Adam Adam ArshenArshen

History and Facts of GPSHistory and Facts of GPS

GPS stands for Global Positioning GPS stands for Global Positioning SystemSystemGPS works by using time to determine GPS works by using time to determine positionpositionIt was developed in the early 1970It was developed in the early 1970’’s by s by and for the United States Department and for the United States Department of Defense (of Defense (USDoDUSDoD))

GPS became available to the public GPS became available to the public in 1996in 1996Before 1996 it was only used for Before 1996 it was only used for military purposesmilitary purposes

The first GPS satellite was launched in The first GPS satellite was launched in February of 1978 by the February of 1978 by the USDoDUSDoDCurrently there are 29 GPS satellites in Currently there are 29 GPS satellites in orbitorbit

Of the 29 satellites in orbit 2 are Of the 29 satellites in orbit 2 are used as backup satellites in case one used as backup satellites in case one of the working ones malfunctionsof the working ones malfunctions

History and Facts of GPS cont.History and Facts of GPS cont.

GPS is remarkable in the fact that it can provide us with GPS is remarkable in the fact that it can provide us with continuous timing, position, and navigation anywhere in the continuous timing, position, and navigation anywhere in the world and under any weather conditions.world and under any weather conditions.Without basic and complex physical properties GPS would Without basic and complex physical properties GPS would not be as powerful of a tool as it is todaynot be as powerful of a tool as it is todayThe uses of GPS range from map making to land surveying to The uses of GPS range from map making to land surveying to basic navigation in a car.basic navigation in a car.GPS costs the United States around $750 million annually to GPS costs the United States around $750 million annually to maintainmaintain

This is considered relatively low as GPS is one of the key This is considered relatively low as GPS is one of the key components for homeland security.components for homeland security.

How GPS WorksHow GPS WorksThere are 3 segments to GPS; the first There are 3 segments to GPS; the first one is the space segment, second the one is the space segment, second the control segment, and third the user control segment, and third the user segmentsegment

Space Segment (satellites)Space Segment (satellites)SatellitesSatellites

There are 29 GPS satellites in orbitThere are 29 GPS satellites in orbitArranged in 6 orbital planes with Arranged in 6 orbital planes with 4 or more satellites in each plane4 or more satellites in each planeThe constellation of satellites is The constellation of satellites is known as the Initial Operational known as the Initial Operational Capability or IOCCapability or IOCThey orbit around the earth at an They orbit around the earth at an altitude of about 20,200kmaltitude of about 20,200kmTheir orbital period is about 12 Their orbital period is about 12 hours at a velocity of 8,646 hours at a velocity of 8,646 miles/hourmiles/hour

Control SegmentControl SegmentConsists of 12 tracking Consists of 12 tracking stations that are located at stations that are located at different points around different points around the worldthe worldThe purpose of them is to The purpose of them is to record the position of the record the position of the satellites, and that satellites, and that position will then be used position will then be used to calculate the position to calculate the position of a receiverof a receiver

User SegmentUser SegmentThis segment of GPS consists of the This segment of GPS consists of the receiver that is connected to a GPS receiver that is connected to a GPS antennaantennaThis segment numerically displays the This segment numerically displays the position of a personposition of a person

To receive the position of a person a receiver has to To receive the position of a person a receiver has to make contact with at least 3 satellitesmake contact with at least 3 satellites

The receiver first sends out a signal to the closest satellite The receiver first sends out a signal to the closest satellite and then that satellite locates two other satellites that are and then that satellite locates two other satellites that are closest to itself. These three satellites then use the property closest to itself. These three satellites then use the property of of trilaterationtrilateration to determine the position of the receiver. to determine the position of the receiver.

TrilaterationTrilateration““TrilaterationTrilateration is a method of determining the relative is a method of determining the relative positions of objects using the geometry of intersecting positions of objects using the geometry of intersecting circles to calculate the subjectcircles to calculate the subject’’s locations. s locations. TrilaterationTrilateration uses uses the known locations of two or more reference points and the known locations of two or more reference points and the measured distance between the subject and each the measured distance between the subject and each reference pointreference point””

When using When using trilaterationtrilateration to determine the position of a person to determine the position of a person only 3 satellites are needed but the more satellites you have thonly 3 satellites are needed but the more satellites you have the e more accurate the position given will bemore accurate the position given will be

Trilateration

Using geometry and algebra you are then able to find the Using geometry and algebra you are then able to find the unknowns; unknowns; xuxu, , yuyu, and , and zuzuOnce you have these unknowns you can then plug these Once you have these unknowns you can then plug these values in the equations below to find the longitude and values in the equations below to find the longitude and latitude of the receiverlatitude of the receiver

Latitude Longitude

GPS SignalsGPS SignalsGPS satellites GPS satellites transmit microwave transmit microwave radio signals which radio signals which are composed of a are composed of a sine wave and travels sine wave and travels at the speed of lightat the speed of light

The wave has two frequencies that are generated at 1,575.42 MHz The wave has two frequencies that are generated at 1,575.42 MHz and at and at 1,226.60 MHZ1,226.60 MHZ

