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
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
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
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.