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Physics Tutorial: GPS
What is GPS?
GPS (global positioning system) can be defined as a collection of satellites and ground stations that allow users with specifically designed radio equipment to obtain position, distance and velocity data. Mariners at one time used constellations and the stars (such as Polaris in the Little Dipper or Alpha Ursae Minoris) as landmarks at night to determine their position and direction at sea. GPS replaces natural stars with artificial satellites which, together with radio signals and computer chips, have taken navigation a quantum leap forward in accuracy and usability.
Initially developed by the United States Department of Defense for missile guidance, now GPS works in commercial and personal navigation, agriculture, construction, law enforcement, mapping, surveying, mining, military and defense, search and rescue applications. GPS transceivers are available as stand alone units or in combination with fish finders, cell phones, lap top computers, or navigation systems.
How GPS Works
A GPS receiver is able to determine its own position from how far it is from each of 3 distinct satellites. The distance from one satellite transcribes a circle of possible positions on the Earth’s surface.
The overlap of 3 such circles pinpoints the location of the receiver.
The distance from a satellite is calculated by the “time of flight” of a radio signal from the satellite. Suppose it takes 0.06 seconds for a radio signal traveling at 186000 miles per second to reach the receiver from the satellite. Knowing this, the distance from the satellite can be calculated as follows:
Velocity (186000 mi/s) x Time (.06 s) = Distance (11160 miles)
The “time of flight” of a radio signal from the satellite is determined by comparing the signal received from the satellite to the same signal sent simultaneously from a nearby ground station. Both the satellite and the ground station send a “pseudo-random code” (PRC) out at the same time. A PRC is a complex signal that is unique for each satellite. Because the signal sent from the satellite has to travel farther, it lags behind the signal received from the ground station.
The GPS receiver automatically adjusts the satellite signal received until it is synchronized with the ground station signal. The amount of adjustment required is time it took the signal to arrive from the satellite.
Since the GPS receiver’s clock is probably not perfectly synchronized with the GPS clock, the three circles mentioned above probably will not overlap precisely. A fourth satellite signal is used to adjust the GPS receiver’s clock and obtain a precise overlap. Four signals are required to locate a point in 4-dimensional space-time, so accurate GPS receivers operate on 4 channels. By "knowing" the correct time, the receiver knows the positions of the satellites.
So far we have described how the position of a GPS receiver is determined relative to satellites. In order to
determine the position relative to the Earth, we have to know the location of all the satellites. The GPS maintains an ephemeris – a table of spatial coordinates which describes the location of each satellite at various times throughout the day. Ephemeris errors, differences between actual locations of satellites and their expected locations, can be caused by such factors as gravitational pulls from the sun and the moon. To minimize such error ground stations use radar to track the satellites and correct the ephemeris on a regular basis.
Other sources of error include “multipath” error, which is caused by signals reflected or being obstructed by buildings or other objects near the ground. Also, the speed of light through the atmosphere and through water vapor is different than the assumed speed of light through space. Differential GPS and individual receiver calibration helps correct these errors.
Differential GPS is a system used to minimize error. A GPS receiver is placed and left in a location that has been accurately surveyed. This stationary receiver uses its known location to determine the most accurate time timing for the satellite signals it receives. This correction factor for time is sent to and used by roving GPS receivers in time of flight calculations.
Components differ from one GPS receiver to another. Of particular importance are differences contributed by GPS antennas. Different types of GPS antennas have different response to radio signals depending on the direction the signal is coming from, and the frequency of the signal. Elevation is as important a factor in directionality as are compass directions. Even with differential GPS, individual GPS receivers still have to be calibrated. They are taken to a location whose coordinates are known and then told what those coordinates are. This enables the onboard computer to determine the appropriate correction factors to be used for all other calculations.
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