A Differential GPS Mapping Project of the
Private Tombs of Sheikh Abd el-Qurnah
October 2005 - June 2006
Data Collection and Field Investigation: Peter A. Piccione, Ph. D.
Lab Investigation: Norman S. Levine, Ph. D.
Differential GPS and
The survey will record GPS coordinates of all the tombs at or above the center of their doorways, or as close to these points as possible. These coordinates must be correct to within a narrow margin of error if the map is to be useful for plotting precise locations and azimuths in the necropolis and for identifying socio-historical relationships among the tombs and archaeological and spatial distributions. In this endeavor, the Geology Department and GIS Laboratory of the College of Charleston and University of Charleston, S.C., have been contributing technology and an understanding of GPS and GIS procedures, as well as the spreadsheets for manually calculating differential GPS coordinates, if necessary.
To take the highly precise GPS readings, the survey will employ a Trimble Pathfinder ProXT®, which is a professional survey-grade GPS receiver capable of sub-meter accuracy. Combining that with Trimble TerraSync® software, the survey will initially gather and log raw and uncorrected GPS data of the tombs that will be accurate to within only several meters. To increase the precision of the data, it must undergo "post-processing." Here the survey will combine the raw GPS coordinates with a different set of coordinates and satellite timings obtained from a separate GPS reference receiver (hopefully one located within several hundred miles of Luxor). Both sets of coordinates are processed through GPS Pathfinder Office®, resulting in differentially corrected GPS coordinates of each tomb that are now accurate to within 10-20 cm. If an acceptable reference receiver is not located or is unaccessible, then the survey will resort to the procedures of pseudo-differential GPS (see below).
In any event, the corrected data could then be loaded (while still in the field) on to the OLGIS-TN satellite map and database running on a portable tablet PC. In this manner, the survey can view the newly corrected GPS coordinates on the Theban photo-map even while still in the Theban necropolis. The OLGIS-TN database operates in ESRI ArcGIS® running with the Trimble GPS Analyst® extension.
A Most Basic Primer:
Origins of the GPS. The first Global Positioning System (GPS) was created by the United States, when the U.S. Department of Defense launched a constellation of GPS satellites to serve the military and economic needs of the United States and its allies. By broadcasting GPS signals on separate military and civilian channels, the U.S. also permits civilians and other nations to utilize the Global Positioning System for non-military uses, including: navigation, transportation, survey, mapping, exploration, mining, recreation, etc., although subject to certain limitations. In times of war or national emergency--and to prevent enemies from using the system to attack America's own resources and interests, the U.S. can (and it has!) shut down the civilian GPS channel. In this process known as "Restricted Availability", it can limit access to the GPS by civilians and foreigners, except military allies. In recent years, the Europeans and the Russians have begun to create their own global positioning systems. Presently, the U.S. is planning to erect an even more advanced and extensive second-generation Global Positioning System.
The basis of the GPS is a constellation of 24 Navistar GPS satellites that orbit 12,000 miles (20,000+ km.) above the earth. At the other end of this system is any GPS receiver located on the surface of the planet. A GPS satellite is essentially a flying radio transmitter with a clock (okay, an atomic clock!). Similarly, the GPS receiver is essentially a radio receiver with a clock plus a calculator. Each satellite in orbit constantly broadcasts to earth an identifying signal with the precise time that the radio signal is sent and some data about the satellite's trajectory. On the earth a GPS receiver receives the signal, and it measures the signal's travel time through the atmosphere by comparing the time when the signal left the satellite to the time that it reaches the receiver. Using the travel time, the receiver then calculates its distance from the satellite.1 Knowing this distance, it can compute a number of possible locations where it might lie on the earth (latitude, longitude, and altitude). With only one satellite, the receiver cannot calculate its single precise location. However, since the GPS receiver is also simultaneously receiving similar transmissions from other GPS satellites in orbit, it can compute all the possible locations from one satellite to the next, "triangulate" the distances, and isolate the coordinates that are common to all the satellites. By this method, it can determine its location. The receiver can also project the course and speed of the satellite. The GPS receiver needs to receive signals from at least four satellites to yield optimum results (latitude, longitude plus altitude.
Satellite Geometry. Satellite geometry also plays a role in reliably calculating position, that is, where the satellites happen to be situated in the sky, while they are transmitting to the receiver. The geometric configuration of the satellites to each other in the sky and to the receiver on the ground will affect the integrity of their signals and their reception, e.g., signals from satellites that are too close to each other in the sky might not allow enough distance between them to triangulate locations reliably, compared to signals from satellites further apart. If a satellite is low on the horizon, its signal must travel a longer path through the atmosphere than if the satellite were higher in the sky.2 That longer path and travel time subjects the signal to more atmospheric distortions and reflections than if the satellite were higher in the sky or straight over head (with less atmosphere for the signal to travel through). Also, if the satellite is too low, the signal could be obstructed, reflected about, or degraded by features on the earth's surface (mountains, hills, trees, buildings, etc.). Satellite signals can easily be blocked by walls, buildings, trees, rooves, etc., even by people (if they stand between the receiver and the signal). A GPS receiver requires an unobstructed line of transmission in order to read a signal clearly. Thus, GPS receivers do not function inside buildings or underground. Similarly, depending on satellite geometry, they might not function effectively under a canopy of trees or closely beside tall buildings. Good GPS receivers contain digital almanacs listing the locations and trajectories of the satellites in the GPS. Thus, depending upon the strength and distribution of the signals and the geometric alignment of the satellites, these receivers can actually tell how useful any given signal is and to what extent it might be degraded or distorted. Thus, their readings also include a measure of a signal's reliability. If a set of signals is weak, the receiver can also tell at what time of day it would otherwise receive the strongest signals from the satellites (since it knows satellite trajectories). In this manner, a person could return to a location at a later time of the day when the signals would be stronger or better aligned.
