The Rudiments of the Modern Global Positioning System

          GPS, or Global Positioning System, is becoming more and more a part of our lives.  GPS is literally taking over.  The FAA recently declared GPS a mature technology, which is making it easier for avionics professionals to install GPS into our general aviation airplanes.  The FAA is implementing more GPS instrument approaches and to a greater accuracy then ever before.  GPS allows even bush pilots to make their own navigation points to find a remote strip and set up for an approach in marginal VFR (visual flight rules) weather. 

            Aviation is not the only one to benefit from GPS.  Anyone can buy a hundred dollar receiver and determine exactly where they are on planet earth within meters.  They can be used for land surveying, hiking, boating, locating remote islands, giving directions, or anything else that requires navigation or plot positioning.  Aviation, nonetheless, has seen the biggest change in navigation since the implementation of the VOR (Very high frequency Omnidirectional Range).  Pilots flying airplanes equipped with GPS have no need to “Climb, Communicate, Confess, Comply.”  Why?  Because its nearly impossible to get lost with a moving map GPS. 

            The fundamentals of GPS are simple and fairly intuitive.  The part that gets complicated is making sure it is reliable and accurate and using the data once we have it and displaying it in a useful manner.  The receiver uses signals from satellites in space

and converts the time it takes to reach the receiver into distance.  It needs to have several satellite signals in order to get a useful three-dimensional position.  A basic understanding of two-dimensional trilateration, three-dimensional trilateration, measuring time, and measuring distance is needed to understand how GPS works. 

            The Global Positioning System is exactly that, a large, well orchestrated, and expansive system.  According to the FAA’s AC 8083-15 (2001), there are 24 satellites operating for GPS in space and there are even three spares to boot!  The United States DOD (Department of Defense) developed GPS for military tactical purposes but soon found that it would benefit the common man as well.  The DOD is still in charge of operating and monitoring the system.  Brain and Harris (2001) write:

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.

Satellites are simply objects that revolve around a planet in an elliptical path.  Satellites can orbit near circular, but cannot orbit in a perfect circle.  This is because Gravity pulls a satellite towards it, but inertial and centrifugal forces throw it outward.  The satellite is essentially falling towards the planet, missing it, and then being pulled back in again by gravity.  This repeating cycle is what makes it orbit indefinitely. According to http://ilrs.gsfc.nasa.gov/satellite_missions, there are 23,000+ satellites/items that we are currently tracking in space.  If even one loose bolt were to hit an operating satellite, there would be extensive damage, as the speeds that keep objects in orbit are tremendous by our standards.  We now have supercomputers that track all of our junk in earth orbit.  Eventually, micro-particles wear on our operating satellites and they need to be replaced.  Orbital velocity is the velocity needed to balance the pull of gravity and the inertia of the satellite.  In very low orbit, about 150 miles, the orbital velocity is approximately 17,000 miles/hour (Brown. G., 2000).  GPS satellites are not geostationary (stationary relative to earth) and they orbit the earth about twice a day.

Trilateration is simply finding a point by using geometry of four or more known locations and the distance you are from each one.  This is not unlike deductive reasoning.  If you are x miles from point A, x miles from point B, x miles from point C, and x miles from point D, then you are at point X.  In two-dimensional trilateration, it is only necessary to have 3 points of known reference (refer to figure 1).

                                Figure 1

Two-dimensional trilateration uses circles.  Three-dimensional trilateration involves spheres.  This is why you can still sometimes navigate with only three satellite signals, but there will be no altitude information and its accuracy will be compromised.  In fact, the more satellites, the better.  RAIM, or Receiver Autonomous Integrity Monitoring, requires a minimum of five satellites to operate. 

            As previously mentioned, three-dimensional trilateration uses spheres of distance to pinpoint your location.  The earth may serve as the required fourth sphere.  The first satellite has a specific distance to someone’s GPS receiver.  Mathematically, this creates a sphere of that distance radii in all directions from the satellite.  A second satellite determines the distance to the receiver.  This provides another mathematical distance radii sphere.  The two spheres will inevitably and necessarily overlap and provide us with a circle of possible points.  Since a circle is a two-dimensional shape that most people can easily come to grips with, imagine the circle is on a piece of paper.  The two satellites previously mentioned are in front of the paper and behind it and their outer distance radii intersect to form the circle on the flat paper.  If a third satellite that is located on the paper somewhere outside the circle determines you are x miles from it, there is now only two distinct possibilities of that person’s location.  Refer to figure 2, as this is a simple rendering of this explanation.  

 
                                                      Figure 2

The earth can act as the fourth sphere because, of the two locations we deduced, one is on earth and the other is far of into outer space.  In order for a GPS receiver to work, it has to have the right location of at least three satellites above and the distance between the receiver and each of those satellites (M. Brain and T. Harris, 2001).

