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POSITIONING MAJOR LANDMARKS

In 1988 a team of surveyors used the signals from the Navstar satellites to reestablish the locations of 250,000 landmarks sprinkled across the United States. According to one early press report, their space-age measurements caused the research team to "move the Washington Monument 94.5 feet to the northwest " And during that same surveying campaign, they moved the Empire State Building 120.5 feet to the northeast, and they repositioned Chicago's Sears Tower 90.1 feet to the northwest.

In reality, of course, the Navstar satellites do not give anyone the power to move large, imposing structures, but the precise signals they broadcast do provide our geodetic experts with amazingly accurate and convenient position-fixing capabilities that have been quietly revolutionizing today's surveying profession. Someday soon the deed to your house may be specified in GPS coordinates. Surveying with a GPS receiver entails a number of critical advantages over classical ground-based methods for pinpointing the locations of widely scattered landmarks on the Earth's undulating surface. For one thing, intervisibility between benchmarks is not required. Navstar receivers positioned at surveyors benchmarks often have access to the signals from the GPS satellites sailing overhead even though they may not be within sight of one another. This can be especially important in tree-shrouded areas, such is the dense rain forests of Indonesia and Brazil. In such cluttered conditions, conventional surveying teams sometimes spend hours E erecting big, portable towers at each site to achieve the required intervisibility high above the forest canopy. When it is time to move on, they tear the towers down one by one and lug their girders to different locations, and then build them back up again. GPS surveying is advantageous because it is essentially weather-independent, and because it permits convenient and accurate day-night operations. With carrier-aided navigation techniques, site-to-site positioning errors as small as a quarter of an inch can sometimes be achieved.

The signals from the space-based Transit Navigation System have been used for many years to aid specialized terrestrial surveying operations. Unfortunately, Transit surveying suffers from a number of practical limitations as compared with similar operations using the GPS. A Transit satellite, for instance, climbs up above the horizon, on average, only every hour or so compared with the continuous GPS satellite observations. Moreover, achieving and accuracy of a foot or so requires approximately 48 hours of intermittent access to the signals from the Transit satellites. By contrast, the GPS provides inch-level accuracies with the satellite observation interval lasting, at most, only about 1 hour.

DETERMINING THE SHAPE OF PLANET EARTH

For thousands of years scientists have tried to determine the size and shape of planet Earth. During those centuries, shapes resembling tabletops, magnifying glasses, turkey eggs, and Bartlett pears have all, at one time or another, been chosen to model its conjectured shape. The ancient Babylonians, for instance, were convinced that the earth was essentially flat, probably due to erroneous everyday observations. But by 900 BC, they had changed their minds and decided it was shaped like a convex disc. This will belief probably arose when some observant mariner noticed that, whenever a sailboat approaches the horizon, it's hull drops out of view while the sail was still clearly visible. By 1000 BC Egyptian and Greek scientists had concluded that the earth was a big, round ball. In that era, in fact , Erastothenes managed to make a surprisingly accurate estimate of the actual circumference of the spherical earth. He realized that such an estimate was possible when he happened to notice that it noontime on a particular day, the sun's rays plunged directly down a well and Aswan, but at that same time due north at Alexandria it's rays came down at a more shallow angle.

Once he had measured the peak elevation angle of the solar disk at Alexandria on the appropriate day (see Figure 1), Erastothenes estimated the distance from Aswan to Alexandria - probably by noting the travel times of sailing boats or camel caravans. He then a value weighted a simple ratio to get an estimate for the circumference of planet Earth. Translating measurement units across centuries is not an easy thing to do, but our best guess indicates that his estimate for the earth's radius was too large by around 15 percent. Twenty-five centuries later, Christopher Columbus underestimated the Earth's radius by 25 percent. He wanted to believe that he inhabited a smaller planet so the Orient would not be prohibitively far away from Europe, sailing west. In 1687, England's intellectual giant, Sir Isaac Newton, displayed his powerful insights when he reasoned that his home planet, Earth must have a slight midriff bulge. Its shape, he reasoned is governed by hydrostatic equilibrium, as it spinning mass creates enough centrifugal force to sling a big curving girdle of water upward against the pull of gravity. Newton's mathematical calculations showed that this enormous water-girdle must be around 17 miles high. But were the landmasses affected in the same way as that bulge of water in the seas? Newton understood that if the earth was rigid enough, the landmasses would not be reshaped by the centrifugal forces but he reasoned that, since there were no mountains 17 miles high, the landmasses must be similarly affected, otherwise, no islands would peak up through the water in the vicinity of the equator.

Figure 1. In 1000 B.C., the highly insightful Greek mathematician Erastothenes estimated the radius of the earth by measuring the elevation angle of the sun at Alexandria when it was known to be overhead due south at Aswan (Syene). Then using a simple ratio, he scaled up the measured distance separating those two Egyptian cities to obtain a surprisingly accurate estimate for the circumference of the spherical earth.

GPS CALIBRATIONS AT THE TURTMANN TEST RANGE

Surveying demonstrations carried out at the Turtmann Test Range in the Swiss Alps have demonstrated that, when a GPS receiver is operated in the carrieraided (interferometry) mode, it can provide positioning inaccuracies comparable to those obtained from the finest available laser-ranging techniques. Figure 2 summarizes the positioning accuracies that the Swiss surveying team was able to achieve in the Turtmann test campaign. In this clever bird's-eye-view depiction of the range, the various baseline lengths or all accurately proportioned. The short vectors are proportional to the surveying errors in the horizontal plane, but they have been magnified 100,000 times, compared with the dimensions of the baseline lengths.

I n one early test series, the one sigma deviations between the GPS measurements and the earlier glacier-ranging calibrations turned out to be

Sigma X = 0.2 inches

Sigma Y = 0.15 inches

Sigma Z = 0.17 inches.

In an earlier test involving only for base stations with three unknown baseline lengths of 382.2 feet, 1644.4 feet, and 333 feet, the average surveying errors were:

Sigma X = 0.2 inches

Sigma Y = 0.35 inches

Sigma Z = 0.35 inches.

Both sets of measurements were estimated using static surveying techniques in which the GPS receiver sits at each site for about a half-hour to record several hundred pseudo-range measurements. All of the measurements from the various sites are then processed simultaneously to achieve the desired results.

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