is approximately $750 million per year, including the replacement of aging satellites, and research and development.

• GPS must have line of sight views can be obstructed by buildings and other objects.

• The more units a receiver can sense, the more accurate the signal is.



So How Does it Work?

• The basis of GPS is trilateration from satellites• To “trilaterate,” a GPS receiver measures distance

using the travel time of radio signals• To measure travel time, GPS needs very accurate

timing which it achieves with some tricks.• Along with distance, you need to know exactly

where the satellites are in space. High orbits and careful monitoring are the secret.

• Finally, you must correct for any delays the signal experiences as it travels through the atmosphere.



Measuring Distance from a Satellite• Remember, Time = Distance / Velocity?• In GPS, we’re measuring a radio signal, so the

velocity is going to be the speed of light• Let’s say the satellite and the receiver start

transmitting code at the same time, we’d hear two different versions. The first is the current transmission from the receiver and the second is the transmission from the satellite. The amount of time between the two versions is the travel time of the satellite’s version.



The timing trick• If our receiver's clocks were perfect, then all our

satellite ranges would intersect at a single point, but with imperfect clocks, a fourth measurement, done as a cross-check, will NOT intersect with the first three.

• Any offset from universal time will affect all of our measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements that would cause them all to intersect at a single point.

• That correction brings the receiver's clock back into sync with universal time, and you've got atomic time accuracy right in the palm of your hand without the ~$50,000 cost.



Satellites in Space

• A satellite is injected into a very precise orbit and all GPS receivers have an almanac programmed into them that tells them where a satellite is located.

• This position is constantly monitored by the Department of Defense by precise radar.

• The earth’s ionosphere and atmosphere cause delays in the GPS signal that translate into position errors.

• Differential GPS utilizes two GPS units to account for the variations caused by factors inhibiting the signal.



Triangulation? Not exactly.• Technically the process which has been called

triangulation is trilateration. Triangulation is typically used in a single plane with angles and at least one known distance, ship navigation for example. Trilateration uses measured distances between known reference points.

• We measure our distance from a satellite and find it to be 11k miles…so we’re on a sphere with satellite in middle w/ radius=11k miles



Triangulation? Not exactly.

• Next, say we measure our distance to a second satellite and find out that it's 12,000 miles away.

• That tells us that we're not only on the first sphere but we're also on a sphere that's 12,000 miles from the second satellite. Or in other words, we're somewhere on the circle where these two spheres intersect.



Triangulation? Not exactly.

• We then make a measurement from a third satellite and find that we're 13,000 miles from that one, that narrows our position down even further, to the two points where the 13,000 mile sphere cuts through the circle that's the intersection of the first two spheres.



Accuracy (Selective Availability)• The GPS traditionally included a feature called Selective

Availability (SA) that introduces intentional, slowly changing random errors of up to a hundred meters into the publicly available navigation signals.

• During the Gulf War, the shortage of military GPS units and the wide availability of civilian ones among personnel resulted in a decision to disable Selective Availability.

• In the 1990s, the FAA started pressuring the military to turn off SA.

• SA was eventually "discontinued"; the amount of error added was "set to zero" at midnight on May 1, 2000 following an announcement by U.S. President Clinton.



Accuracy (Interference & Jamming)• Since GPS signals at terrestrial receivers tend to be

relatively weak, it is easy for other sources of electromagnetic radiation to overpower the receiver.

• Solar flares are a naturally occurring emission with the potential to degrade GPS reception, and their impact can affect reception over the half of the Earth facing the sun. GPS signals can also be interfered with by geomagnetic storms.

• Man-made interference can also disrupt, GPS signals. Intentional jamming is also possible. Generally, stronger signals can interfere with GPS receivers when they are within radio range, or line of sight.



Accuracy (Electronic Error)• The satellites also broadcast two forms of clock

information, the Coarse / Acquisition code, or C/A which is freely available to the public, and the restricted Precise code, or P-code.

• Modern electronics can measure signal offset to within about 1% of a bit time, or approximately 10 nanoseconds for the C/A code. Since GPS signals propagate nearly at the speed of light, this represents an error of about 3 meters. This is the minimum error possible using only the GPS C/A signal.

• Position accuracy can be improved by using the higher-speed P(Y) signal. Assuming the same 1% bit time accuracy, the high frequency P(Y) signal results in an accuracy of about 30 centimeters.



Accuracy (Sources of variability)• Sources of User Equivalent Range Errors (UERE)• Ionospheric effects ± 5 meter• Ephemeris errors ± 2.5 meter• Satellite clock errors ± 2 meter• Multipath distortion ± 1 meter• Tropospheric effects ± 0.5 meter• Numerical errors ± 1 meter or less



GPS Applications

• The Global Positioning System, while originally a military project, is considered a dual-use technology, meaning it has significant applications for both the military and the civilian industry.

• Military Applications?• Civilian Applications?• An almost unlimited number of civilian

applications benefit from GPS signals, all of which utilize one or more of three basic components of the GPS; absolute location, relative movement, time transfer.



GPS distribution



Helpful information• How to turn the unit on? • How do GPS units record position?• What does the display mean?• What else can my GPS do?• Additional questions?



Rules for the Scavenger Hunt

• Think about the possibilities of using the handheld GPS units as an extension or motivation for classroom instruction.

• You may use the GPS unit in any manner to complete the scavenger hunt.

• Watch out for traffic and Have Fun!



Scavenger Hunt

• At each station there will be a card for each team, take the card with you team letter on it as each team will have a different route.

• If you need to grab a drink or go to the restroom feel free to take a quick break. When you are ready to begin your scavenger hunt head outside and I will give you your first card.

eges-504 02/21/2006 p-1 engineering division colorado school of mines gk-12 gk-12 gps

Documents