GPS Basics

We introduce Global Positioning System (GPS) technologies as a natural complement to geographic information systems.  A GPS receiver is a portable device which calculates and records its own geographic position.  In fact, you can think of a GPS receiver as a 1:1-scale digitizer; you digitize the earth itself rather than some paper map representation of it.  In fact, GPS is quickly becoming integrated into everyday life. Many cars and most planes have onboard GPS navigation systems, and GPS is part of GM's OnStar system, signalling location when an airbag deploys, for example. Commercial trucking companies use GPS to track their drivers. FCC regulations now require cell phones to be trackable by emergency system dispatchers, so some cell phones have GPS chips installed while others use Assisted GPS (described below).

GPS is supported by a constellation of at least 24 NAVSTAR satellites that orbit the earth about once every 24 hours. Four satellites orbit in each of six orbital planes at an altitude of 20,200 KM (10,900 nautical miles). The six orbital planes are tilted 55 degrees from the equator, and cross the equator at 30-degree longitude intervals. The satellites broadcast precisely syncronized signals that GPS receivers use to triangulate their position anywhere on the earth. 

Triangulation geometry is pretty straightforward.  If you know your distance is X miles from a single point (satellite), it defines your position as somewhere on an imaginary sphere of radius X.  If you know your distances are X and Y from two dispersed points, it defines your position somewhere on the imaginary circle at which two imaginary spheres with radii X and Y intersect.  If you know your distances from three dispersed points are X, Y and Z, it defines your position as one of two points where the three spheres interesect (one sphere intersects the circle representing the intersection of the other two spheres)  If you know your distances from four dispersed points, it defines one of these two points as your location.

With 24 satellites in well-dispersed orbits, there are never fewer than four satellites above the horizon anywhere on earth, so a GPS receiver can always triangulate its position to a unique X-Y-Z point in space.  The GPS satellites' orbits are precisely known, and they use precisely-synchronized on-board atomic clocks to broadcast exactly simultaneous signal patterns as well as information about any minor deviations in orbit.

A typical GPS receiver has an almanac programmed into it which tells it which satellites should be above the horizon.  When powering up, it acquires the signals from these satellites on separate channels.  (Most receivers, including the Garmin units we use in this class, can receive and process signals from as many as 12 satellites at once.)  The satellite signals are broadcast exactly simultaneously, but received with different time delays depending on the relative distances of the satellites. The time delays are measured in nano-seconds (a nano-second is 10^-9 or one billionth of a second). The signals are traveling at the speed of light--186,000 miles per second, or about 1 foot per nano-second. 

If the receiver has acquired more than four satellites, it can calculate triangulated positions from each combination of four signals.  The clock on the GPS receiver doesn't have to be as accurate as the atomic clocks on the satellites; the receiver's processor can correct for its own clock error to derive a mathematically consistent fix corrected for that error.

In the simplified diagram above, the receiver's clock is slightly slow, so its calculated distances based on signal offsets from the satellites are systematically biased upward, yielding the gray overlap area.  The alternative triangulations A, B and C can be averaged to determine the final triangulated position.

Most GPS receivers also report  elevation (Z-dimension), although Z-accuracy is much lower than X,Y-accuracy because the satellites are most frequently low on the horizon (about three quarters of the visible sky is below 45 degrees).

Sources of GPS position error include ionospheric and atmospheric delays of satellite signals (generally worse when satellites are low on the horizon), tiny deviations in satellites' atomic clocks or orbits (clock and orbit correction data are calculated at least daily), rounding errors in receiver processors, and multi-path errors due to signal reflections off of features near the receiver.  Error magnitudes depend in part on satellite positions: a constellation of satellites well distributed around the horizon will give more accurate X-Y fixes than a clustered constellation.  Most GPS units calculate and report an accuracy measure (e.g., "figure of merit") with each fix.  To maximize accuracy, you can check the published almanac for times when you will have many well-dispersed satellites, and schedule your GPS fieldwork then.

Accuracy Enhancements

GPS began as US military technology. Until 2000, for "security reasons," the military added an artificial noise called "selective availability" (SA) to the NAVSTAR satellite signals that degraded the positional accuracy of civilian GPS units by 30 meters or more. Military-grade units included classified firmware to filter out SA noise. With SA, the positional accuracy of ordinary civilian GPS units was only about 35-45 meters, while military-grade receivers were typically accurate to 5-10 meters. 

