(By Ed D'Antoni ed.dantoni@bbs.logicnet.com)

After writing an article on Global Positioning Systems (GPS) for Ultralights and small aircraft, I was asked how a GPS determines location speed and time. First a clarification of the use of the words Global Positioning System and the abbreviation GPS. I will use the written words Global Positioning System to mean the complete system of Satellites and Ground Stations. The abbreviation GPS will refer to earth based receivers that provides the user with location, speed, and time. The basic principal seems simple enough, a ground based GPS calculates the time if takes for individual signals from at least 3 Satellites to reach a specific GPS receiver. The GPS multiplies the time interval to each satellite by the speed of light to obtain distance. The GPS then calculates it’s location by triangulation. Speed and direction can also be obtained from a moving GPS. This is done from calculations of differences between successive locations over a given period of time. Time and date data is transmitted from satellites and decoded and displayed on your GPS. That is the basic concept, the amount of information processing and error correcting required to obtain any kind of position accuracy is mind boggling. In the following paragraphs I will try to explain:

  1. How the GPS knows the moving SVs location especially when SV position, with respect to time, on it’s Earth track changes every day.
  2. How the GPS determines time (distance) between transmission and reception of a signal when the GPS clock has nowhere near the accuracy of SVs Clocks?
  3. If location accuracy is only 100 metres how the GPS determines velocity from time between two locations probably less than 100 metres apart?

The Global Positioning system was developed by the U.S. Department of Defense and is referred to as the Navigation Satellite Timing and Ranging Global Positioning System, or Navstar GPS. The Space Segment consists of Satellites referred to as Space Vehicles and abbreviated SVs. Each satellite is about the size and weight of a Cessna 182; it consists of solar power panels, 4 Atomic Clocks, communication and computing equipment and rechargeable batteries for eclipse periods. The GPS Constellation has 24 Satellites in 20200 Kilometres orbits rotating around the earth in 6 orbital planes. Each satellite tracks over the earth’s surface at a velocity of 1800 Knots ( 2000 mph, or 3330 Km/hr.)completing one orbit every 12 hours. The orbits are configured such that each satellite repeats the same Earth Track once every 24 hrs.(actually 4 minutes less than 24 hours). Five to eight operational satellites are visible from any point on earth at any given time. The Standard Positioning System Accuracy (RMS) for Civilian users is 100 metres horizontally and 156 metres Vertically. The Military is capable of obtaining 22 metre horizontal and 28 metre vertical accuracy. Random errors are introduced into the system to reduce Civilian use accuracy. It is not hard to imagine what a military adversary or terrorist could do with a GPS, Computer, Explosives and a bad attitude. Accuracy’s of 10 metres can be obtained with differential GPS. Differential GPS use, in addition to SVs, a ground based transmitter of know location for a reference. Similarly surveying accuracy’s of 1 millimeter can be achieved when two special use transmitters of known location and at least 30 km apart are used.

In answers to "How the GPS knows the exact SV location." -- The Global Position System consists of Space, Master Control, and GPS segments. The Global Positioning System Master Control Station is located at Falcon Air Force Base, Colorado Springs, Colorado. There are 4 Monitoring Stations throughout the world. One station is located in Hawaii and the rest are located as close as possible to the equator in the Mid Atlantic, just below India and North of New Zealand.

The Master Control and Monitor stations Control the satellite system. They track satellite location, process time, Ephemeris and other data which is transmitted to the SVs. The SVs in turn transmit this data for GPS use. Each SV has its own identification, often referred to as it’s PRN number. Predicted SV locations are referred to as Ephemeris Data. An Ephemeris is a log of predicted sun and star locations with respect to time. Early Sailors and Explorers used Ephemeris data along with a Sextant to determine their location. Ephemeris’s in book form are available at most university bookstores. They are used today by Surveyors, Sailors and some Pilots. Using Ephemeris data and the exact time the GPS calculates it’s position using at least 3 SVs for position. If 4 SVs are available altitude can also be determined. Each SV transmits bursts of position and time data. The GPS uses the position information in a preloaded algorithm to calculate and predict SV location with respect to time (Ephemeris data). A GPS can reliably use this stored data for up to 4 hours. To verify SV time and location the GPS compares the SV data streams with its own data information. When these data bits match, the GPS "locks on" and accepts the location as being correct.

The GPS System operates on its own time system. Time is controlled by Atomic Clocks at Edwards Air Force Base, ground monitoring stations and space vehicles. Atomic clocks don’t run on atomic energy, they use the precise atomic oscillations of rubidium and cesium for accurate timekeeping. Four clocks per satellite ensure correct time is always available. The clock started January 5, 1980. Since GPS time does not make year end error corrections, (Leap Seconds) GPS time is now several seconds ahead of UCT (Zulu time). This is not of problem for GPS users as the system makes corrections that ensure the time displayed by your GPS is indeed UCT. Since the speed of light is 300,000 km. per second it takes only 6/100ths of a second for a signal from a satellite 18,000 km overhead to reach a ground based GPS, therefore time measurement is critical. Atomic clocks are accurate to on billionth of a second (.000000001 second). When setting their own internal clock, ground based GPS units must account for th e time it takes for a signal to get from the SV to the GPS. The accuracy of your GPS clock is nowhere near that of the $100,000 SVs Atomic Clocks. The inaccuracy between the SVs and GPS clock is automatically detected when the GPS calculates position. An analogy to determining location is to draw arcs of specific distance from 3 or 4 satellites. All of the arcs should cross at the same location. If they do not meet at the same location, a computer program in the GPS appropriately adds or subtracts distance (time) to each location and again checks to see if all distances meet at the same location. This process is repeated until a MATCH is made. Most GPS’s continuously calculate and display the estimated probable error (EPE) due to these timing discrepancies.

Direction of movement is determined from changes in geographical position over time. Speed is calculated by dividing distance traveled over time and /or use the Doppler effect. The Doppler effect is the phase shift of signals or sounds received when a constant frequency source is moved away from or towards a receiver. An example of this is a loud Motorcycle traveling at constant speed past a pedestrian. The noticeable difference between the approaching and departing frequency is a result of the Doppler effect. The phase shift of a signal from or between moving objects can be measured. This phase shift is then used to calculate speed between objects.

Besides the US Global positioning system, a Russian system, Glonass is in position. The Glonass orbits are such that when one satellite goes below the horizon, another one rises at the same time. This and the fact that random errors are not introduced into the system makes for a simpler and more accurate system. It is expected that more accurate GPS units making use of both the US and Russian Satellites will soon be available.

I hope the above helped. It is written to explain the basics of the GPS system yet throw some light onto the complexity of the system. The text includes liberalization for the benefits of those of us that are not engineers surveyors or mathematicians. For example triangulation is not used to calculate location. Instead the cosine law and error correction of 3 calculated positions is used. Triangulation is imaginable for most, --using "The Cosine Law" in the above text would cause most readers to stop right there. Any comments questions or suggestions to improve this article are welcomed. (ed.dantoni@bbs.logicnet.com)

Note: This article was contributed during November of 1996. The passing of time will no doubt render some of the information contained herein obsolete. Please bear this in mind.
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Jon N. Steiger / jon@ultralighthomepage.com