NCPMA
Advanced Mapping
NORTH CAROLINA PROPERTY MAPPERS ASSOCIATION
ADVANCED MAPPING COURSE
SECTION 2
GLOBAL POSITIONING SYSTEM
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2.1 Global Positioning System
The Global Positioning System (GPS) was initiated by the Department of Defense in 1973.
The system uses satellites orbiting the earth to determine the positions of specially designed
ground receivers. GPS, formally known as the Navistar Global Positioning System,
overcame the limitations of many existing navigation systems. It has been successful
because its capabilities are accessible using small, inexpensive equipment. The first GPS
satellite, a Block I developmental model, was launched in February 1978. The launch of
Block II, the first operational launch for the GPS program in February 1989, marked the
beginning of steady progress towards a full constellation of 27 satellites. The system gained
fame during Desert Storm by providing unprecedented navigational accuracy for allied air
and ground forces, but it is rapidly being integrated into a wide variety of civilian uses as
well.
Satellites are launched from The Cape Canaveral Space Center from Delta II rockets. In
order to get into the correct orbit, the rocket must be fired straight up, and then levels off at
the predetermined altitude. It then orients itself downrange at an angle of 55° to the equator,
and uses a booster rocket to “throw” the GPS Satellite forward at a speed that will put it into
a near circular orbit.
“How does the satellite stay in orbit? Picture this. If you were to gently throw a baseball,
the ball would move forward a short distance then immediately begin to drop toward the
ground, before hitting it. Now, if you throw harder, it will still fall to the ground, however,
this time the ball lands further away. In both scenarios, the ball takes the same amount of
time to actually “fall” to the ground. Gravity is the reason for the similar “fall” time. The
gravity field of the earth pulls objects downward. The downward pull is independent of how
fast or slow you throw the baseball in a horizontal direction.
Suppose now that you can throw the baseball hard enough so that in the time gravity pulls
the ball one foot closer to the ground, the earth curves downward by one foot. If this
happened, the ball would never hit the ground. The ball would be in a trajectory (the path a
satellite follows through space). So, nothing keeps the satellite up. Gravity holds the
satellite down by deflecting the forward motion to follow the curvature of the earth.
When the GPS Satellite is in orbit 12,000 above the earth, it is affected by gravitation, not
gravity. Gravitation is the force documented by Sir Isaac Newton that causes all objects to
be attracted to each other. Gravity is the resultant force of gravitation and the centrifugal
force caused by the rotation of the earth. Therefore, while a satellite is “falling” in its orbit,
the earth is rotating underneath it, or curving away; the orbit does not rotate with the earth.
So how fast does the booster throw the satellite; 17,000 miles per hour. Now let’s suppose
that your throw the ball slightly faster than required to maintain circular orbit velocity. In the
time that gravity would normally pull the ball downward a foot, the ball would travel forward
enough for the earth to curve downward more than one foot. This allows the baseball to
actually gain altitude even though it was not thrown upward. As the ball falls around the
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earth, gaining altitude, gravity gradually slows the upward progress to the point where the
ball reaches a maximum altitude halfway around the earth from the point where the ball was
thrown. The baseball then begins to descend around the other half of the earth, losing
altitude as it moves. Eventually the ball returns to its original launch position with its
original velocity and the process is then repeated. This orbit is now an ellipse, not a circle.
Currently there are 27 GPS Satellites orbiting the earth. As previously mentioned these
satellites are tilted toward the earth’s equator by 55 degrees to ensure coverage of the earth,
including the polar regions. Powered by solar cells they continuously orient themselves to
point their solar panels toward the sun and their antennas toward the earth.
Back on the ground, a GPS receiver is used to determine its position on the earth’s surface by
computing the difference between the time that a signal is sent from one of the satellites and
the time it reaches the receiver. This time information is placed within codes broadcasted by
the satellite so that the receiver can continuously determine the time the signal was broadcast
and received. The receiver then computes the distance, or range, from the receiver to the
satellite by multiplying the time it took the signal to travel from the satellite to the receiver
by 186,000 miles per second (the speed of light). With information from at least four
satellites and knowing the location of the satellite when the signals were sent, the receiver
can compute its own unique three-dimensional position relative to the entire earth and the
entire satellite constellation.
GPS receivers determine their position by computing the difference between the time that a
signal is sent from a satellite and the time it reaches the receiver. GPS satellites carry atomic
clocks that provide extremely accurate time. The time information is placed within codes
broadcast by the satellite so that a receiver can continuously determine the time the signal
was broadcast. The receiver computes the distance, or range, from the receiver to the
satellite. With information about the ranges to four satellites and the location of the satellites
when the signals were sent, the receiver can compute its own three-dimensional position.
For example, if a receiver calculates that it is 11,000 miles from satellite “A”, the receiver
must be located somewhere on an imaginary sphere that is centered on the satellite and has a
radius of 11,000 miles. If the receiver also calculates that it is 12,000 miles from satellite
“B”, the receiver must be located somewhere on a circle formed by the intersection of the
two spheres. If, at the same time, the receiver calculates its distance from a third and fourth
satellite, its precise position can be determined. Range can be computed by R=t.1; R=
distance from satellite to receiver, t= time lapse, 1= speed of light.