The US government terminated SA under pressure from the FAA, and because it was easy to circumvent in any case.  SA made any stationary GPS receiver appear to wander randomly around its true position. But you could obtain the exact position for stationary point by simply averaging fixes taken over a week or two.  And since SA errors were identical for all GPS receivers, you could record the apparent "wander" of a stationary base unit GPS receiver while recording simultaneous fixes with a mobile unit, and then difference out the SA from the mobile unit's recorded positions.

Actually, you didn't even need your own base unit. The Coast Guard maintained differential GPS beacons around the coastal US, including one at Lewes, that broadcast correction data for civilian boaters, so all you really needed in coastal states was a beacon receiver with your mobile unit.  (Yes, one branch of the military provided the means to circumvent security measures implemented by another branch.)  In inland states you could subscribe to a commercial GPS beacon service.  The US military still maintains some classified accuracy enhancement technologies for GPS, but various other accuracy enhancements are available to civilian users.

Since the elimination of SA, civilian GPS within the US has been further enhanced by the Wide Area Augmentation System (WAAS), a network of about 25 ground reference stations developed by the FAA and Dept. of Transportation that calculate satellite signal errors caused by atmospheric disturbances, satellite clock drift, and orbital drift. Master stations on the east and west coasts broadcast these corrections to geostationary satellites, and WAAS-enabled GPS receivers download these corrections along with the positioning signals from the NAVSTAR satellites. WAAS is available for North America; other nations are developing equivalent correction systems for their GPS users.

Another accuracy enhancement for locating cell phones is Assisted GPS. Mobile phones themselves typically have poor positioning accuracy, but an "assistance server" maintains strong satellite signal reception and relays highly accurate positioning signals that cell phones can use to locate themselves accurately. The assistance server can then relay the phone's accurate location to an emergency dispatcher.

The most accurate positioning is achieved by accounting for doppler shifts in the carrier signal frequencies of the NAVSTAR satellites at a base location vis-a-vis a mobile location. This typically requires post-processing of the receiver data, but it can yield positions with less than 10 cm error.

The NAVSTAR system cost billions of dollars to design and launch, and costs about $700 million a year to maintain. But anyone can access the technology for the cost of a receiver.  Basic 12-channel GPS receivers are now avilable for less than $120 for hunters, boaters and hikers.  The 12-channel Garmin units used in this class cost $149 each, and there are better units on the market now that sell for less. These units calculate position, direction and speed of movement, determine direction and distance to any waypoint, store and download waypoints and routes to a computer, and can be interfaced with a differential GPS beacon receiver.  In contrast, the Trimble differential unit bought by the College of Agriculture & Natural Resources about 10 years ago cost about $11,000, and includes a backpack with antenna, large (and heavy) battery pack and larger hand-held data logger. Its accuracy advantages vis-a-vis our cheap little Garmin units have largely disappeared since termination of SA.

Precision Agriculture

GPS is a foundation technology for precision agriculture technologies, where nutrient applications are continuously adjusted or harvest quantities continuously monitored in real time by a GPS unit and computer that are mounted on the tractor or combine.  Precision farming techniques enable farmers to apply correct quantities of nutrients and pesticides exactly where they are needed.  This reduces production costs as well as environmental damage from runoff of excess nutrients and pesticides.

Many companies are now selling bundled precision farming technologies to farmers.  A full implementation might begin with a  mapping of soil tests performed at regular grid intervals on a field.  These points would be interpolated via kriging or some other method to obtain continuous grid surfaces representing pH, moisture retention, concentrations of each nutrient, etc.  The farmer would calibrate his or her nutrient applications to add only the additional nutrients that the crop would require.

The on-board computer provides real-time control of the applicator based on the map data and current position determined by the GPS receiver.  The harvester would throw grain against a pressure plate, pass vegetables over a scale under a conveyor belt, or perform some equivalent real-time yield monitoring; data from the yield sensor are combined with GPS coordinates to create a continous yield map.  The farmer can then compare micro-level production costs and yields on different sections of individual fields, and fine-tune field management to maximize the profitability of each field section.