Differential GPS (DGPS)
The entire Global Positioning System is subject to a number of basic error factors, some that are inborne in the system, others that are man-made. Errors can result from the evolving geometry of the GPS process, calculation anomalies, imperfect orbits, inaccurate clocks, and from geographical and atmospheric issues affecting the transmission and delay of radio signals, all of which results in inaccurately computed travel times.3
Restricted Availability. Added to the foregoing errors, the U.S. military in the past has purposefully introduced "noise" into the timing signals of the satellites as part of its defense posture. These added signals reduced the accuracy of the distance computations to about 100 meters (328 ft). American and allied military GPS receivers contain a decryption key to decode these purposeful errors in order to obtain immediately the highest precision for tactical purposes, perhaps within 15 meters (less than 50 ft.). However, non-military GPS receivers are not encoded to correct these signal errors in real time. Still, civilians and foreigners can achieve the same level of accuracy as the military by an additional step of processing the output of the GPS receiver. While this additional step is inefficient and inconvenient for military and strategic purposes, it is acceptable for all other civilian uses of the GPS. It involves using two receivers to calculate a position; one is the roving GPS receiver that is trying to compute its location; the other is a stationary receiver known as a "reference station" or "reference receiver" (also "base station") which already knows its exact location. This method of employing two receivers to calculate precisely corrected GPS locations is called, "differential GPS (DGPS)". 4
The reference receiver is permanently mounted at its location, and it constantly receives signals from all available GPS satellites. Since it already knows the satellites' positions and its own precise location, it uses its known position to calculate the precise timing (instead of an ordinary receiver which uses possibly imprecise timing to calculate position). By this method, the reference station can compute the error factor or time delay in any satellite's signal at a given moment in a particular area. This error factor, or "differential," can be applied to any other GPS receiver operating simultaneously within several hundred miles (250-500 km.) to correct the latter's timing. The result is very accurate "differentially corrected" GPS coordinates. This system works because the satellites are very high in space, and their signals travel over a wide area. Since the two receivers share the same section of atmosphere, they experience the same satellite time delays. Some reference receivers also have radio transmitters, and they continuously broadcast their corrective timing data to all differential GPS receivers in their range. These GPS receivers then immediately correct their measurements and locations. This system of real time, on-the-run, differential correction is used in moving vehicles, e.g., planes, ships, etc. Other reference receivers transmit to the Internet where their timing data is stored and logged in digital files.
Another method of differential GPS is to "post-process" the location and timing data. If on-the-run, immediate differential correction is unnecessary (e.g., in surveying and mapping), then one could gather GPS data and corrective timings separately from the reference station and the GPS receiver. One could then combine and process the GPS data and the timings at a later time in special software to calculate the correct differential coordinates. However, here, it is important to include the date and time of day when each GPS coordinate was recorded at the receiver.
Across the world, many countries and agencies have a established networks of permanently-based GPS reference stations (e.g., the CORS system in the U.S.) to provide accurate differential GPS reference data to any civilians requiring highly precise GPS coordinates, including: ships at sea, airplanes in the sky, trains, trucks, oil explorers, drillers, miners, surveyors, mappers, builders, etc.
Pseudo-Differential GPS. If a network of GPS reference stations does not exist in any given area, and yet one still requires very precise differentially corrected coordinates, then a person could use a single GPS receiver as both a receiver and a reference station. This method is not always convenient, but it is functional. On any day that a person wishes to take GPS coordinates, one must first establish the GPS receiver at a known location and continuously log a series of reference-coordinates and satellite timings over a period of time (e.g., 20 mins.); thereafter one goes about the normal procedure of taking roving GPS coordinates. One then returns to this known location about every three hours and repeats the process of logging reference coordinates and timings. Later, the two sets of data are post-processed in a spreadsheet or special software, which calculates the corrected differential GPS coordinates. The more frequently one records and logs reference-coordinates, the more correct will be the final results. In this regard, one must determine the acceptable level of precision required by the particular project in order to know how often to take the reference-coordinates in a given workday.
A simpler but less convenient method of correcting GPS coordinates is to auto-average each GPS reading. The longer that a GPS receiver receives a signal and calculates its location, the more accurate is the resulting coordinate, since the receiver is actually averaging together a continuous series of the same coordinate to reach a more correct figure. However, this method could ultimately require inordinate amounts of time, probably over several days, to take each coordinate, depending upon the level of accuracy one is seeking.
1 The receiver calculates its distance from the satellite by multiplying the travel time of the signal by the speed of light (3x1010 cm/sec).
2 "Atmosphere" here technically means the ionosphere and the troposphere.
3 Added to the error factors is that the speed of light is treated as a constant for the purposes of calculation. However, in reality it is not constant outside of a vacuum. It can change depending on the density of the medium through which the light is passing. The ionosphere contains charged particles, while the troposphere contains water vapor, both of which slow down the speed of light. In this manner, error can creep into the calculations.
4 In certain ways, differential GPS is akin to "back-sighting" the GPS receiver--almost as a theodolite. To calibrate a theadolite's measurement of an unknown coordinate, it must be turned to measure and log a coordinate that is already absolutely known, and which serves as a reference point. Similarly in differential GPS, one compares one's GPS coordinates with a nearby set of coordinates and timings that are also absolutely known. The difference between the 2 sets of timings yields a differential factor that can be added or subtracted to the first set of coordinates.