- Introduction to the Global Positioning System
The

**Global Positioning System (GPS)**is the only fully functionalGlobal Navigation Satellite System (GNSS). The GPS uses a constellation of between 24 and 32Medium Earth Orbit satellite s that transmit precisemicrowave signals, that enable GPS receivers to determine their location, speed, direction, and time. GPS was developed by theUnited States Department of Defense . Its official name is**NAVSTAR-GPS**. The GPS satellite constellation is managed by theUnited States Air Force 50th Space Wing .Similar satellite navigation systems include the Russian

GLONASS (incompleteas of 2008 ), the upcoming EuropeanGalileo positioning system , the proposedCOMPASS navigation system of China, and IRNSS of India.Following the shooting down of

Korean Air Lines Flight 007 in 1983, PresidentRonald Reagan issued a directive making the system available free for civilian use as a common good.cite news|url=http://usinfo.state.gov/xarchives/display.html?p=washfile-english&y=2006&m=February&x=20060203125928lcnirellep0.5061609 |title=History of GPS|publisher= [*http://usinfo.state.gov usinfo.state.gov*] |date=February 3 ,2006 ] Since then, GPS has become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, scientific uses, and hobbies such asgeocaching . GPS also provides a precise time reference used in many applications including scientific study ofearthquake s, andsynchronization of telecommunications networks.**History**The design of GPS is based partly on similar ground-based radio navigation systems, such as

LORAN and the Decca Navigator developed in the early 1940s, and used duringWorld War II . Additional inspiration for the GPS came when theSoviet Union launched the first Sputnik in 1957. A team of U.S. scientists led by Dr. Richard B. Kershner were monitoring Sputnik's radio transmissions. They discovered that, because of theDoppler effect , the frequency of the signal being transmitted by Sputnik was higher as the satellite approached, and lower as it continued away from them. They realized that since they knew their exact location on the globe, they could pinpoint where the satellite was along its orbit by measuring the Doppler distortion.The first satellite navigation system, Transit, used by the

United States Navy , was first successfully tested in 1960. Using a constellation of five satellites, it could provide a navigational fix approximately once per hour. In 1967, the U.S. Navy developed theTimation satellite which proved the ability to place accurate clocks in space, a technology the GPS relies upon. In the 1970s, the ground-basedOmega Navigation System , based on signal phase comparison, became the first world-wide radio navigation system.The first experimental Block-I GPS satellite was launched in February 1978.Hydrographic Society Journal. [

*http://www.hydrographicsociety.org/Articles/journal/2002/104-1.htm Developments in Global Navigation Satellite Systems*] . Issue #104, April 2002. AccessedApril 5 ,2007 .] The GPS satellites were initially manufactured byRockwell International (now part ofBoeing ) and are now manufactured byLockheed Martin (IIR/IIR-M) andBoeing (IIF).**Method of operation**A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS

satellites high above the Earth. Each satellite continually transmits messages containing the time the message was sent, a precise orbit for the satellite sending the message (theephemeris ), and the general system health and rough orbits of all GPS satellites (the almanac). These signals travel at thespeed of light through outer space, and slightly slower through the atmosphere. The receiver uses the arrival time of each message to measure the distance to each satellite thereby establishing that the GPS receiver is approximately on the surfaces of spheres centered at each satellite. The GPS receiver also uses when appropriate the knowledge that the GPS receiver is on (if vehicle altitude is known) or near the surface of a sphere centered at the earth center. This information is then used to estimate the position of the GPS receiver as the intersection of sphere surfaces. The resulting coordinates are converted to a more convenient form for the user such as latitude and longitude, or location on a map, then displayed.It might seem that three sphere surfaces would be enough to solve for position, since space has three dimensions. However a fourth condition is needed for two reasons. One has to do with position and the other is to correct the GPS receiver clock.

It turns out that three sphere surfaces usually intersect in two points. Thus a fourth sphere surface is needed to determine which intersection is the GPS receiver position. For near earth vehicles, this knowledge that it is near earth is sufficient to determine the GPS receiver position since for this case there is only one intersection which is near earth.

A fourth sphere surface is also needed to correct the GPS receiver clock. More precise information is needed for this task. An estimate of the radius of the sphere is required. Therefore an approximation of the earth altitude or radius of the sphere centered at the satellite must be known.