The wavelength of these two frequencies can be found using the The wavelength of these two frequencies can be found using the formula formula λλ = c / f = c / f

Frequency = 1,575.42 MHzFrequency = 1,575.42 MHz Frequency = 1,227.60 MHzFrequency = 1,227.60 MHzλλ = (3*10^8 = (3*10^8 m/sm/s) / (1,575.42 MHz) ) / (1,575.42 MHz) λλ = (3*10^8 = (3*10^8 m/sm/s) / (1,227.60) / (1,227.60 MHz) MHz) λλ = (3*10^10 cm/s) / (1.57524*10^9 Hz) = (3*10^10 cm/s) / (1.57524*10^9 Hz) λλ = (3*10^10 cm/s) / (1.22760 *10^9 Hz)= (3*10^10 cm/s) / (1.22760 *10^9 Hz)λλ = 19.044 cm = 19.044 cm λλ = 24.438 cm= 24.438 cm

The frequency at 1,575.42 MHZ is called the L1 frequency The frequency at 1,575.42 MHZ is called the L1 frequency and carries the navigation frequency and standard positioning and carries the navigation frequency and standard positioning service codedservice codedThe frequency at 1,227.60 MHz is called the L2 frequency and The frequency at 1,227.60 MHz is called the L2 frequency and is also called the PPS signal which stands for Precise is also called the PPS signal which stands for Precise Positioning ServicePositioning ServiceThe L1 frequency is available for civilian usesThe L1 frequency is available for civilian usesWhile the L2 frequency is only available for military purposes While the L2 frequency is only available for military purposes and is much more accurate than the L1 frequencyand is much more accurate than the L1 frequencyThe L1 frequency carries a code which is basically the address The L1 frequency carries a code which is basically the address of the satellite called the C/A of the satellite called the C/A –– code code ““Coarse AcquisitionCoarse Acquisition””There is also a code called the PThere is also a code called the P--code code ““Precision codingPrecision coding””which is on the L2 code and this Pwhich is on the L2 code and this P--code carries much more code carries much more data than the C/A data than the C/A -- codecode

PseudorangePseudorange

PseudorangePseudorange is very important concept when talking is very important concept when talking about GPSabout GPS

PseudorangePseudorange refers to the error in distance between a GPS refers to the error in distance between a GPS satellite and a GPS receiver.satellite and a GPS receiver.Since the receiver clocks and the satellites are never Since the receiver clocks and the satellites are never synchronized due to outside effects such as relativity, a synchronized due to outside effects such as relativity, a pseudorangepseudorange measurement can be taken to determine the measurement can be taken to determine the difference in time between the satellite clock and the difference in time between the satellite clock and the receiverreceiver’’s clocks clockSince there is time delay the signals will be off and the Since there is time delay the signals will be off and the pseudorangepseudorange has to be measured and factored in when has to be measured and factored in when determining the position of a person.determining the position of a person.

PseudorangePseudorange Cont.Cont.

•The top line in the illustration is the satellite code and the bottom line is the same code generated in the receiver.

•ΔT is the pseudo measurement that will then give the time error between the two codes.

•By knowing ΔT we are able to get a much more precise measurement, by adjusting formulas to account for this time delay.

GPS ReceiversGPS Receivers

There are many different types of GPS receivers: that range fromThere are many different types of GPS receivers: that range fromvery complex ones to very basic in the features that it hasvery complex ones to very basic in the features that it has

GPS receiver contain two parts: the software and the hardwareGPS receiver contain two parts: the software and the hardwareWhen GPS became available to the public there was only one GPS When GPS became available to the public there was only one GPS receiver available to themreceiver available to themNow there are well over 500 different GPS receiver that the publNow there are well over 500 different GPS receiver that the public can ic can choose fromchoose fromThey come with different number of tracking channels with 12 beiThey come with different number of tracking channels with 12 being the ng the most.most.The public only has access to single frequency receivers that caThe public only has access to single frequency receivers that can only pick n only pick up the L1 frequency while the military has dualup the L1 frequency while the military has dual--frequency receiver which frequency receiver which can pick up both L1 and L2 making them much more accuratecan pick up both L1 and L2 making them much more accurateEven though some GPS receivers are much more complex than othersEven though some GPS receivers are much more complex than others at at the heart of them they are all the samethe heart of them they are all the same

They all must contain an antenna and without an antenna a receivThey all must contain an antenna and without an antenna a receiver would be er would be uselessuseless

GPS Receivers cont.GPS Receivers cont.All GPS receivers have this basic setup:

•The hardware is the top line in the diagram and contains the Antenna the RF Chain and the ADC

•The software is the bottom line in the diagram and contains many different programs to convert the signals into readable terms

HardwareHardwareThe role of the antenna is to receive signals from the GPS The role of the antenna is to receive signals from the GPS satellites. satellites. The radio frequency chain abbreviated as RF amplifies the The radio frequency chain abbreviated as RF amplifies the signal acquired from the antenna to a desired amplitude. signal acquired from the antenna to a desired amplitude. This signal is then converted to a desired output frequency This signal is then converted to a desired output frequency and which is digitized, at the analogand which is digitized, at the analog--toto--digital converter digital converter abbreviated as ADC abbreviated as ADC

GPS Receivers cont.GPS Receivers cont.