Radio waves travel at the speed of light: 186,000 miles per second. To determine its
position, a receiver must be able to calculate the point in time that the GPS satellite started
sending its radio message and the point in time that the receiver captured it. Synchronizing
the satellites and ground receivers causes them to generate the same signal codes at exactly
the same time. Once a code is received from the satellite, the receiver "looks back" to
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determine how long ago our receiver generated the same code. Figure 2-1 illustrates this.
Figure 2-1
Code-matching concept for measuring distances from GPS receivers to satellites.
Receiver
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The codes are called pseudo random sequences that actually repeat every millisecond. The
receiver then multiplies that time in seconds by 186,000 miles per second to calculate
distances to each satellite.
Each of the 27 satellites are in a precise orbit. Figure 2-2 illustrates the constellation of
Global Positioning Satellites. Each satellite will travel around the earth twice every sidereal
day (which is 3 minutes and 56 seconds shorter than a solar day), and will be visible to an
observer for a maximum of approximately 10 hours per day. The geometry and dynamics of
this constellation ensure that at nearly every location on earth, at any given time, from four to
six (and sometimes more) satellites will always be visible.
Figure 2-2
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The signals emitted from a satellite are picked up at ground stations by receivers like the one
shown in Figure 2-3.
Figure 2-3
It should be noted that the GPS is first and foremost a military system, which is used only
secondarily for civilian purposes.
GPS position determinations require precise satellite orbital information. This information is
compiled by the GPS Operational Control System (OCS), which monitors the satellites from
five tracking stations spaced uniformly in longitude throughout the world. The master
control station at Falcon Air Force Base in Colorado Springs, Colorado and monitor stations
at Hawaii, Ascension Island in the Atlantic Ocean, Diego Garcia Atoll in the Indian Ocean
and Kwajalein Island in the South Pacific Ocean. The GPS satellites fly in circular orbits at
an altitude of 12,500 miles and are tilted to the earth’s equator by 55 degrees to ensure
coverage of polar regions. Powered by solar cells, the satellites continuously orient
themselves to point their solar panels toward the sun and their antennas toward the earth.
From the monitored data, precise near-future predictions of all satellite orbits are determined,
uploaded into the satellites as often as three times daily, and broadcast by each satellite along
with the satellite’s pseudo random code signals. This broadcast orbital information is called
ephemeris. It enables GPS receivers to make real-time positioning computations.
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2.2 Airborne GPS
Mounting a GPS receiver in an aircraft during photographic missions makes it possible to
determine the geographic coordinates of the focal center of the aerial camera at the instant
each frame of aerial film is exposed. A specially designed GPS receiver antenna is mounted
on the top of the aircraft at a point directly above the center of the camera. The antenna is
mounted so that it points directly upward when the aircraft is in level flight attitude. Figure
2-4 shows a typical airborne GPS (AGPS) antenna installation.
Figure 2-4
The position calculated by a single GPS receiver is not precise enough to be useful for a
photogrammetric mapping project. The precision of the coordinates must be enhanced using
a process called differential correction.
During aerial photographic projects a ground GPS station is placed directly over a precisely
surveyed ground point with known geographic coordinates. The ground receiver is activated
during the aerial photo mission and is left to record positional information while the mission
is flown. Both the ground and airborne receivers typically record positions once every
second. After the mission, data from the ground receiver is compared to data from the
airborne receiver. The recorded coordinates of the ground based receiver are compared to
the receiver’s known, surveyed coordinates. The difference between the recorded and known
coordinates represents the error in the position recorded by the ground station. This error is
determined for each of the positions recorded by the ground receiver during the mission.
Corrections for the errors are then applied to each position recorded by the airborne receiver–
essentially making its recorded positional information for each aerial film exposure as
accurate as the known coordinates of the ground station. The tasks involved in downloading,
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comparing and applying the corrections to the positional data are known collectively as “post
processing”.
Air crews using AGPS must constantly monitor the onboard GPS receiver to ensure that it is
receiving signals from a sufficient number of satellites and that it can continuously calculate
an accurate position. Pilots must make shallow turns and avoid steep banks so that the
externally mounted antenna can continue to receive signals from all of the necessary
satellites. All turns, ascents and descents, must be as gradual and as gentle as possible.
Figure 2-5 illustrates an airborne GPS system in flight. It is possible to perform
aerotriangulation using the photo center coordinates fixed from the GPS. It is anticipated
that with this system, future mapping control for orthophotographs may be gathered without
intensive ground control throughout the county.
Figure 2-5
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Section 2
Review Questions
1.
GPS is an acronym for ____________ ________________ _______________.
2.
GPS measures distance by computing the time it takes a signal to be sent from a
_________________ to a ____________________.
3.
How many Global Positioning Satellites are in orbit around the earth? ________
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