**Calculating Position**To describe how a GPS receiver works, errors will be ignored. Using messages received from satellites and is some cases knowledge of vehicle altitude for a minimum of four sphere surfaces (3 satellites and the vehicle altitude or 4 satellites), a GPS receiver is able to determine the satellite positions and time sent. The x, y, and z components of position and the time sent are designated as $left\; [x\_i,\; y\_i,\; z\_i,\; t\_i\; ight\; ]$ where the subscript i denotes the satellite number. Knowing the indicated time the message was received $tr\_i$, the GPS receiver can compute the indicated transit time, $left\; (tr\_i-t\_i\; ight\; )$. Assuming the message traveled at the speed of light,

c , the distance travelled, $p\_i$ can be computed as $left\; (tr\_i-t\_i\; ight\; )c$. Knowing the distance from GPS receiver to a satellite and the position of a satellite implies that the GPS receiver is on the surface of a sphere centered at the position of a satellite. The GPS receiver can also use knowledge of the vehicle altitude to determine a sphere surface which contains the GPS reciver. Thus we know that the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. In the ideal case of no errors, the GPS receiver will be at an intersection of the surfaces of four spheres. The surfaces of two spheres if they intersect in more than one point intersect in a circle. A figure, two sphere surfaces intersecting in a circle, is shown below. clearly show this mathematically. The correct position of the GPS receiver is the one that is closest to the fourth sphere.**Correcting the GPS Receiver Clock**The method of calculating position for the case of no errors has been explained. We now discuss one of the most important errors, the error in the GPS receiver Clock. Because of the very large value of c, the

speed of light , the estimated distances from the GPS receiver to the satellites, the pseudoranges, are very sensitive to errors in the GPS receiver clock. This seems to suggest that an extremenly accurate and expensive clock is required for the GPS receiver to work. On the other hand, manufacurers would like to make an inexpensive GPS receiver which can be mass marketed. The manufacturers were thus faced with a difficult design problem. A clever technique was used to solve this problem. This technique is based on the way sphere surfaces intersect in the GPS problem.Consider the intersection of three sphere surfaces centered at three satellites or two sphere surfaces centered at the satellite and the sphere surface corresponding to vehicle altitude if that information is being used in lieu of a fourth satellite. It is likely the surfaces of the three spheres intersect since the circle of intersection of the first two spheres is normally quite large and thus the third sphere surface is likely to intersect this large circle. It is very unlikely that the sphere surface corresponding to the fourth satellite will intersect either of the two points of intersection of the first three since any clock error could cause it to miss intersecting a point. However the distance from the valid estimate of GPS receiver position to the surface of the fourth sphere surface can be used to estimate clock error. Let $r\_4$ denote the distance from the valid estimate of GPS receiver position to the satellite corresponding to the fourth sphere and let $p\_4$ denote the radius of this sphere. Let $da\; =\; r\_4\; -\; p\_4$. Note that $da$ is the distance from the computed GPS receiver position to the surface of the fourth sphere surface. Thus the quotient, $b\; =\; da\; /\; c$, provides an estimate of

(correct time) - (time indicated by the receiver's on-board clock)

and the GPS receiver clock can be moved forward if $b$ is positive or backwards if $b$ is negative.**GPS Frequencies***

**L1**(1575.42 MHz): Mix of Navigation Message, coarse-acquisition (C/A) code and encrypted precision P(Y) code, plus the newL1C on future Block III satellites.

***L2**(1227.60 MHz): P(Y) code, plus the newL2C code on the Block IIR-M and newer satellites.

***L3**(1381.05 MHz): Used by the Nuclear Detonation (NUDET) Detection System Payload (NDS) to signal detection of nuclear detonations and other high-energy infrared events. Used to enforce nuclear test ban treaties.

***L4**(1379.913 MHz): Being studied for additional ionospheric correction.

***L5**(1176.45 MHz): Proposed for use as a civilian safety-of-life (SoL) signal (seeGPS modernization ). This frequency falls into an internationally protected range for aeronautical navigation, promising little or no interference under all circumstances. The first Block IIF satellite that would provide this signal is set to be launched in 2009 [*[*] .*http://mg.gpsworld.com/gpsmg/Military+%26+Government+News/First-GPS-IIF-Satellite-Undergoes-Environmental-Te/ArticleStandard/Article/detail/470408?contextCategoryId=33824 First GPS IIF Satellite Undergoes Environmental Testing*] . GPS World.November 5 ,2007 .**References**

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