SoftwareSoftwareOnce the signal acquired by the antenna is digitized, the signalOnce the signal acquired by the antenna is digitized, the signalgoes through many different software components where the goes through many different software components where the useruser’’s position is determined after being converted from a s position is determined after being converted from a digitized signal to readable terms. digitized signal to readable terms.

GPS ErrorsGPS ErrorsAlthough GPS is the best method of determining Although GPS is the best method of determining ones positions there are effects that can make them ones positions there are effects that can make them not accuratenot accurate

Errors include:Errors include:Ephemeris errors which are errors in the perceived position of Ephemeris errors which are errors in the perceived position of the satellitesthe satellites

The position of a GPS satellites is predicted from previous sateThe position of a GPS satellites is predicted from previous satellites llites locations and recorded at one of the tracking stationslocations and recorded at one of the tracking stationsSince we are human predicting the positions of satellites will nSince we are human predicting the positions of satellites will not always ot always be perfectbe perfectThis accounts for an error that is about 2 metersThis accounts for an error that is about 2 metersTo try to and correct this error 6 more monitoring stations are To try to and correct this error 6 more monitoring stations are being being constructedconstructed

Selective Availability Selective Availability ““SASA””This is an error that is manThis is an error that is man--mademadeIts an artificial falsification of Its an artificial falsification of the time in the L1 signal the time in the L1 signal transmitted by the satellitetransmitted by the satellite-- it it creates a greater creates a greater pseudorangepseudorangeThe The USDoDUSDoD instated this instated this error to limit the accuracy of error to limit the accuracy of civilian GPS accuracy for civilian GPS accuracy for security reasonssecurity reasonsErrors can be as great as 100 Errors can be as great as 100 meters.meters.

MultipathMultipath effecteffectSignals bounce off Signals bounce off buildings or other solid buildings or other solid objects which causes the objects which causes the signals going from the signals going from the satellite to the receiver to satellite to the receiver to take more time than the take more time than the signal going form the signal going form the receiver to the satellitereceiver to the satelliteThis will cause an error of This will cause an error of about 1 meterabout 1 meter

Relativity and GPSRelativity and GPS

Einstein's theories of relativity Einstein's theories of relativity play a crucial role in the accuracy play a crucial role in the accuracy of GPSof GPS

Special RelativitySpecial RelativityStates that when a object is moving States that when a object is moving very fast its time will be slowervery fast its time will be slowerSince the satellites are moving Since the satellites are moving relative to the earth at high speeds relative to the earth at high speeds the satellites clock will be slowerthe satellites clock will be slowerThe clock in the satellite and The clock in the satellite and receiver have to be within 30 receiver have to be within 30 nanoseconds of each othernanoseconds of each otherThe relativistic effects of special The relativistic effects of special relativity give an error of about 7.2 relativity give an error of about 7.2 mincominco seconds per dayseconds per day

General RelativityGeneral RelativityCombines the principles of Combines the principles of special relativity with Newtonspecial relativity with Newton’’s s laws of gravitylaws of gravityStates that time moves slower States that time moves slower when therewhen there’’s a stronger field of s a stronger field of gravitationgravitationSince the forces on earth are Since the forces on earth are much stronger than the forces much stronger than the forces of gravity at the satellite the of gravity at the satellite the satellites clock will tick much satellites clock will tick much faster than the receivers clockfaster than the receivers clockIt causes an error of about 38 It causes an error of about 38 milliseconds per day which milliseconds per day which translates to about an error of translates to about an error of 10km10kmTo counter this effect scientists To counter this effect scientists alter the frequencies of the alter the frequencies of the signals transmitted by the signals transmitted by the satellites to include this time satellites to include this time delaydelay

GPS EvolutionGPS Evolution

After Block I was taken out of commission in 1995 Block II/IIA wAfter Block I was taken out of commission in 1995 Block II/IIA was as launchedlaunched

The difference between these and Block I was that their data stoThe difference between these and Block I was that their data storage was much rage was much greater and could go without ground support for up to 180 days mgreater and could go without ground support for up to 180 days making the self aking the self sufficientsufficient

GPS started as a constellation of only 11 satellites known as BlGPS started as a constellation of only 11 satellites known as Block I satellites in 1978ock I satellites in 1978These were built primarily for experimental purposesThese were built primarily for experimental purposes

We now use Block II/IIA and Block IIRWe now use Block II/IIA and Block IIRBlock IIR can go up to 7.5 years without ground supportBlock IIR can go up to 7.5 years without ground support

GPS UsesGPS Uses

GPS is used in map GPS is used in map making, flying, boating, making, flying, boating, driving, farming, and the driving, farming, and the list can go on foreverlist can go on forever

Physical EquationsPhysical Equations

General Relativity General Relativity

Special RelativitySpecial Relativity

LorentzLorentz FactorFactor

Velocity equationVelocity equation

NewtonNewton’’s law of gravitys law of gravity

Wave equationWave equation