            The exact location of the satellites must be known in order to determine the position of the receiver.  The FAA’s AC 8083-15 (2001) says “In addition to knowing the distance to a satellite, a receiver needs to know the satellite’s exact position in space; this is known as its ephemeris.”  Each satellite transmits information of  its exact position to the receiver.  Since the receiver knows exactly where the satellite is in relation to earth and its distance (converted mathematically from time), it can use this as the geometry needed to trilerate its position.

            The GPS receivers figure out the location and distance to satellites using low power radio signals.  Since radio waves are part of the electromagnetic spectrum, they travel at maximum speed, which is 186,000 miles/second.  The time it takes to get to the receiver is mathematically translated into distance, since it is known that the speed of the radio waves is a constant, barring any electromagnetic solar storms or the like. 

            Okay, so time is distance.  The satellite transmits a pseudo-random code.  A pseudo-random code is a random number that is not truly random.  The only truly random thing we could generate digitized numbers from would be radioactive isotope decay and other nature based systems.  Computers work only on logic, so a random seed (starting number) is used and then multiplied by 1,103,515,245 and added to 12,345 (http://computer.howstuffworks.com/question697.htm).  The last digit or digits are the pseudo-random numbers.  Each time this process is done, it creates a new pseudo-random number that works in conjunction with the receiver.  The satellite and receiver both have instructions to start the same random seed at the same time.  They also both use the same formula to generate infinitely more pseudo-random numbers.  When the GPS receiver gets the code, it will lag behind the time that the receiver generated that same code and make note of the time of delay.  Time is crucial in accuracy of GPS because the speed of electromagnetic energy is a constant. 

            As mentioned, time very sensitive in this equation and both the receiver and satellite need to be able to become synchronized down to the nanosecond (M. Brain and T. Harris, 2001).  In order to have two completely synchronized clocks that never shift apart in time it would be necessary to have to independent atomic clocks.  Atomic clocks rely on an oscillating mass and a spring, just like ordinary clocks.  But as the name implies, they are on an atomic level. The oscillation frequencies within the atom are determined by the mass of the nucleus and the gravity and electrostatic "spring" between the positive charge on the nucleus and the electron cloud surrounding it (Dywer, D. 1999).  Without atomic clocks, the world would never be fully synchronized, and GPS and other time synchronized technologies would not be possible.  However, atomic clocks are expensive and obviously the GPS receivers need a solution to solve this time-synch problem.

            GPS receivers utilize an ordinary quartz clock.  While not accurate down to nanoseconds, quartz technology is good enough to provide a reliable time signal if it constantly resets itself.  The receiver “looks” at four or more different signals from GPS satellites in earth orbit, which have atomic clocks, and judges its own accuracy.  It is simply amazing someone figured this out.  If there are three satellite signals, they will all intersect radii at some point.  But when there is a fourth signal, the radii should all intersect one point only.  If the radii do not touch, the amount of error will be proportionally incorrect and the receiver will reset itself to the correct time required to bring all four spheres to intersect at one point.

            GPS is America’s satellite based positioning system, but it is not the only one.  The Russian Federation has a satellite positioning system called GLONASS (GLObal NAvigation Satellite System).  It is very similar to the United States’.  Some people worry that we have already become too reliant on GPS for our cross-countries and that there will be no backup in the future in case GPS needs to be shut down.  The two GPS systems are still under independent military control.  Already, though, we are looking into designing a third system called GNSS that will be owned and operated by the civilians internationally (Jeppesen, 2000, p.8-59).  Some receivers are built to use either system.  This may prove to be a benefit when operating in areas that have weak signal coverage because of surrounding terrain.

            GPS is a technology that is simply amazing.  Small technologies brought about larger technologies which eventually brought about the Global Positioning System.  Through the use of satellite, radio, quartz, digital, and atomic clock technologies, the United States has achieved a navigation aid that will continue to provide pilots of all types of vehicles with the reliable positioning they need to get where they are going.  It has seemingly endless applications.  The FAA is implementing LNAV/VNAV approaches that blow the doors off older navaid technology.  The VORs, NDBs, and other primitive navaids are being phased out slowly but surely.  Does this mean that our enroute charts will be blank except for airports in the future?  My best Guess is that we will keep many of the same waypoints that we use now so that airplanes can still be funneled into the major hubs, but our routes will be much more direct.

Works Cited

Brain, M., Harris, T. (2001). Electronics – gadgets. How GPS Receivers Work. Retrieved

February 2, 2004 from the world wide web: http://electronics.howstuffworks.com/gps.htm

Brown, G. (2000). Science. How Satellites Work. Retrieved February 4, 2004 from the

            world wide web: http://science.howstuffworks.com/satellite.htm

Dywer, D.(2000). Science. How Atomic Clocks Work.  Retrieved February 3, 2004 from

            the world wide web:  http://science.howstuffworks.com/atomic-clock.htm

 Federal Aviation Administration. (2001). Instrument Flying Handbook (AC 8083-15).

Washington, DC: U.S. Government Printing Office.

Jeppesen. (2000). Instrument Commercial Manual. Englewood, CO: Jeppesen

             Sanderson Inc.