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locations for the receiver – one of which would be located in space above the planet and could be eliminated as a pos- sible location. In reality, though, range data from a fourth satellite is used to cor- rect the time of the clock in the receiver and adjust the distance calculations. Satellite time is measured using atomic clocks, and this same level of accuracy is needed by ground-based receivers to precisely define position. Since atomic clocks are expensive, and would be cost prohibitive if included in hand-held com- mercial grade receivers, the time from an independent, fourth satellite, is used to verify or adjust the time recorded by the receiver. If the measurement of distance to a fourth satellite intersects the identified location from the other three satellites, then the position of the receiver is precisely known; however, if it does not intersect, the receiver time is invalidated compelling the receiver to seek a single time correction that will unite all of the distance measurements in a common intersection point (Trimble Navigation Limited, 2015). The overall effect is to sync the receiver clock back up with satellite time.
There is the potential for several sources of error in the determination of position using GPS, including: iono- spheric disruption; atmospheric refrac- tion, or the slowing down of transmitted signals as they pass through the atmo- sphere; signal blockage and reflection from tall, ground-based objects; quality of the receiver; whether an augmenta- tion system is used or not2; distribution of satellites in the sky (Dana, 1994; Trimble Navigation Limited, 2015). Additionally, the positions of the satel- lites in their orbits fluctuate slightly and decay over time, so ground-based monitoring stations use radar to track the satellites and send corrected posi- tion data to the satellites routinely. In this way, valid distance and time data is continuously available via satellite transmission to update the almanacs of satellite position in receiver units.
How does GPS work (more advanced)?
GPS satellites transmit on specific frequencies (e.g., 575.42 MHz, 1227.60 MHz), which are coded using complex pseudorandom noise (PRN) codes.3 The
PRNs allow for distinguishing between individual satellites (each having a unique code), minimizing the potential for receivers to lock onto other similar signals (natural or artificial), compli- cating possible jamming attempts, and enabling receivers to identify cycles for phase comparison (Dana, 1994; Trimble Navigation Limited, 2015). The data transmitted along with the code includes: transmission time, orbital data, almanac data, clock corrections, coefficients for ionospheric delay, and other informa- tion (NAVSTAR GPS User, 1996). The receiver determines which satellites it is receiving signals from, and then uses the best signals available for ranging. A receiver compares the transmitted satellite codes to the identical codes it uses, by shifting its code to align with the satellite code, and thereby, deter- mining travel time from the phase shift (NAVSTAR GPS User, 1996). There are openly available codes for civilian use, and also restricted codes for the military.
Another, critical consideration of GPS, routinely omitted in many articles on the subject, relates to the relativistic effects (i.e., general and special) of satellites in orbit versus receivers on the surface of the Earth. Believe it or not, without also accounting for the relativistic effects, GPS would not work accurately enough to be useful!
The principles of general relativity pertain to observed effects and differ- ences within gravitational fields, such as that of the Earth’s. Time is observed to vary depending on proximity to a gravitational source (or, more correctly, varies based on the geometry of space- time, which is affected by the mass of objects like planets, stars, black holes, etc.). Clocks at different distances from gravitational sources record time at dif- ferent rates, with those farther away running faster (Taylor & Wheeler, 2000). The clocks on satellites keep different time than clocks in the receivers, and the differences must be taken into account. Similarly, special relativity explains that clocks in orbit, which are traveling much faster, will keep time at a differ- ent rate than the slower-moving clocks on the surface of the planet (Taylor & Wheeler, 2000). It turns out that these two relativistic effects oppose each other: the satellites orbiting high above the
Earth experience an increase in the rate of time, due to the gravitational relativ- istic effects, and a decrease in the rate of time as a consequence of their velocity (special relativistic effect) compared to the Earth-based receivers. The gravita- tional effect, the more pronounced of the two relativistic effects, causes an overall increase in the time measured by the satellites, in comparison to the receiv- ers, when both effects are combined (on the order of a few tens of thousands of nanoseconds) (Taylor & Wheeler, 2000).
There is more to GPS than a brief article on the topic can cover, so inter- ested readers are encouraged to examine the references. For many of us, just having a basic understanding of the principles is enough. GPS is a multi- component system comprised of at least three parts: space-based satellites, and ground-based receivers and monitoring stations. Simply put, satellites transmit signals to receivers, which decode the transmissions and translate them into coordinates of latitude, longitude, and elevation. Control and monitoring sta- tions ensure the proper positioning of satellites in their orbits, and verify the transmitted signal data. The accuracy of position data depends on a variety of potential error sources and making appropriate corrections. Receivers with different capabilities and purposes may be purchased, with the major difference being cost. Even inexpensive GPS devic- es typically provide relatively accurate position data to within a few meters of true position.
GPS as a STEM Teaching Topic
At first glance, GPS may seem like a simple way to determine very accurate position information for a variety of uses. However, a closer inspection reveals that it is quite intricate, relying on a number of scientific principles, and consequent- ly, presenting an excellent topic for an integrated STEM (science, technology, engineering, and mathematics) lesson. For example, the exploration of: orbital mechanics, atmospheric effects on light transmissions, embedding data in car- rier waves, and time dilation [science]; the operation of atomic clocks, electron- ics and functioning of GPS receivers, and satellite advancements [technology];
2. Augmentation is any way to enhance GPS capability. An example is the network of Continuously Operating GPS Reference Stations (CORS) that receive GPS signals and transmit position data allowing users to gain greater accuracy in the coordinates of their posi- tion.
3. For details about the nuances of PRN and phase shifts, see the references.
www.aipg.org
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